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Text mining - from Bayes rule to dependency parsing

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Text mining - from Bayes rule to dependency parsing

Jul. 24, 2015
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The updated slides for my introductory course on text mining. The slides take you from basic Bayesian statistics over Markov chains and language models (incl. neural embeddings) to text similarity measures (Locality Sensitive Hashing, Latent Semantic Analysis, and Latent Dirichlet Allocation) and classification techniques (Naïve Bayes, MaxEnt [logistic regression]). Finally, they introduce you to shallow parsing with dynamic graphical models (HMMs, MEMMs, and CRFs) and provide you with a glimpse at dependency parsing (shift-reduce, arc-standard).

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  1. 1. 10th Madrid Summer School on
 Advanced Statistics and Data Mining ! Module C9 :: Text Mining 6th July - 10th of July 2015 ! Florian Leitner florian.leitner@upm.es License:
  2. 2. Text Mining 1 Introduction ! Madrid Summer School on Advanced Statistics and Data Mining ! Florian Leitner florian.leitner@upm.es License:
  3. 3. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining “Text mining” or
 “text analytics” The discovery of new or existing facts from text by applying natural language processing (NLP), statistical learning techniques, or both. 3 Machine Learning Inferential Statistics Computat. Linguistics RulesModels Predictions
  4. 4. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Is language understanding key to artificial intelligence? “Her” Movie, 2013 “The singularity: 2030” Ray Kurzweil
 (Google’s director of engineering) “Watson” & “CRUSH” IBM 4 “predict crimes before they happen” Criminal Reduction Utilizing Statistical History (IBM, reality) ! Precogs (Minority Report, movie) if? when? cognitive computing: “processing information more like a human than a machine” GoogleGoogle
  5. 5. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Applications of text mining and language processing (Web) Search engines Information retrieval Spam filtering Document classification Twitter brand monitoring Opinion mining Finding similar items (Amazon) Content-based recommender systems Event detection in e-mail Information extraction Spelling correction Statistical language modeling Siri (Apple) and Google Now Language understanding Website translation (Google) Machine translation “Clippy” assistant (Microsoft) Dialog systems Watson in Jeopardy! (IBM) Question answering 5 Textmining Languageprocessing
  6. 6. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Document or text
 classification and clustering 6 1st Principal Component 2ndPrincipalComponent document distance 1st Principal Component 2nd PrincipalComponent Centroid Cluster Supervised (“learning to classify from examples”, e.g., spam filtering) vs. Unsupervised (“exploratory grouping”, e.g., topic modeling)
  7. 7. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Tokens and n-grams 7 This is a sentence . This is is a a sentence sentence . This is a is a sentence a sentence . This is a sentence. { { { { { { { NB: “tokenization” Character-based, Regular Expressions, Probabilistic, … Token n-grams unigram! shingle! ! bigram! 2-shingle! ! trigram! 3-shingle all trigrams of “sentence”:
 [sen, ent, nte, ten, enc, nce] Beware: the terms “shingle”, “token” and “n-gram” are not used consistently… Character n-grams Token or Shingle
  8. 8. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The inverted index 8 Text 1: He that not wills to the end neither wills to the means. Text 2: If the mountain will not go to Moses, then Moses must go to the mountain. tokens Text 1 Text 2 end 1 0 go 0 2 he 1 0 if 0 1 means 1 0 Moses 0 2 mountain 0 2 must 0 1 not 1 1 that 1 0 the 2 2 then 0 1 to 2 2 will 2 1 unigrams T1 1 T2 p(T1) p(T2) end 1 0 0.09 0.00 go 0 2 0.00 0.13 he 1 0 0.09 0.00 if 0 1 0.00 0.07 means 1 0 0.09 0.00 Moses 0 2 0.00 0.13 mountain 0 2 0.00 0.13 must 0 1 0.00 0.07 not 1 1 0.09 0.07 that 1 0 0.09 0.00 the 2 2 0.18 0.13 then 0 1 0.00 0.07 to 2 2 0.18 0.13 will 2 1 0.18 0.07 SUM 11 15 1.00 1.00 factors, normalization (len[text]), probabilities, and n-grams bigrams Text 1 Text 2 end, neither 1 0 go, to 0 2 he, that 1 0 if, the 0 1 Moses, must 0 1 Moses, then 0 1 mountain, will 0 1 must, go 0 1 not, go 0 1 not, will 1 0 that, not 1 0 the, means 1 0 the, mountain 0 2 then, Moses 0 1 to, Moses 0 1 to, the 2 1 will, not 0 1 will, to 2 0
  9. 9. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Word vectors 9 0 1 2 3 4 5 6 7 8 9 10 10 0 1 2 3 4 5 6 7 8 9 count(Word1) count(Word2) Text1 Text2 α γ β Similarity(T1 , T2 ) := cos(T1 , T2 ) count(Word3 ) Comparing word vectors: Cosine similarity Collections of vectorized texts: Inverted index Text 1: He that not wills to the end neither wills to the means. Text 2: If the mountain will not go to Moses, then Moses must go to the mountain. tokens Text 1 Text 2 end 1 0 go 0 2 he 1 0 if 0 1 means 1 0 Moses 0 2 mountain 0 2 must 0 1 not 1 1 that 1 0 the 2 2 then 0 1 to 2 2 will 2 1 INDRI eachtoken/word isadimension! wordvector wordvector
  10. 10. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The essence of statistical learning 10 ×= y = h✓(X) XTy θ Rank, Class, Expectation, Probability, Descriptor*, … Inverted index (transposed) Parameters
 (θ) “texts”(n) n-grams (p) instances, observations variables, features per feature
  11. 11. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The essence of statistical learning 10 ×= y = h✓(X) XTy θ Rank, Class, Expectation, Probability, Descriptor*, … Inverted index (transposed) Parameters
 (θ) “texts”(n) n-grams (p) instances, observations variables, features per feature “Nonparametric” per instance
  12. 12. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The curse of
 dimensionality
 (RE Bellman, 1961) [inventor
 of dynamic programming] • p ≫ n (far more
 tokens/features than
 texts/documents) • Inverted indices are
 (discrete) sparse matrices. • Even with millions of training examples, unseen tokens will keep coming up during evaluation or in production. • In a high-dimensional hypercube, most instances are closer to the face of the cube (“nothing”, outside) than their nearest neighbor. 11
  13. 13. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Dimensionality reduction ✓ The remedy to “the curse” (aka. the “blessing of non-uniformity”) ‣ Feature extraction (compression): PCA/LDA (projection), factor analysis (regression), compression, auto-encoders (“deep learning”, “word embeddings”), … ‣ Feature selection (elimination): LASSO (regularization), SVM (support vectors), Bayesian nets (structure learning), locality sensitivity hashing, random projections, … 12
  14. 14. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Ambiguity 13 Anaphora resolution Carl and Bob were fighting: “You should shut up,” Carl told him. Part-of-Speech tagging The robot wheels out the iron. Paraphrasing Unemployment is on the rise. vs The economy is slumping. Named entity recognition Is Paris really good for you?
  15. 15. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The conditional probability for dependent events 14 Conditional Probability P(X | Y) = P(X ∩ Y) ÷ P(Y) *Independence P(X ∩ Y) = P(X) × P(Y) P(X | Y) = P(X) P(Y | X) = P(Y) ` ` Joint Probability P(X ∩ Y) = P(X, Y) = P(X × Y) The multiplication principle for dependent* events: P(X ∩ Y) = P(Y) × P(X | Y) and therefore, by using a little algebra: X Y 1/3 1/2 1 given
  16. 16. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Marginal, conditional and joint probabilities 15 Joint Probability* P(xi, yj) = P(xi) × P(yj) Marginal Probability P(yi) X=x X=x M Y= y a/n = P(x b/n = P(x (a+b)/n = P(y Y= y c/n = P(x d/n = P(x (c+d)/n = P(y M (a+c)/n = P(x (b+d)/n = P(x ∑ / n = 1 = P(X) = P(Y) Conditional Probability P(xi | yj) = P(xi, yj) ÷ P(yj) contingency table *for independent events variable/factor variable/factor margin
  17. 17. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Point-wise mutual information • Mutual information (MI) measures the degree of
 dependence of two variables: how similar is P(X,Y) to P(X)·P(Y) ? ! ! • Point-wise MI: MI of two individual events [only] ! ! ‣ e.g., neighboring words, phrases in a document, … ‣ incl. a mix of two different co-occurring event types (e.g. a word and a phrase or label) ‣ Can be normalized to a [-1,1] range: ! • Interpretation: -1: the events do not occur together; 0: the events are independent; +1: the events always co-occur 16 I(X; Y ) = X Y X X P(x, y) log2 P(x, y) P(x)P(y) PMI(w1, w2) = log2 P(w1, w2) P(w1)P(w2) PMI(w1, w2) log2 P(w1, w2) “how much you can learn about X from knowing Y”
  18. 18. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Bayes’ rule: Diachronic interpretation 17 H - Hypothesis X D - Data Y prior/belief likelihood posterior P(H|D) = P(H) ⇥ P(D|H) P(D) “normalizing constant” (law of total probability)
  19. 19. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Bayes’ rule: The Monty Hall problem 18 1 2 3 Prior p(H) 1/3 1/3 1/3 Likelihood p(D|H) 1/2 1 0 p(D) =∑ p(H)* p(D|H) 1/3×1/2 =1/6 1/3×1 =1/3 1/3×0 =0 1/6+1/3 =1/2 Posterior p(H|D) 1/6÷1/2 =1/3 1/3÷1/2 =2/3 0÷1/2 =0 P(H|D) = P(H) ⇥ P(D|H) P(D) similar case: a trickster hiding a stone in one of three cups… Images Source: Wikipedia, Monty Hall Problem, Cepheus your pick given the car is behind H=1, Monty Hall opens D=(2 or 3) H=2 ! H=3 D=3 ! D=3 Monty Hall
  20. 20. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The chain rule of
 conditional probability P(A,B,C,D) = P(A) × P(B|A) × P(C|A,B) × P(D|A,B,C) 19 P(B,Y,B) = P(B) × P(Y|B) × P(B|B,Y) 1/10 = 2/5 × 3/4 × 1/3 P(B) 2/5 P(Y|B) 3/4 P(B|B,Y) 1/3 P(w1, ..., wn) = nY i=1 P(wi|w1, ..., wi 1) = nY i=1 P(wi|wi 1 1 ) NB: the ∑ of all “trigrams” will be 1! NB: without replacement! joint conditional …to wi-1 from w1… Notation: i-1 is an index, not the power!
  21. 21. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Zipf’s law: Pareto distributions Word frequency is inversely proportional to its rank (ordered by counts) Words of lower rank “clump” within a region of a document Word frequency is inversely proportional to its length Almost all words are rare 20 f ∝ 1 ÷ r k = E[f × r] 5 10 15 20 25 0.20.40.60.81.0 Word Frequency lexical richness k Word rank This is what makes language modeling hard! the, be, to, of, … …, malarkey, quodlibet E = Expected Value the “true” mean dim. reduction Cumulativeprobabilitymass count(wi) ∝ P(wi) = pow(α, ranki) = 1/k (0, 1] “power law”
  22. 22. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Parts of Speech (PoS) • The Parts of Speech: ‣ noun: NN, verb: VB, adjective: JJ, adverb: RB, preposition: IN,
 personal pronoun: PRP, … ‣ e.g. the full Penn Treebank PoS tagset contains 48 tags: ‣ 34 grammatical tags (i.e., “real” parts-of-speech) for words ‣ one for cardinal numbers (“CD”; i.e., a series of digits) ‣ 13 for [mathematical] “SYM” and currency “$” symbols, various types of punctuation, as well as for opening/closing parenthesis and quotes 21 I ate the pizza with green peppers . PRP VB DT NN IN JJ NN . “PoS tags”
  23. 23. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Parts of Speech (2/2) • Automatic PoS tagging ➡ supervised machine learning ‣ Maximum Entropy Markov models ‣ Conditional Random Fields ‣ Convolutional Neural Networks ‣ Ensemble methods (bagging, boosting, etc.) 22 I ate the pizza with green peppers . PRP VB DT NN IN JJ NN .
  24. 24. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Linguistic morphology • [Verbal] Inflections ‣ conjugation (Indo-European languages) ‣ tense (“availability” and use varies across languages) ‣ modality (subjunctive, conditional, imperative) ‣ voice (active/passive) ‣ … ! • Contractions ‣ don’t say you’re in a man’s world…
 • Declensions • on nouns, pronouns, adjectives, determiners ‣ case (nominative, accusative, dative, ablative, genitive, …) ‣ gender (female, male, neuter) ‣ number forms (singular, plural, dual) ‣ possessive pronouns (I➞my, you➞your, she➞her, it➞its, … car) ‣ reflexive pronouns (for myself, yourself, …) ‣ … 23 not a contraction: possessive s ➡ token normalization
  25. 25. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Stemming → Lemmatization • Stemming ‣ produced by “stemmers” ‣ produces a word’s “stem” ! ‣ am ➞ am ‣ the going ➞ the go ‣ having ➞ hav ! ‣ fast and simple (pattern-based) ‣ Snowball; Lovins; Porter ! • Lemmatization ‣ produced by “lemmatizers” ‣ produces a word’s “lemma” ! ‣ am ➞ be ‣ the going ➞ the going ‣ having ➞ have ! ‣ requires: a dictionary and PoS ‣ LemmaGen; morpha; BioLemmatizer; geniatagger 24 ➡ token normalization a.k.a. token “regularization” (although that is technically the wrong wording)
  26. 26. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining PoS tagging and lemmatization for
 Named Entity Recognition (NER) 25 Token PoS Lemma NER Constitutive JJ constitutive O binding NN binding O to TO to O the DT the O peri-! NN peri-kappa B-DNA B NN B I-DNA site NN site I-DNA is VBZ be O seen VBN see O in IN in O monocytes NNS monocyte B-cell . . . O de facto standard
 PoS tagset {NN, JJ, DT, VBZ, …} Penn Treebank B-I-O chunk encoding common alternatives: I-O I-E-O B-I-E-W-O End token (unigram) Word Begin-Inside-Outside (relevant) token } chunk noun-phrase (chunk) N.B.: This is all supervised (i.e., manually annotated corpora)!
  27. 27. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String matching with regular expressions ‣ /^[^@]{1,64}@w(?:[w.-]{0,254}w)?.w{2,}$/ • (provided w has Unicode support) • http://ex-parrot.com/~pdw/Mail-RFC822-Address.html ! ‣ username@server.domain.tld ‣ florian.leitner@upm.es ‣ 123$%&-@dfa-asdf.asdf-123.wow 26 delimiters - like “quotes” in strings
 (will be omitted for clarity)
  28. 28. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Regular expressions
 quick reference 1/2 • String literals abc… ‣ abc → axc abc xca • Wild card . (any character) ‣ a.c → axc abc xca • Start ^ or end $ of string ‣ ^a.c → axc abc xca ‣ bc$ → axc abc xca ! • Word boundaries b ‣ bxc → axc abc xca ‣ bcb → axc abc xca • Character choice […] ‣ [ax][xbc][ac] →
 axc abc xca • Negations [^…] (“not”) ‣ [ax][^b][^xb] →
 axc abc xca 27 no match: …bc not at end of string (compare with word boundaries!)
  29. 29. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Regular expressions quick reference 2/2 • Groups (can be referenced for repetitions and substitutions): ‣ (…) and (…)(…)12 ‣ a(bc)1 → ac abc abcbc abcbcbc • Pattern repetitions ‣ ? “zero or one”; * “zero or more”; + “one or more”: ‣ a(bc)?d → ad abc abcd abcbcd abcbcbcd
 a(bc)*d → ad abc abcd abcbcd abcbcbcd
 a(bc)+d → ad abc abcd abcbcd abcbcbcd • Counted pattern repetitions ‣ {n} “exactly n times”, {n,} “n or more times”, {n,m} “n to m times” ‣ a(b){2}c → ac abc abbd abbbc
 ab{2,}c → ac abc abbd abbbc
 ab{0,2}c → ac abc abbd abbbc 28
  30. 30. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining An overview of free open source NLP frameworks • General Architecture for Text Engineering ‣ GATE - Java • Stanford NLP Framework ‣ CoreNLP - Java • Apache OpenNLP Framework ‣ OpenNLP (& OpenNER) - Java • Unstructured Information Management Architecture ‣ UIMA - Java • Natural Language ToolKit ‣ NLTK - Python • FreeLing NLP Suite ‣ FreeLing - C++ • The Lemur Toolkit ‣ Lemur - C++ • The Bow Toolkit ‣ Bow - C (language modeling) • Factorie Toolkit ‣ Factorie - Scala 29
  31. 31. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Sentence segmentation • Sentences are the fundamental linguistic unit ‣ Sentences are the boundaries or “constraints” for linguistic phenomena. ‣ Collocations [“United Kingdom”, “vice president”], idioms [“drop me a line”], phrases [PP: “of great fame”], clauses, statements, … all occur within a sentence. • Rule/pattern-based segmentation ‣ Segment sentences if the marker is followed by an upper-case letter ‣ Works well for “clean text” (news articles, books, papers, …) ‣ Special cases: abbreviations, digits, lower-case proper nouns (genes, “amnesty international”, …), hyphens, quotation marks, … • Supervised sentence boundary detection ‣ Use some Markov model or a conditional random field to identify possible sentence segmentation tokens ‣ Requires labeled examples (segmented sentences) 31
  32. 32. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Punkt Sentence Tokenizer (PST) 1/2 • Unsupervised sentence boundary detection • P(●|w-1) > ccpc • Determines if a marker ● is used as an abbreviation marker by comparing the conditional probability that the word w-1 before ● is followed by the marker against some (high) cutoff probability. ‣ P(●|w-1) = P(w-1, ●) ÷ P(w-1) ‣ K&S set c = 0.99 • P(w+1|w-1) > P(w+1) • Evaluates the likelihood that w-1 and w+1 surrounding the marker ● are more commonly collocated than would be expected by chance: ● is assumed an abbreviation marker (“not independent”) if the LHS is greater than the RHS. • Flength(w)×Fmarkers(w)×Fpenalty(w) ≥ cabbr • Evaluates if any of w’s morphology (length of w w/o marker characters, number of periods inside w (e.g., [“U.S.A”]), penalized when w is not followed by a ●) makes it more likely that w is an abbreviation against some (low) cutoff. • Fortho(w); Psstarter(w+1|●); … • Orthography: lower-, upper-case or capitalized word after a probable ● or not • Sentence Starter: Probability that w is found after a ● 32 Dr. Mrs. Watson U.S.A. . Therefore
  33. 33. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Punkt Sentence Tokenizer (PST) 2/2 • Unsupervised Multilingual Sentence Boundary Detection ‣ Kiss & Strunk, MIT Press 2006. ‣ Available from NLTK: nltk.tokenize.punkt (http:// www.nltk.org/api/nltk.tokenize.html) • PST is language agnostic ‣ Requires that the language uses the sentence segmentation marker as an abbreviation marker ‣ Otherwise, the problem PST solves is not present ! ! • PST factors in word length ‣ Abbreviations are relatively shorter than regular words • PST takes “internal” markers into account ‣ E.g., “U.S.A” • Main weakness: long lists of abbreviations ‣ E.g., author lists in citations ‣ Can be fixed with a pattern-based post- processing strategy • NB: a marker must be present ‣ E.g., chats or fora 33
  34. 34. Text Mining 2 Language Modeling ! Madrid Summer School on Advanced Statistics and Data Mining ! Florian Leitner florian.leitner@upm.es License:
  35. 35. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Motivation for statistical models of language Two sentences: “Colorless green ideas sleep furiously.” (from Noam Chomsky’s 1955 thesis) “Furiously ideas green sleep colorless.” Which one is (grammatically) correct? ! An unfinished sentence: “Adam went jogging with his …” What is a correct phrase to complete this sentence? 35
  36. 36. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Incentive and applications ! • Manual rule-based language processing would become cumbersome. • Word frequencies (probabilities) are easy to measure, because large amounts of texts are available to us. • Modeling language based on probabilities enables many existing applications: ‣ Spelling correction ‣ Machine translation ‣ Voice recognition ‣ Predictive keyboards ‣ Langauge generation ‣ Linguistic parsing & chunking • (analyses of the part-of-speech and grammatical structure of sentences; word semantics) 36
  37. 37. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Probabilistic language modeling ‣ Manning & Schütze. Statistical Natural Language Processing. 1999 • A sentence W is defined as a sequence of words w1, …, wn • Probability of next word wn in a sentence is: P(wn |w1, …, wn-1) ‣ a conditional probability • The probability of the whole sentence is: P(W) = P(w1, …, wn) ‣ the chain rule of conditional probability • These counts & probabilities form the language model
 [for a given document collection (=corpus)]. ‣ the model variables are discrete (counts) ‣ only needs to deal with probability mass (not density) 37
  38. 38. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Modeling the stochastic process of “generating words” using the chain rule “This is a long sentence with many words…” ➡ P(W) = P(this) × P(is | this) × P(a | this, is) × P(long | this, is, a) × P(sentence | this, is, a, long) × P(with | this, is, a, long, sentence) × P(many | this, is, a, long, sentence, with) × …. 38 n-grams for n > 5: insufficient (sparse) data (and expensive to calculate)
  39. 39. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Markov property A Markov process is a stochastic process who’s future (next) state only depends on the current state S, but not its past. 39 S1 S2S3 a token (i.e., any word, symbol, …) in S transitions with likelihood of that (next) token given the current token 3 word (S1,2,3) bigram model
  40. 40. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Modeling the stochastic process of “generating words” assuming it is Markovian ! ! • 1st Order Markov Chains ‣ Bigram Model, k=1, P(be | this) • 2nd Order Markov Chains ‣ Trigram Model, k=2, P(long | this, be) • 3rd Order Markov Chains ‣ Quadrigram Model, k=3,
 P(sentence | this, be, long) • … 40 Ti−0Ti−1 Ti−0Ti−1Ti−2Ti−3 Ti−0Ti−1Ti−2 dependencies could span over a dozen tokens, but these sizes are generally sufficient to work by Y P(wi|wi 1 1 ) ⇡ Y P(wi|wi 1 i k) Ti stochastic process: Unigram “model” NB: these are the Dynamic Bayesian Network representations of the Markov Chains (see lesson 5)
  41. 41. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining • Unigrams: • Bigrams: • N-grams (n=k+1): Calculating n-gram probabilities 41 P(wi|wi 1) = count(wi 1, wi) count(wi 1) P(wi) = count(wi) N N = total word count P(wi|wi 1 i k) = count(wi i k) count(wi 1 i k) k = n-gram size - 1 ‣ Language Model: Practical tip: transform probabilities to logs to avoid underflows and work with addition P(W) = Y P(wi|wi 1 i k) = = Y P(wi|wi k, ...wi 1)
  42. 42. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Calculating probabilities for the initial tokens • How to calculate the first/last [few] tokens in n-gram models? ‣ “This is a sentence.” ➡ P(this | ???) ‣ P(wn|wn-k, …, wn-1) • Fall back to lower-order Markov models ‣ P(w1|wn-k,…,wn-1) = P(w1); P(w2|wn-k,…,wn-1) = P(w2|w1); … • Fill positions prior to n = 1 with a generic “start token”. ‣ left and/or right padding ‣ conventionally, a strings like “<s>” and “</s>”, “*”, or “·” are used
 (but anything will do, as long as it cannot collide with a possible, real token) 42 NB: it is important to maintain sentence terminal tokens (., ?, !) to generate robust probability distributions; do not drop them!
  43. 43. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The inverted index 43 Text 1: He that not wills to the end neither wills to the means. Text 2: If the mountain will not go to Moses, then Moses must go to the mountain. tokens Text 1 Text 2 end 1 0 go 0 2 he 1 0 if 0 1 means 1 0 Moses 0 2 mountain 0 2 must 0 1 not 1 1 that 1 0 the 2 2 then 0 1 to 2 2 will 2 1 unigrams T1 1 T2 p(T1) p(T2) end 1 0 0.09 0.00 go 0 2 0.00 0.13 he 1 0 0.09 0.00 if 0 1 0.00 0.07 means 1 0 0.09 0.00 Moses 0 2 0.00 0.13 mountain 0 2 0.00 0.13 must 0 1 0.00 0.07 not 1 1 0.09 0.07 that 1 0 0.09 0.00 the 2 2 0.18 0.13 then 0 1 0.00 0.07 to 2 2 0.18 0.13 will 2 1 0.18 0.07 SUM 11 15 1.00 1.00 bigrams Text 1 Text 2 end, neither 1 0 go, to 0 2 he, that 1 0 if, the 0 1 Moses, must 0 1 Moses, then 0 1 mountain, will 0 1 must, go 0 1 not, go 0 1 not, will 1 0 that, not 1 0 the, means 1 0 the, mountain 0 2 then, Moses 0 1 to, Moses 0 1 to, the 2 1 will, not 0 1 will, to 2 0 factors, normalization (len[text]), probabilities, and n-grams REMINDER
  44. 44. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Unseen n-grams and the zero probability issue • Even for unigrams, unseen words will occur sooner or later • The longer the n-grams, the sooner unseen cases will occur • “Colorless green ideas sleep furiously.” (Chomsky, 1955) • As unseen tokens have zero probability, the probability of the whole sentence P(W) = 0 would become zero, too ! ‣ Intuition/idea: Divert a bit of the overall probability mass of each [seen] token to all possible unseen tokens • Terminology: model smoothing (Chen & Goodman, 1998) 44
  45. 45. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Additive (Lidstone) and Laplace smoothing • Add a smoothing factor α to all n-gram counts: ! ! • V is the size of the vocabulary ‣ the number of unique words in the training corpus • α ≤ 1 usually; if α =1, it is known as Add-One Smoothing • Very old: first suggested by Pierre-Simon Laplace in 1816 • But it performs poorly (compared to “modern” approaches) ‣ Gale & Church, 1994 45 P(wi|wi 1 i k) = count(wi i k) + ↵ count(wi 1 i k) + ↵V
  46. 46. Neural network models of language 46 Log-linear nodes; Training: SGD with backpropagation Input layer size: log2 V Projection layer: N ∙ D Output layer: N ∙ log2 V Input layer size: N ∙ log2 V (200) Projection layer: N ∙ D (500-20k) Output layer size: log2 V (20) N - window size (typically 10) D - projection dimensionality (50-1000) V - vocabulary size (1M unique tokens) [log2: represented as Huffmann binary tree] “generative mode” ! predict next word “descriminative mode”
 predict a word’s surrounding Trained on corpora for 40M to 6B tokens (in 300 CPU-days) word2vec - Thomas Mikolov et al. - Google - 2013
  47. 47. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Statistical models of language and polysemy • Polysemous words have multiple meanings (e.g., “bank”). ‣ This is a real problem in scientific texts because polysemy is frequent. • One idea: Create context vectors for each sense of a word (vector). ‣ MSSG - Neelakantan et al. - 2015 • Caveat: Performance isn’t much better than for the skip-gram model by Mikolov et al., while training is ~5x slower. 47
  48. 48. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Neural embeddings: Applications in TM & NLP • Opinion mining (Maas et al., 2011) • Paraphrase detection (Socher et al., 2011) • Chunking (Turian et al., 2010; Dhillon and Ungar, 2011) • Named entity recognition (Neelakantan and Collins, 2014; Passos et al., 2014; Turian et al., 2010) • Dependency parsing (Bansal et al., 2014) 48
  49. 49. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Language model evaluation • How good is the model you just trained? • Did your update to the model do any good…? • Is your model better than someone else’s? ‣ NB: You should compare on the same test set! 49
  50. 50. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Extrinsic evaluation: Error rate • Extrinsic evaluation: minimizing the error rate ‣ evaluates a model’s error frequency ‣ estimates the model’s per-word error rate by comparing the generated sequences to all true sequences (which cannot be established) using a manual classification of errors (therefore, “extrinsic”) ‣ time consuming, but can evaluate non-probabilistic approaches, too 50 a “perfect prediction” would evaluate to zero
  51. 51. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Intrinsic evaluation: Cross-entropy • Intrinsic evaluation: minimizing perplexity (Rubinstein, 1997) ‣ Compares a model’s probability distribution to a “perfect” model ‣ Estimates a distance based on cross-entropy (Kullback-Leibler divergence; explained next) between the generated word distribution and the true distribution (which cannot be observed) using the empirical distribution as a proxy ‣ Efficient, but can only evaluate probabilistic language models and is only an approximation of the model quality 51 again, a “perfect prediction” would evaluate to zero perplexity: roughly, “confusion”
  52. 52. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining • Answers the questions: ‣ “How much information (bits) will I gain when I see wn?” ‣ “How predictable is wn from its past?” ! • Each outcome provides -log2 P bits of information (“surprise”). ‣ Claude E. Shannon, 1948 • The more probable an event (outcome), the lower its entropy. • A certain event (p=1 or 0) has zero entropy (“no surprise”). ! • Therefore, the entropy H in our model P for a sentence W is: ‣ H = 1/N × -∑ P(wn|w1, …, wn-1) log2 P(wn|w1, …, wn-1) Shannon entropy 52 H(X) = P(X)log2[P(X)] (1 P(X))log2[1 P(X)]Bernoulli process:
  53. 53. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining From cross-entropy to model perplexity • Cross-entropy then compares the model probability distribution P to the true distribution PT: ‣ H(PT, P, W) = 1/N × -∑ PT(wn|wn-k, …, wn-1) log2 P(wn|wn-k, …, wn-1) • CE can be simplified if the “true” distribution is a “stationary, ergodic process”: ‣ H(P, W) = 1/N × -∑ log2 P(wn|wn-k, …, wn-1) • Then, the relationship between perplexity PPX and cross- entropy is defined as: ‣ PPX(W) = 2H(P, W) = P(W)1/N • where W is the sentence, P(W) is the Markov model, and N is the number of tokens in it 53 (an “unchanging” language, i.e., a naïve assumption) our “surprise” for the observed sentence given the true model
  54. 54. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Interpreting perplexity • The lower the perplexity, the better the model (“less surprise”) • Perplexity is an indicator of the number of equiprobable choices at each step ‣ PPX = 26 for a model generating an infinite random sequence of Latin letters • An unigram Markov model having equal transition probabilities to each letter ‣ Perplexity produces “big numbers” rather than cross-entropy’s “small bits” • Typical (bigram) perplexities in English texts range from 50 to almost 1000 corresponding to a cross- entropy from about 5.6 to 10 bits/word. ‣ Chen & Goodman, 1998 ‣ Manning & Schütze, 1999 54
  55. 55. Text Mining 3 Text Similarity ! Madrid Summer School on Advanced Statistics and Data Mining ! Florian Leitner florian.leitner@upm.es License:
  56. 56. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Incentive and applications • Goals of string similarity matching: ‣ Detecting syntactically or semantically similar words ! • Grouping/clustering similar items ‣ Content-based recommender systems; plagiarism detection • Information retrieval ‣ Ranking/searching for [query-specific] documents • Entity grounding ‣ Recognizing entities from a collection of strings (a “gazetteer” or dictionary) 56
  57. 57. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining • Finding similarly spelled or misspelled words • Finding “similar” texts/documents ‣ N.B.: no semantics (yet…) • Detecting entries in a gazetteer ‣ a list of domain-specific words • Detecting entities in a dictionary ‣ a list of words, each mapped to some URI ‣ N.B.: “entities”, not “concepts” (no semantics…) String matching 57
  58. 58. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Jaccard’s set similarity
 (Jaccard’s sim. coeff.) 58 “words” “woody” w o r s d y J(A, B) = |A B| |A [ B| = 3 7 = 0.43 vs o
  59. 59. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Jaccard’s set similarity
 (Jaccard’s sim. coeff.) 58 “words” “woody” w o r s d y J(A, B) = |A B| |A [ B| = 3 7 = 0.43 vs o 6 o.5 ABC vs. ABCABCABC
  60. 60. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String similarity measures • Edit Distance Measures ‣ Hamming Distance [1950] ‣ Levenshtein-Damerau Distance [1964/5] ‣ Needelman-Wunsch [1970] and
 Smith-Waterman [1981] Distance • also align the strings (“sequence alignment”) • use dynamic programming • Modern approaches: BLAST [1990], BWT [1994] • Other Similarity Metrics ‣ Jaro-Winkler Similarity [1989/90] • coefficient of matching characters within a dynamic window minus transpositions ‣ Soundex (➞ homophones; spelling!) ‣ … • Basic Operations: “indels” ‣ Insertions • ac ➞ abc ‣ Deletions • abc ➞ ac ! • “Advanced” Operations ‣ Require two “indels” ‣ Substitutions • abc ➞ aBc ‣ Transpositions • ab ➞ ba 59
  61. 61. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef 60
  62. 62. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 60
  63. 63. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 • Damerau-Levenshtein D. ‣ also allows transpositions ‣ has quadratic complexity ‣ karlo ⬌ carol = 2 ‣ karlos ⬌ carol = 3 60
  64. 64. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 • Damerau-Levenshtein D. ‣ also allows transpositions ‣ has quadratic complexity ‣ karlo ⬌ carol = 2 ‣ karlos ⬌ carol = 3 60 typos!
  65. 65. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 • Damerau-Levenshtein D. ‣ also allows transpositions ‣ has quadratic complexity ‣ karlo ⬌ carol = 2 ‣ karlos ⬌ carol = 3 • Jaro Similarity (a, b) ‣ calculates (m/|a| + m/|b| + (m-t)/m) / 3 ‣ 1. m, the # of matching characters ‣ 2. t, the # of transpositions ‣ window: !max(|a|, |b|) / 2" - 1 chars ‣ karlos ⬌ carol = 0.74 ‣ (4 ÷ 6 + 4 ÷ 5 + 3 ÷ 4) ÷ 3 60 typos!
  66. 66. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 • Damerau-Levenshtein D. ‣ also allows transpositions ‣ has quadratic complexity ‣ karlo ⬌ carol = 2 ‣ karlos ⬌ carol = 3 • Jaro Similarity (a, b) ‣ calculates (m/|a| + m/|b| + (m-t)/m) / 3 ‣ 1. m, the # of matching characters ‣ 2. t, the # of transpositions ‣ window: !max(|a|, |b|) / 2" - 1 chars ‣ karlos ⬌ carol = 0.74 ‣ (4 ÷ 6 + 4 ÷ 5 + 3 ÷ 4) ÷ 3 60 [0,1] range typos!
  67. 67. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 • Damerau-Levenshtein D. ‣ also allows transpositions ‣ has quadratic complexity ‣ karlo ⬌ carol = 2 ‣ karlos ⬌ carol = 3 • Jaro Similarity (a, b) ‣ calculates (m/|a| + m/|b| + (m-t)/m) / 3 ‣ 1. m, the # of matching characters ‣ 2. t, the # of transpositions ‣ window: !max(|a|, |b|) / 2" - 1 chars ‣ karlos ⬌ carol = 0.74 ‣ (4 ÷ 6 + 4 ÷ 5 + 3 ÷ 4) ÷ 3 • Jaro-Winkler Similarity ‣ adds a bonus for matching prefixes 60 [0,1] range typos!
  68. 68. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Gazetteers:
 Dictionary matching • Finding all tokens that match the entries ‣ hash table lookups: constant complexity - O(1) • Exact, single token matches ‣ regular hash table lookup (e.g., MURMUR3) • Exact, multiple tokens ‣ prefix tree of hash tables (each node being a token) • Approximate, single tokens ‣ use some string metric - but do not compare all n-to-m cases… • Approximate, multiple tokens ‣ a prefix tree of whatever the single token lookup strategy… 61 LSH (next) hash table hash table hash table default/traditional approach: character n-gram similarity (e/g. databases)
  69. 69. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Locality Sensitive Hashing (LSH) 1/2 • A hashing approach to group near neighbors. • Map similar items into the same [hash] buckets. • LSH “maximizes” (instead of minimizing) hash collisions. • It is another dimensionality reduction technique. • For documents, texts or words, minhashing can be used. ‣ Approach from Rajaraman & Ullman, Mining of Massive Datasets, 2010 • http://infolab.stanford.edu/~ullman/mmds/ch3a.pdf 62
  70. 70. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Locality Sensitive Hashing (LSH) 2/2 63 M Vogiatzis. micvog.com 2013.
  71. 71. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Minhash signatures (1/2) 65 shingleorn-gramID Create character n-gram × token or word k-shingle × document matrix (likely very sparse!) Lemma: Two texts will have the same first “true” shingle/n-gram when looking from top to bottom with a probability equal to their Jaccard (Set) Similarity. ! Idea: Create sufficient permutations of the row (shingle/n-gram) ordering so that the Jaccard Similarity can be approximated by comparing the number of coinciding vs. differing rows. 0 1 2 3 4 T T F F T F T F F T F F T F T F T T T T F T T F h 1 2 3 4 0 h 1 4 2 0 3 a family of hash functions hi h1(x) = (x+1)%n ! h2(x) = (3x+1)%n ! n=5 T: shingle/n-gram in Ti F: shingle/n-gram not in Ti “permuted” row IDs
  72. 72. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Locality Sensitive Hashing (LSH) 2/2 66 M Vogiatzis. micvog.com 2013.
  73. 73. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Minhash signatures (2/2) 67 shingleorn-gramID S T T T T h h 0 T F F T 1 1 1 F F T F 2 4 2 F T F T 3 2 3 T F T T 4 0 4 F F T F 0 3 h1(x) = (x+1)%n ! h2(x) = (3x+1)%n ! n=5 M T T T T h ∞ ∞ ∞ ∞ h ∞ ∞ ∞ ∞ init matrix M = ∞ for each shingle c, hash h, and text t: if S[t,c] and M[t,h] > h(c): M[t,h] = h(c) perfectly map-reduce-able and embarrassingly parallel!
  74. 74. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Minhash signatures (2/2) 67 shingleorn-gramID S T T T T h h 0 T F F T 1 1 1 F F T F 2 4 2 F T F T 3 2 3 T F T T 4 0 4 F F T F 0 3 h1(x) = (x+1)%n ! h2(x) = (3x+1)%n ! n=5 M T T T T h ∞ ∞ ∞ ∞ h ∞ ∞ ∞ ∞ init matrix M = ∞ for each shingle c, hash h, and text t: if S[t,c] and M[t,h] > h(c): M[t,h] = h(c) perfectly map-reduce-able and embarrassingly parallel! c=0 T T T T h ∞ ∞ ∞ ∞ h ∞ ∞ ∞ ∞ c=1 T T T T h 1 ∞ ∞ 1 h 1 ∞ ∞ 1
  75. 75. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Minhash signatures (2/2) 67 shingleorn-gramID S T T T T h h 0 T F F T 1 1 1 F F T F 2 4 2 F T F T 3 2 3 T F T T 4 0 4 F F T F 0 3 h1(x) = (x+1)%n ! h2(x) = (3x+1)%n ! n=5 M T T T T h ∞ ∞ ∞ ∞ h ∞ ∞ ∞ ∞ init matrix M = ∞ for each shingle c, hash h, and text t: if S[t,c] and M[t,h] > h(c): M[t,h] = h(c) perfectly map-reduce-able and embarrassingly parallel! c=0 T T T T h ∞ ∞ ∞ ∞ h ∞ ∞ ∞ ∞ c=1 T T T T h 1 ∞ ∞ 1 h 1 ∞ ∞ 1 c=2 T T T T h 1 ∞ 2 1 h 1 ∞ 4 1 c=3 T T T T h 1 3 2 1 h 1 2 4 1 c=4 T T T T h 1 3 2 1 h 0 2 0 0 M T T T T h 1 3 0 1 h 0 2 0 0
  76. 76. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Locality Sensitive Hashing (LSH) 2/2 68 M Vogiatzis. micvog.com 2013.
  77. 77. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining T T T T T T T T … h 1 0 2 1 7 1 4 5 h 1 2 4 1 6 5 5 6 h 0 5 6 0 6 4 7 9 h 4 0 8 8 7 6 5 7 h 7 7 0 8 3 8 7 3 h 8 9 0 7 2 4 8 2 h 8 5 4 0 9 8 4 7 h 9 4 3 9 0 8 3 9 h 8 5 8 0 0 6 8 0 … Banded locality sensitive minhashing 69 T T T T T T T T … h 1 0 2 1 7 1 4 5 h 1 2 4 1 6 5 5 6 h 0 5 6 0 6 4 7 9 h 4 0 8 8 7 6 5 7 h 7 7 0 8 3 8 7 3 h 8 9 0 7 2 4 8 2 h 8 5 4 0 9 8 4 7 h 9 4 3 9 0 8 3 9 h 8 5 8 0 0 6 8 0 … Bands 1 2 3 … Bands b ∝ pagreement Hashes/Band r ∝ 1/pagreement pagreement = 1 - (1 - sr )b s = Jaccard(A,B) (in at least one band) typical: r=10, b=30
  78. 78. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Document similarity • Similarity measures ✓Cosine similarity (of document/text vectors) ‣ Correlation coefficients • Word vector normalization ‣ TF-IDF • Dimensionality Reduction/Clustering ✓Locality Sensitivity Hashing ‣ Latent semantic indexing ‣ Latent Dirichlet allocation (tomorrow) 70
  79. 79. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Word vectors 71 0 1 2 3 4 5 6 7 8 9 10 10 0 1 2 3 4 5 6 7 8 9 count(Word1) count(Word2) Text1 Text2 α γ β Similarity(T1 , T2 ) := cos(T1 , T2 ) count(Word3 ) Comparing word vectors: Cosine similarity Collections of vectorized texts: Inverted index Text 1: He that not wills to the end neither wills to the means. Text 2: If the mountain will not go to Moses, then Moses must go to the mountain. tokens Text 1 Text 2 end 1 0 go 0 2 he 1 0 if 0 1 means 1 0 Moses 0 2 mountain 0 2 must 0 1 not 1 1 that 1 0 the 2 2 then 0 1 to 2 2 will 2 1 INDRI eachtoken/word isadimension! wordvector wordvector REMINDER
  80. 80. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Cosine similarity • Define a similarity score between two document vectors
 (or the query vector in Information Retrieval) • Euclidian vector distance is length dependent • The cosine [angle] between two vectors is not 72 sim(~x, ~y) = cos(~x, ~y) = ~x · ~y |~x||~y| = P xiyi pP x2 i pP y2 i sim(~x, ~y) = cos(~x, ~y) = ~x · ~y |~x||~y| = P xiyi pP x2 i pP y2 i can be dropped if using unit vectors (“length-normalized” a.k.a. “cosine normalization”) only dot-product is now left: extremely efficient ways to compute
  81. 81. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Alternative similarity coefficients • Spearman’s rank correlation coefficient ρ (r[ho]) ‣ Ranking is done by term frequency (TF; count) ‣ Critique: sensitive to ranking differences that are likely to occur with high- frequency words (e.g., “the”, “a”, …) ➡ use the log of the term count, rounded to two significant digits • NB that this is not relevant when only short documents (e.g. titles) with low TF counts are compared • Pearson’s chi-square test χ2 ‣ Directly on the TFs (counts) - intuition:
 Are the TFs “random samples” from the same base distribution? ‣ Usually, χ2 should be preferred over ρ (Kilgarriff & Rose, 1998) • NB that both measures have no inherent normalization of document size ‣ preprocessing might be necessary! 73
  82. 82. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Term Frequency times Inverse Document Frequency (TF-IDF) • Motivation and background • The problem ‣ Frequent terms contribute most to a document vector’s direction, but not all terms are relevant (“the”, “a”, …). • The goal ‣ Separate important terms from frequent, but irrelevant terms in the collection. • The idea ‣ Frequent terms appearing in all documents tend to be less important versus frequent terms in just a few documents. • Also dampens the effect of topic-specific noun phrases or an author’s bias for a specific set of adjectives 74 Zipf’s Law!
  83. 83. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Term Frequency times Inverse Document Frequency (TF-IDF) ‣ tf.idf(w) := tf(w) × idf(w) • tf: (document-specific) term frequency • idf: inverse (global) document frequency ! ! ‣ tfnatural(w) := count(w) • tfnatural: n. of times term w occurs in a document ‣ tflog(w) := log(count(w) + 1) • tflog: the TF is smoothed by taking its log ! ! ! ! ! ‣ idfnatural(w) := N / ∑N {wi > 0} • idfnatural: n. documents divided by n. documents in which term w occurs ‣ idflog(w) := log(N / ∑N {wi > 0}) • idflog: the IDF is smoothed by taking its log • where N is the number of documents,
 wi the count of word w in document i, and {wi>0} is 1 if document i has word w or 0 otherwise 75
  84. 84. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining TF-IDF in
 information retrieval • Document vectors = tflog • Query vector = tflog idflog ‣ Terms are counted on each individual document & the query • Cosine vector length normalization for TF-IDF scores: ‣ Document W normalization ! ‣ Query Q normalization ! • IDF is calculated over the indexed collection of all documents 76 i.e. the DVs do not use any IDF weighting (simply for efficiency: QV already has IDF
 that gets multiplied with DV values) s X w2W tflog(w)2 sX q2Q (tflog(q) ⇥ idflog(q))2
  85. 85. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining TF-IDF query score:
 An example 77 Collection Query Q Document D Similarity Term df idf tf tf tf.idf norm tf tf tf.1 cos(Q,D) best 3.5E+05 1.46 1 0.30 0.44 0.21 0 0.00 0.00 0.00 text 2.4E+03 3.62 1 0.30 1.09 0.53 10 1.04 0.06 0.03 mining 2.8E+02 4.55 1 0.30 1.37 0.67 8 0.95 0.06 0.04 tutorial 5.5E+03 3.26 1 0.30 0.98 0.48 3 0.60 0.04 0.02 data 9.2E+05 1.04 0 0.00 0.00 0.00 10 1.04 0.06 0.00 … … … … ! … ! 0.00 0.00 … ! 16.00 … ! 0.00 Sums 1.0E+07 4 2.05 ~355 16.11 0.09 3 out of hundreds of unique words match (Jaccard < 0.03) √ of ∑ of 2 Example idea from: Manning et al. Introduction to Information Retrieval. 2009 free PDF! √ of ∑ of 2 ÷÷ × ×
  86. 86. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining From syntactic to
 semantic similarity Cosine Similarity, χ2 , Spearman’s ρ, LSH, etc. all compare equal tokens. But what if you are talking about “automobiles” and I am lazy, calling it a “car”? We can solve this with Latent Semantic Indexing! 78
  87. 87. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Semantic Analysis (LSI 1/3) • a.k.a. Latent Semantic Indexing (in Text Mining):
 dimensionality reduction for semantic inference • Linear algebra background ‣ Singular value decomposition of a matrix Q: Q = UΣVT ! ! ! ! ! • SVD in text mining ‣ Inverted index = doc. eigenvectors × singular values × term eigenvectors 79 singular values:
 scaling factor orthonormal factors of Q (QQT and QT Q) the factors “predict” Q in terms of similarity (Frobenius
 norm) using as many factors as the lower dimension of Q Q P1 P2 P3 G1 G2 G3 G4 P1 P2 P3Players U G1 G2 G3 G4 Â Â’ Â’’ Games avrggamescore player ability avrgscore
 deltas player ability deltas = × S S S scaling factors ! ! ! ! (U and V are eigenvectors) ×
  88. 88. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Semantic Analysis (LSI 2/3) • Image taken from: Manning et al. An Introduction to IR. 2009 80 ‣ Inverted index = doc. eigenvectors × singular values × term eigenvectors docs terms
  89. 89. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Semantic Analysis (LSI 2/3) • Image taken from: Manning et al. An Introduction to IR. 2009 80 ‣ Inverted index = doc. eigenvectors × singular values × term eigenvectors docs terms C = DimRed by selecting only the largest n eigenvaluesˆ
  90. 90. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Semantic Analysis (LSI 3/3) 81 From: Landauer et al. An Introduction to LSA. 1998 C Cˆ top 2 dim [Spearman’s] rho(human, user) = -0.38 rho(human, minors) = -0.29 rho(human, user) = 0.94 rho(human, minors) = -0.83 test # dim to use via synonyms or missing words
  91. 91. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Principal Component vs. Latent Semantic Analysis • LSA seeks for the best linear subspace in Frobenius norm, while PCA aims for the best affine linear subspace. • LSA (can) use TF-IDF weighting as preprocessing step. • PCA requires the (square) covariance matrix of the original matrix as its first step and therefore can only compute term-term or doc-doc similarities. • PCA matrices are more dense (zeros occur only when true independence is detected). 82 best Frobenius norm: minimize “std. dev.” of matrix best affine subspace: minimize dimensions while maintaing the form
  92. 92. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining From similarity to labels • So far, we have seen how to establish if two documents are syntactically (kNN/LSH) and even semantically (LSI) similar. ! • But how do we now assign a label (a “class”) to a document? ‣ E.g., relevant/not relevant; polarity (positive, neutral, negative);
 a topic (politics, sport, people, science, healthcare, …) ‣ We could use the distances (e.g., from LSI) to cluster the documents ‣ Instead, let’s look at supervised methods next. 83
  93. 93. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Text classification approaches • Multinomial naïve Bayes* • Nearest neighbor classification (ASDM Course) ‣ incl. locality sensitivity hashing* (already seen) • Latent semantic indexing* (already seen) • Cluster analysis (ASDM Course) • Maximum entropy classification* • Latent Dirichlet allocation* • Random forests • Support vector machines (ASDM Course) • Artificial neural networks (ASDM Course) 84 efficient/fasttraininghighaccuracy * this course
  94. 94. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Three text classifiers • Multinomial naïve Bayes • Maximum entropy (multinomial logistic regression) • Latent Dirichlet allocation unsupervised! 85
  95. 95. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum A Posterior (MAP) estimator • Issue: Predict the class c ∈ C for a given document d ∈ D • Solution: MAP, a “perfect” Bayesian estimator: ! ! ! • Problem: d is really the set {w1, …, wn} of dependent words W ‣ exponential parameterization: one for each possible combination of W and C 86 CMAP (d) = argmax c2C P(c|d) = argmax c2C P(d|c)P(c) P(d) redundantthe posterior
  96. 96. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Multinomial naïve Bayes classification • A simplification of the MAP Estimator ‣ count(w) is a discrete, multinomial variable (unigrams, bigrams, etc.) ‣ Reduce space by making a strong independence assumption (“naïve”) ! ! • Easy parameter estimation ! ! ‣ V is the entire vocabulary (collection of unique words/n-grams/…) in D ‣ uses Laplacian/add-one smoothing 87 independence assumption: “each word is on its own” “bag of words/features” ˆP(wi|c) = count(wi, c) + 1 |V | + P w2V count(w, c) CMAP (d) = argmax c2C P(d|c)P(c) ⇡ argmax c2C P(c) Y w2W P(w|c) count(wi, c): the total count of word i in all documents of class c [in our training set]
  97. 97. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Multinomial naïve Bayes: Practical aspects • Can gracefully handle unseen words • Has low space requirements: |V| + |C| floats • Irrelevant (“stop”) words cancel each other out • Opposed to SVM or Nearest Neighbor, it is very fast ‣ (Locality Sensitivity Hashing was another very efficient approach we saw) ‣ But fast approaches tend to result in lower accuracies (➡ good “baselines”) • Each class has its own n-gram language model • Logarithmic damping (log(count)) might improve classification 88 sum ∏ using logs! ˆP(wi|c) = log(count(wi, c) + 1) log(|V | + P w2V count(w, c))
  98. 98. Text Mining 4 Text Classification ! Madrid Summer School on Advanced Statistics and Data Mining ! Florian Leitner florian.leitner@upm.es License:
  99. 99. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Incentive and applications • Assign one or more “labels” to a collection of “texts”. ! • Spam filtering • Marketing and politics (opinion mining) • Topic clustering • … 90
  100. 100. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Generative vs. discriminative models • Generative models describe how the [hidden] labels “generated” the [observed] input as joint probabilities: P(class, data) ‣ They learn the distributions of each individual class. ‣ Examples: Markov Chain, Naïve Bayes, Latent Dirichlet Allocation, Hidden Markov Model, … ‣ Graphical models for detecting outliers or when there is a need to update models (change) • Discriminative models predict (“discriminate”) the [hidden] labels conditioned on the [observed] input: P(class | data) ‣ They (“only”) learn the boundaries between classes. ‣ Ex.: Logistic Regression, Support Vector Machine, Conditional Random Field, Random Forest, … • Both can identify the most likely labels and their likelihoods • Only generative models: ‣ Most likely input value[s] and their likelihood[s] ‣ Likelihood of input value[s] for some particular label[s] 91 D D C D D D C D P(H|D) = P(H) ⇥ P(D|H) P(D)
  101. 101. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum entropy (MaxEnt) intuition 92 go to up outside home out { w ∈W ∑ w∈ W P(w |go)= 1 1/5 1/5 1/5 1/5 1/5 The principle of maximum entropy Observations: 1/6 1/6 1/6 1/4 1/4 P(out|go)+ P(hom e|go)= 0.5 ?? ?? ?? ?? ?? P(to |go)+ P(hom e|go)= 0.75
  102. 102. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Supervised MaxEnt classification • a.k.a. multinomial logistic regression • Does not assume independence between the features • Can model mixtures of binary, discrete, and real features • Training data are per-feature-label probabilities: P(F, L) ‣ I.e., count(fi, li) ÷ ∑N i=1 count(fi, li) ➡ words → very sparse training data (zero or few examples) • Model parameters are commonly learned using gradient descent ‣ Expensive if compared to Naïve Bayes, but efficient optimizers exist (L-BFGS) 93 logistic function p p(x) = 1 1 + exp( ( 0 + 1x)) ln p(x) 1 p(x) = 0 + 1x p(x) 1 p(x) = exp( 0 + 1x)odds-ratio! ln e Image Source: WikiMedia Commons, Qef
  103. 103. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Example feature functions for MaxEnt classifiers • Examples of indicator functions (a.k.a. feature functions) ‣ Assume we wish to classify the general polarity (positive, negative) of product reviews: • f(c, w) := {c = POSITIVE ∧ w = “great”} ‣ Equally, for classifying words in a text, say to detect proper names, we could create a feature: • f(c, w) := {c = NAME ∧ isCapitalized(w)} • Note that while we can have multiple classes, we cannot require more than one class in the whole match condition of a single indicator (feature) function. 94 NB: typical text mining models can have a million or more features: unigrams + bigrams + trigrams + counts + dictionary matchs + …
  104. 104. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximizing the
 conditional entropy • The conditioned (on X) version of Shannon’s entropy H: ! ! ! ! ! • MaxEnt training then is about selecting the model p* that maximizes H: 95 H(Y |X) = X x2X P(x) H(Y |X = x) = X x2X P(x) X y2Y P(y|x) log2 P(y|x) = X x,y2X,Y P(x, y) log2 P(x) P(x, y) (swapped nom/denom to remove the minus) p⇤ = argmax p2P H(P) = argmax p2P H(Y |X) P(x, y) = P(x) P(y|x) NB: the chain rule
  105. 105. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum entropy (MaxEnt 1/2) • Some definitions: ‣ The observed probability of y (the class) with x (the words) is: ! ‣ An indicator function (“feature”) is defined as a binary valued function that returns 1 iff class and data match the indicated requirements (constraints): ! ! ! ‣ The probability of a feature with respect to the observed distribution is: 96 f(x, y) = ( 1 if y = ci ^ x = wi 0 otherwise ˆP(x, y) = count(x, y) ÷ N ˆP(fi, X, Y ) = E ˆP [fi] = X ˆP(x, y)fi(x, y) real/discrete/binary features now are all the same!
  106. 106. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Getting lost? Reality check: • I have told you: ‣ MaxEnt is about maximizing “conditional entropy”: ‣ By multiplying binary (0/1) feature functions for observations with the joint (observation, class) probabilities, we can calculate the conditional probability of a class given its observations H(Y=y|X=x) • We will still have to do: ‣ Find weights (i.e., parameters) for each feature [function] that lead to the best model of the [observed] class probabilities. • And you want to know: ‣ How do we use all this to actually classify new input data? 97
  107. 107. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum entropy (MaxEnt 2/2) ‣ In a linear model, we’d use weights (“lambdas”) that identify the most relevant features of our model, i.e., we use the following MAP to select a class: ! ! ! ‣ To do multinomial logistic regression, expand with a linear combination: ! ! ! ‣ Next: Estimate the λ weights (parameters) that maximize the conditional likelihood of this logistic model (MLE) 98 “exponential model”argmax y2Y exp( P ifi(X, y)) P y2Y exp( P ifi(X, y)) argmax y2Y X ifi(X, y)
  108. 108. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum entropy (MaxEnt 2/2) ‣ In summary, MaxEnt is about selecting the “maximal” model p*: ! ! ! ‣ That obeys the following conditional equality constraint: ! ! ! ‣ Next: Using, e.g., Langrange multipliers, one can
 establish the optimal λ parameters of the model that
 maximize the entropy of this probability: 99 X x2X P(x) X y2Y P(y|x) f(x, y) = X x2X,y2Y P(x, y) f(x, y) p⇤ = argmax p2P X x2X p(x) X y2Y p(y|x) log2 p(y|x) …using a conditional model that matches the (observed) joint probabilities select some model that maximizes the conditional entropy… [again] Image Source: WikiMedia Commons, Nexcis p⇤ (y|X) = exp( P ifi(X, y)) P y2Y exp( P ifi(X, y))
  109. 109. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Newton’s method for paramter optimization • Problem: find the λ parameters ‣ an “optimization problem” • MaxEnt surface is concave ‣ one single maximum • Using Newton’s method ‣ iterative, hill-climbing search for max. ‣ the first derivative f´ is zero at the [global] maximum (the “goal”) ‣ the second derivative f´´ indicates rate of change: ∆λi (search direction) ‣ takes the most direct route to the maximum • Using L-BFGS ‣ a heuristic to simplify Newton’s method ‣ L-BFGS: limited memory Broyden– Fletcher–Goldfarb–Shanno ‣ normally, the partial second derivatives would be stored in the Hessian, a matrix that grows quadratically with respect to the number of features ‣ only uses the last few [partial] gradients to approximate the search direction 100 it is said to be “quasi-Newtonian” as opposed to gradient descent, which will follow a possibly curved path to the optimum
  110. 110. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining MaxEnt vs. naïve Bayes • P(w) = 6/7 • P(r|w) = 1/2 • P(g|w) = 1/2 101 Note that the example has dependent features: the two stoplights! MaxEntmodel (asobserved) NaïveBayesmodel MaxEnt adjusts the Langrange multipliers (weights) to model the correct (observed) joint probabilities. • P(r,r,b) = (1/7)(1)(1) = 4/28 • P(r,g,b) = P(g,r,b) = P(g,g,b) = 0 • P(*,*,w) = (6/7)(1/2)(1/2) = 6/28 • P(b) = 1/7 • P(r|b) = 1 • P(g|b) = 0 P(g,g,w) = 6/28??? Image Source: Klein & Manning. Maxent Models, Conditional Estimation, and Optimization. ACL 2003 Tutorial
  111. 111. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining But even MaxEnt cannot detect feature interaction 102 A, B a a b 1 3 b 3 0 Klein & Manning. MaxEnt Models, Conditional Estimation and Optimization. ACL 2003 Empirical (joint) observations Correct (target) distribution A, B a a b 1/7 3/7 b 3/7 0 2 feature model: A=r or B=r observed A, B a a b 16/49 12/49 b 12/49 9/49 A, B a a b b 4 feature model: any a,b observed A, B a a b 1/7 3/7 b 3/7 0 A, B a a b b A, B a a b 4/14 3/14 b 4/14 3/14 A, B a a b 4/14 4/14 b 3/14 3/14 only A=r only B=r
  112. 112. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining A first look at probabilistic graphical models • Latent Dirichlet Allocation: LDA ‣ Blei, Ng, and Jordan. Journal of Machine Learning Research 2003 ‣ For assigning “topics” to “documents” ‣ An unsupervised, generative model 103 i.e., for text classification
  113. 113. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Dirichlet Allocation (LDA 1/3) • Intuition for LDA • From: Edwin Chen. Introduction to LDA. 2011 ‣ “Document Collection” • I like to eat broccoli and bananas. • I ate a banana and spinach smoothie for breakfast. • Chinchillas and kittens are cute. • My sister adopted a kitten yesterday. • Look at this cute hamster munching on a piece of broccoli. ! ! 104 ➡ Topic A ➡ Topic B ➡ Topic 0.6A + 0.4B Topic A: 30% broccoli, 15% bananas, 10% breakfast, 10% munching, … ! Topic B: 20% chinchillas, 20% kittens, 20% cute, 15% hamster, …
  114. 114. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Dirichlet process • A Dirichlet is a [possibly continuos] distribution over [discrete/multinomial] distributions (probability masses). ! ! ! • The Dirichlet Process samples multiple independent, discrete distributions θi with repetition from θ (“statistical clustering”). 105 D(✓, ↵) = ( P ↵i) Q (↵i) Y ✓↵i 1 i Xnα N A Dirichlet process is like drawing from an (infinite) ”bag of dice“ (with finite faces). 1. Draw a new distribution X from D(θ, α) 2. With probability α ÷ (α + n - 1) draw a new X
 With probability n ÷ (α + n - 1), (re-)sample an Xi from X ∑ i = 1; a Probability Mass Function Gamma function -> a “continuous” factorial [!] Dirichlet prior: ∀ i ∈ : i > 0
  115. 115. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Dirichlet prior α 106 bluered green Frigyik et al. Introduction to the Dirichlet Distribution and Related Processes. 2010 ⤳ equal, =1 ➡ uniform distribution ⤳ equal, <1 ➡ marginal distrib. (”choose few“) ⤳ equal, >1 ➡ symmetric, mono-modal distrib. ⤳ not equal, >1 ➡ non-symmetric distribution Documents and topic distributions (N=3)
  116. 116. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Dirichlet Allocation (LDA 2/3) • α - per-document Dirichlet prior • θd - topic distribution of document d • zd,n - word-topic assignments • wd,n - observed words • βk - word distrib. of topic k • η - per-topic Dirichlet prior 107 βkwd,nzd,nθdα η ND K Documents Words Topics P(B, ⇥, Z, W) = KY k P( k|⌘) ! DY d P(✓d|↵) NY n P(zd,n|✓d)P(wd,n| 1:K, zd,n) ! P(Topics) P(Document-T.) P(Word-T. | Document-T.) P(Word | Topics, Word-T.) Joint Probability termscorek,n = ˆk,n log ˆk,n ⇣QK j ˆj,n ⌘1/K dampens the topic-specific score of terms assigned to many topics What Topics is a Word assigned to?
  117. 117. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Dirichlet Allocation (LDA 3/3) • LDA inference in a nutshell ‣ Calculate the posterior probability that Topic t generated Word w. ‣ Initialization: Choose K, the number of Topics, and randomly assign one out of the K Topics to each of the N Words in each of the D Documents. • The same word can have different Topics at different positions in the Document. ‣ Then, for each Topic:
 And for each Word in each Document: 1. Compute P(Word-Topic | Document): the proportion of [Words assigned to] Topic t in Document d 2. Compute P(Word | Topics, Word-Topic): the probability a Word w is assigned a Topic t (using the general distribution of Topics and the Document-specific distribution of [Word-] Topics) • Note that a Word can be assigned a different Topic each time it appears in a Document. 3. Given the prior probabilities of a Document’s Topics and that of Topics in general, reassign
 P(Topic | Word) = P(Word-Topic | Document) * P(Word | Topics, Word-Topic) ‣ Repeat until P(Topic | Word) stabilizes (e.g., MCMC Gibbs sampling, Course 04) 108
  118. 118. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Evaluation metrics for classification tasks Evaluations should answer questions like: ! How to measure a change to an approach? Did adding a feature improve or decrease performance? Is the approach good at locating the relevant pieces or good at excluding the irrelevant bits? How do two or more different methods compare? 109
  119. 119. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Essential evaluation metrics: Accuracy, F-Measure, MCC Score • True/False
 Positive/Negative ‣ counts; TP, TN, FP, FN • Precision (P) ‣ correct hits [TP] ÷
 all hits [TP + FP] • Recall (R; Sensitivity, TPR) ‣ correct hits [TP] ÷
 true cases [TP + FN] • Specificity (True Negative Rate) ‣ correct misses [TN] ÷
 negative cases [FP + TN] ! • Accuracy ‣ correct classifications [TP + TN] ÷
 all cases [TP + TN + FN + FP]) ‣ highly sensitive to class imbalance • F-Measure (F-Score) ‣ the harmonic mean between P & R
 = 2 TP ÷ (2 TP + FP + FN)
 = (2 P R) ÷ (P + R) ‣ does not require a TN count • MCC Score (Mathew’s Correlation Coefficient) ‣ χ2 -based: (TP TN - FP FN) ÷
 sqrt[(TP+FP)(TP+FN)(TN+FP)(TN+FN)] ‣ robust against class imbalance 110
  120. 120. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Essential evaluation metrics: Accuracy, F-Measure, MCC Score • True/False
 Positive/Negative ‣ counts; TP, TN, FP, FN • Precision (P) ‣ correct hits [TP] ÷
 all hits [TP + FP] • Recall (R; Sensitivity, TPR) ‣ correct hits [TP] ÷
 true cases [TP + FN] • Specificity (True Negative Rate) ‣ correct misses [TN] ÷
 negative cases [FP + TN] ! • Accuracy ‣ correct classifications [TP + TN] ÷
 all cases [TP + TN + FN + FP]) ‣ highly sensitive to class imbalance • F-Measure (F-Score) ‣ the harmonic mean between P & R
 = 2 TP ÷ (2 TP + FP + FN)
 = (2 P R) ÷ (P + R) ‣ does not require a TN count • MCC Score (Mathew’s Correlation Coefficient) ‣ χ2 -based: (TP TN - FP FN) ÷
 sqrt[(TP+FP)(TP+FN)(TN+FP)(TN+FN)] ‣ robust against class imbalance 110 NB: no result order Patient! Doctor has cancer is healthy diagnose cancer TP FN detects nothing FP TN
  121. 121. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Ranked evaluation results: AUC ROC and PR . 111 Image Source: WikiMedia Commons, kku (“kakau”, eddie) Area Under the Curve Receiver-Operator Characteristic Precision-Recall TPR / Recall! TP ÷ (TP + FN) ! FPR! FP ÷ (TN + FP) ! Precision! TP ÷ (TP + FP) (aka. Sensitivity) (not Specificity!) Davis & Goadrich.
 ICML 2006 toplast
  122. 122. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining To ROC or to PR? 112 • Davis & Goadrich. The Relationship Between PR and ROC Curves. ICML 2006 • Landgrebe et al. Precision-recall operating characteristic (P-ROC) curves in imprecise environments. Pattern Recognition 2006 • Hanczar et al. Small-Sample Precision of ROC-Related Estimates. Bioinformatics 2010 “An algorithm which optimizes the area under the ROC curve is not guaranteed to optimize the area under the PR curve.” Davis & Goadrich, 2006 Curve I: 10 hits in the top 10, and 10 hits spread over the next 1500 results. ! AUC ROC 0.813 Curve II: Hits spread evenly over the first 500 results. ! AUC ROC 0.875 Results: 20 T ≪ 1980 N → Use (AUC) PR in imbalanced scenarios!
  123. 123. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Sentiment Analysis as an example domain for text classification (only if there is time left after the exercises) ! 113 Cristopher Potts. Sentiment Symposium Tutorial. 2011 http://sentiment.christopherpotts.net/index.html
  124. 124. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Opinion/Sentiment Analysis • Harder than “regular” document classification ‣ irony, neutral (“non-polar”) sentiment, negations (“not good”),
 syntax is used to express emotions (“!”), context dependent • Confounding polarities from individual aspects (phrases) ‣ e.g., a car company’s “customer service” vs. the “safety” of their cars • Strong commercial interest in this topic ‣ “Social” (commercial?) networking sites (FB, G+, …; advertisement) ‣ Reviews (Amazon, Google Maps), blogs, fora, online comments, … ‣ Brand reputation and political opinion analysis 114
  125. 125. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Polarity of Sentiment Keywords in IMDB 115 Cristopher Potts. On the negativity of negation. 2011 Note: P(rating | word) = P(word | rating) ÷ P(word) count(w, r) ÷ ∑ count(w, r) “not good”
  126. 126. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining 5+1 Lexical Resources for Sentiment Analysis 116 Disagree- ment Opinion Lexicon General Inquirer SentiWordNet LIWC Subjectivity Lexicon 33/5402 (0.6%) 49/2867 (2%) 1127/4214 (27%) 12/363 (3%) Opinion Lexicon 32/2411 (1%) 1004/3994 (25%) 9/403 (2%) General Inquirer 520/2306 (23%) 1/204 (0.5%) SentiWord
 Net 174/694 (25%) MPQA Subjectivity Lexicon: http://mpqa.cs.pitt.edu/ Liu’s Opinion Lexicon: http://www.cs.uic.edu/~liub/FBS/sentiment-analysis.html General Inquirer: http://www.wjh.harvard.edu/~inquirer/ SentiWordNet: http://sentiwordnet.isti.cnr.it/ LIWC (commercial, $90): http://www.liwc.net/ NRC Emotion Lexicon (+1): http://www.saifmohammad.com/ (➡Publications & Data) Cristopher Potts. Sentiment Symposium Tutorial. 2011
  127. 127. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Detecting the Sentiment of Individual Aspects • Goal: Determine the sentiment for a particular aspect or establish their polarity. ‣ An “aspect” here is a phrase or concept, like “customer service”. ‣ “They have a great+ customer service team, but the delivery took ages-.” • Solution: Measure the co-occurrence of the aspect with words of distinct sentiment or relative co-occurrence with words of the same polarity. ‣ The “sentiment” keywords are taken from some lexical resource. 117
  128. 128. Google’s Review Summaries 118
  129. 129. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Using PMI to Detect Aspect Polarity • Polarity(aspect) := PMI(aspect, pos-sent-kwds) - PMI(aspect, neg-sent-kwds) ‣ Polarity > 0 = positive sentiment ‣ Polarity < 0 = negative sentiment • Google’s approach: ! ! ! ! ! • Blair-Goldensohn et al. Building a Sentiment Summarizer for Local Service Reviews. WWW 2008 119 nouns and/or noun phrases keyword gazetteer
  130. 130. Text Mining 5 Information Extraction ! Madrid Summer School on Advanced Statistics and Data Mining ! Florian Leitner florian.leitner@upm.es License:
  131. 131. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Retrospective We have seen how to… • Design generative models of natural language. • Segment, tokenize, and compare text and/or sentences. • [Multi-] labeling whole documents or chunks of text. ! Some open questions… • How to assign labels to individual tokens in a stream? ‣ without using a dictionary/gazetteer: sequence taggers • How to detect semantic relationships between tokens? ‣ dependency parsers 121
  132. 132. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Incentive and applications ➡ Statistical analyses of [token] sequences ! • Part-of-Speech (PoS) tagging & chunking ‣ noun, verb, adjective, … & noun/verb/preposition/… phrases • Named Entity Recognition (NER) ‣ organizations, persons, places, genes, chemicals, … • Information extraction ‣ locations/times, phys. constants & chem. formulas, entity linking, event extraction, entity-relationship extraction, … 122
  133. 133. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Probabilistic graphical models • Graphs of hidden (blank) and observed (shaded) variables (vertices/nodes). • The edges depict dependencies, and if directed, show [ideally causal] relationships between nodes. 123 H O S3S2S1 directed ➡ Bayesian Network (BN) undirected ➡ Markov Random Field (MRF) mixed ➡ Mixture Models Koller & Friedman. Probabilistic Graphical Models. 2009
  134. 134. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Hidden vs. observed state and statistical parameters Rao. A Kalman Filter Model of the Visual Cortex. Neural Computation 1997 124
  135. 135. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining A Bayesian network for the Monty Hall problem 125 Choice 1 Choice 2 Goat Winner Car
  136. 136. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Markov random field 126 normalizing constant (partition function Z) factor (clique potential) A D B C θ(A, B) θ(B, C) θ(C, D) θ(D, A) a b 30 b c 100 c d 1 d a 100 a b 5 b c 1 c d 100 d a 1 a b 1 b c 1 c d 100 d a 1 a b 10 b c 100 c d 1 d a 100 P(a1, b1, c0, d1) = 10·1·100·100 ÷ 7’201’840 = 0.014 factor table factor graph P(X = ~x) = Q cl2~x cl(cl) P ~x2X Q cl2~x cl(cl) cl … [maximal] clique; a subset of factors
 in the graph where every pair is connected History class: Ising developed a linear field to model (binary) atomic spin states (Ising, 1924); the 2-dim. model problem then was solved by Onsager in 1944.
  137. 137. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Probabilistic models for sequential data • a.k.a. Temporal or dynamic Bayesian networks ‣ Static process w/ constant model ➡ temporal process w/ dynamic model ‣ Model structure and parameters are [still] constant ‣ The model topology within a [constant] “time slice” is depicted • Markov Chain (MC; Markov. 1906) • Hidden Markov Model (HMM; Baum et al. 1970) • MaxEnt Markov Model (MEMM; McCallum et al. 2000) • [Markov] Conditional Random Field (CRF; Lafferty et al. 2001) ‣ Naming: all four models make the Markov assumption (see part 2) 127 generativediscriminative
  138. 138. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining From a Markov chain to a Hidden Markov Model (HMM) 128 WW’ SS’ W hidden states observed state S1S0 W1 S2 W2 S3 W3 “unrolled” (for 3 words) “time-slice” W depends on S and S in turn depends on S’ P(W | W’) P(W | S) P(S | S’)
  139. 139. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining A language-based intuition for HMMs • A Markov Chain: P(W) = ∏ P(w | w’) ‣ assumes the observed words are in and of themselves the cause of the observed sequence. • A HMM: P(S, W) = ∏ P(s | s’) P(w | s) ‣ assumes the observed words are emitted by a hidden (not observable) sequence, for example the chain of part-of-speech-states. 129 S DT NN VB NN . The dog ran home ! again, this is the “unrolled” model that does not depict the conditional dependencies
  140. 140. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The two matrices of a HMM 130 P(s | s’) DT NN VB … DT 0.03 0.7 0 NN 0 0 0.5 VB 0 0.5 0.2 … P(w | s) word word word … DT 0.3 0 0 NN 0.0001 0.002 0 VB 0 0 0.001 … SS’ W very sparse (W is large) ➡ Smoothing! Transition Matrix Observation Matrix underflow danger ➡ use “log Ps”! a.k.a. “CPDs”: Conditional Probability Distributions (measured as discrete factor tables from annotated PoS corpora)
  141. 141. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Three tasks solved by HMMs Evaluation: Given a HMM, infer the P of the observed sequence (because a HMM is a generative model). Solution: Forward Algorithm Decoding: Given a HMM and an observed sequence, predict the hidden states that lead to this observation. Solution: Viterbi Algorithm Training: Given only the graphical model and an observation sequence, learn the best [smoothed] parameters. Solution: Baum-Welch Algorithm 131 all three algorithms are are implemented using dynamic programming in Bioinformatics: Likelihood of a particular DNA element in Statistical NLP: PoS annotation
  142. 142. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Three limitations of HMMs Markov assumption: The next state only depends on the current state. Example issue: trigrams Output assumption: The output (observed value) is independent of all previous outputs (given the current state). Example issue: word morphology Stationary assumption: Transition probabilities are independent of the actual time when they take place. Example issue: position in sentence 132 (label bias problem, see next!) (long-range dependencies!) (inflection, declension!) MEMMCRF“unsolved” (CRF)
  143. 143. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining From generative to discriminative Markov models 133 SS’ W S’ S W S’ S W Hidden Markov Model Maximum Entropy Markov Model Conditional Random
 Field this “clique” makes CRFs expensive to compute generative model; lower bias is beneficial for small training sets (linear chain version)(first oder version) P(S, W) P(S | S’, W) NB boldface W: all words! (first oder version) P(S | S’, W)
  144. 144. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum entropy (MaxEnt 2/2) ‣ In summary, MaxEnt is about selecting the “maximal” model p*: ! ! ! ‣ That obeys the following conditional equality constraint: ! ! ! ‣ Next: Using, e.g., Langrange multipliers, one can
 establish the optimal λ parameters of the model that
 maximize the entropy of this probability: 134 X x2X P(x) X y2Y P(y|x) f(x, y) = X x2X,y2Y P(x, y) f(x, y) p⇤ = argmax p2P X x2X p(x) X y2Y p(y|x) log2 p(y|x) …using a conditional model that matches the (observed) joint probabilities select some model that maximizes the conditional entropy… [again] Image Source: WikiMedia Commons, Nexcis p⇤ (y|X) = exp( P ifi(X, y)) P y2Y exp( P ifi(X, y)) REMINDER “Exponential Model”
  145. 145. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum Entropy Markov Models (MEMM) Simplify training of P(s | s’, w)
 by splitting the model into |S| separate transition functions Ps’(s | w) for each s’ 135 P(S | S’, W) S’ S W Ps0 (s|w) = exp ( P ifi(w, s)) P s⇤2S exp ( P ifi(w, s⇤)) P(s | s’, w) = Ps’(s | w) (The MaxEnt slide had {x, y} which here are {w, s}.)
  146. 146. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The label bias problem of directional Markov models 136 The robot wheels are round. The robot wheels Fred around. The robot wheels were broken. DT NN VB NN RB DT NN NN VB JJ DT NN ?? — — yet unseen! Wallach. Efficient Training of CRFs. MSc 2002 because of their directionality constraints, MEMMs & HMMs suffer from the label bias problem S’ S W MEMM HMM SS’ W
  147. 147. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Conditional Random Field 137 SS’ W w1, …, wn Models a per-state exponential function of joint probability over the entire observed sequence W. (max.) clique MRF: The label bias problem is “solved” by conditioning the MRF Y-Y’ on the entire observed sequence. CRF: note W (upper-case/bold), not w (lower-case): all words are used in each step! P(X = ~x) = Q cl2~x cl(cl) P ~x2X Q cl2~x cl(cl) P(Y = ~y |X = ~x) = Q y2~y cl(y0 , y, ~x) P ~y2Y Q y2~y cl(y0, y, ~x) P(S|W) = exp ( P ifi(W, s0 , s)) P s⇤2S exp ( P ifi(W, s0⇤, s⇤)) Wallach. Conditional Random Fields: An introduction. TR 2004
  148. 148. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Parameter estimation and L2 regularization of CRFs • For training {Y(n), X(n)}N n=1 sequence pairs with K features • Parameter estimation using conditional log-likelihood ! ! • Substitute log P(Y(n) | X(n)) with log exponential model ! ! • Add a penalty for parameters with a to high L2-norm 138 free regularization parameter `( ) = NX n=1 X y2Y (n) KX i=1 ifi(y0 , y, X(n) ) NX n=1 log Z(X(n) ) `( ) = NX n=1 X y2Y (n) KX i=1 ifi(y0 , y, X(n) ) NX n=1 log Z(X(n) ) KX i=1 2 i 2 2 (regularization reduces the effects of overfitting) normalizing constant (partial function Z) = argmax 2⇤ NX n log P(Y (n) |X(n) ; )
  149. 149. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Parameter estimation and L2 regularization of CRFs • For training {Y(n), X(n)}N n=1 sequence pairs with K features • Parameter estimation using conditional log-likelihood ! ! • Substitute log P(Y(n) | X(n)) with log exponential model ! ! • Add a penalty for parameters with a to high L2-norm 138 free regularization parameter `( ) = NX n=1 X y2Y (n) KX i=1 ifi(y0 , y, X(n) ) NX n=1 log Z(X(n) ) `( ) = NX n=1 X y2Y (n) KX i=1 ifi(y0 , y, X(n) ) NX n=1 log Z(X(n) ) KX i=1 2 i 2 2 (regularization reduces the effects of overfitting) normalizing constant (partial function Z) = argmax 2⇤ NX n log P(Y (n) |X(n) ; ) L2: Euclidian norm (∑ of squared errors) k⇤k2 2 2 2
  150. 150. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Model summaries:
 HMM, MEMM, CRF • A HMM ‣ generative model ‣ efficient to learn and deploy ‣ trains with little data ‣ generalizes well (low bias) • A MEMM ‣ better labeling performance ‣ modeling of features ‣ label bias problem ! • CRF ‣ conditioned on entire observation ‣ complex features over full input ‣ training time scales exponentially • O(NTM2 G) • N: # of sequence pairs;
 T: E[sequence length];
 M: # of (hidden) states;
 G: # of gradient computations for parameter estimation 139 a PoS model w/45 states and 1 M words can take a week to train… Sutton & McCallum. An Introduction to CRFs for Relational Learning. 2006
  151. 151. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Information extraction: Application of dynamic graphical models 140
  152. 152. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Parts of Speech • Corpora for the [supervised] training of PoS taggers ‣ Brown Corpus (AE from ~1961) ‣ British National Corpus: BNC (20th century British) ‣ Wall Street Journal Corpus: WSJ Corpus (AE from the 80s) ‣ American National Corpus: ANC (AE from the 90s) ‣ Lancaster Corpus of Mandarin Chinese: LCMC (Books in Mandarin) ‣ The GENIA corpus (Biomedical abstracts from PubMed) ‣ NEGR@ (German Newswire from the 90s) ‣ Spanish and Arabian corpora should be (commercially…) available… ??? 141 I ate the pizza with green peppers . PRP VB DT NN IN JJ NN . ! Best tip: Ask on the “corpora list” mailing list!
  153. 153. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Noun and verb phrase chunking with BIO-encoded labels 142 The brown fox quickly jumps over the lazy dog . a pangram (hint: check the letters) DT JJ NN RB VBZ IN DT JJ NN . B-N I-N I-N B-V I-V O B-N I-N I-N O Performance (2nd order CRF) ~ 94% Main problem: embedded & chained NPs (N of N and N) ! Chunking is “more robust to the highly diverse corpus of text on the Web” and [exponentially] faster than [deep] parsing. Banko et al. Open Information Extraction from the Web. IJCAI 2007 a paper with over 700 citations Wermter et al. Recognizing noun phrases in biomedical text. SMBM 2005 error sources “shallow parsing”
  154. 154. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Word Sense Disambiguation (WSD) • Basic Example: hard [JJ] ‣ physically hard (a hard stone) ‣ difficult [task] (a hard task) ‣ strong/severe (a hard wind) ‣ dispassionate [personality] (a hard bargainer) • Entity Disambig.: bank [NN] ‣ finance (“bank account”) ‣ terrain (“river bank”) ‣ aeronautics (“went into bank”) ‣ grouping (“a bank of …”) ! • SensEval ‣ http://www.senseval.org/ ‣ SensEval/SemEval Challenges ‣ Provides corpora where every word is tagged with its sense • WordNet ‣ http://wordnet.princeton.edu/ ‣ A labeled graph of word senses • Applications ‣ Named entity recognition ‣ Machine translation ‣ Language understanding 143 Note the PoS-tag “dependency”: otherwise, the two examples would have even more senses!
  155. 155. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Word vector representations: Unsupervised WSD • Idea 1: Words with similar meaning have similar environments. • Use a word vector to count a word’s surrounding words. • Similar words now will have similar word vectors. ‣ See lecture 2, neural network models of language and lecture 4, cosine similarity ‣ Visualization: Principal Component Analysis ! • Idea 2: Words with similar meaning have similar environments. • Use the surrounding of unseen words to “smoothen” language models (i.e., the correlation between word wi and its context cj). ‣ see Text Mining 4: TF-IDF weighting, Cosine similarity and point-wise MI ‣ Levy & Goldberg. Linguistic Regularities in Sparse and Explicit Word Representations. CoNLL 2014 144 Levy & Goldberg took two words on each side to “beat” a neural
 network model with a four word window! Turian et al. Word representations. ACL 2010
  156. 156. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Named Entity Recognition (NER) 145 Date Location Money Organization Percentage Person ➡ Conditional Random Field ➡ Ensemble Methods; +SVM, HMM, MEMM, … ➡ pyensemble
 NB these are corpus-based approaches (supervised) CoNLL03: http://www.cnts.ua.ac.be/conll2003/ner/ ! How much training 
 data do I need? “corpora list” Image Source: v@s3k [a GATE session; http://vas3k.ru/blog/354/]
  157. 157. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining PoS tagging and lemmatization for
 Named Entity Recognition (NER) 146 Token PoS Lemma NER Constitutive JJ constitutive O binding NN binding O to TO to O the DT the O peri-! NN peri-kappa B-DNA B NN B I-DNA site NN site I-DNA is VBZ be O seen VBN see O in IN in O monocytes NNS monocyte B-cell . . . O de facto standard
 PoS tagset {NN, JJ, DT, VBZ, …} Penn Treebank B-I-O chunk encoding common alternatives: I-O I-E-O B-I-E-W-O End token (unigram) Word Begin-Inside-Outside (relevant) token } chunk noun-phrase (chunk) N.B.: This is all supervised (i.e., manually annotated corpora)! REMINDER
  158. 158. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The next step: Relationship extraction Given this piece of text: The fourth Wells account moving to another agency is the packaged paper-products division of Georgia-Pacific Corp., which arrived at Wells only last fall. Like Hertz and the History Channel, it is also leaving for an Omnicom-owned agency, the BBDO South unit of BBDO Worldwide. BBDO South in Atlanta, which handles corporate advertising for Georgia-Pacific, will assume additional duties for brands like Angel Soft toilet tissue and Sparkle paper towels, said Ken Haldin, a spokesman for Georgia-Pacific in Atlanta. Which organizations operate in Atlanta? (BBDO S., G-P) 147
  159. 159. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Tesnière’s dependency relations (1959) 148 He ate pizza with anchovies. He ate pizza with friends. ate(he, pizza with anchovies) ate(he, pizza) ate(he, with friends) Relationships ate(he, with anchovies)
  160. 160. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Dependency parsing 1/2 • Transition-based, arc-standard, shift-reduce, greedy parsing. • The default approach to dependency parsing today in O(n). ‣ Transition-based: Move from one token to the next. ‣ Arc-standard: assign arcs when the dependent token (arrowhead) is fully resolved (alternative: arc-eager → assign the arcs immediately). ‣ Shift-reduce: A stack of words and a stream buffer: either shift next word from the buffer to the stack or reduce a word from the stack by “arcing”. ‣ Greedy: Make locally optimal transitions (assume independence of arcs). 149
  161. 161. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Buffer A shift-reduce parse Stack 150 ROOT Economic marketsfinancialoneffectlittlenews had . ROOT Economic marketsfinancialoneffectlittlenews had . (left-arc, right-arc) Dependency Parsing. Kübler et al., 2009
  162. 162. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Buffer A shift-reduce parse Stack 150 ROOT marketsfinancial . ROOT Economic marketsfinancialoneffectlittlenews had . Shift: Economic Shift: news Left-arc: Economic←news Shift: had Left-arc: news←had Shift: little Shift: effect Left-arc: little←effect had effect on Shift: on (left-arc, right-arc) Dependency Parsing. Kübler et al., 2009
  163. 163. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Buffer A shift-reduce parse Stack 150 ROOT ROOT Economic marketsfinancialoneffectlittlenews had . Shift: Economic Shift: news Left-arc: Economic←news Shift: had Left-arc: news←had Shift: little Shift: effect Left-arc: little←effect Shift: on Shift: financial Shift: markets Shift: . Left-arc: financial←markets Right-arc: on→markets Right-arc: effect→on Right-arc: had→effect Right-arc: had→. Right-arc: ROOT→had (left-arc, right-arc) Dependency Parsing. Kübler et al., 2009
  164. 164. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Dependency parsing 2/2 • (Arc-standard) Transitions: shift or reduce (left-arc, right-arc) • Transitions are chosen using some classifier ‣ Maximum entropy classifier, support vector machine, single-layer perceptron, perceptron with one hidden layer (→ Stanford parser, 2014 edition) • Main issues: ‣ Few large, well annotated training corpora (“dependency treebanks”).
 Biomedical domain: GENIA; Newswire: WSJ, Prague, Penn, … ‣ Non-projective trees (i.e., trees with arcs crossing each other; common in a number of other languages) with arcs that have to be drawn between nodes that are not adjacent on the stack. 151
  165. 165. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Four approaches to relationship extraction • Co-mention window ‣ E.g.: if ORG and LOC entity within same sentence and no more than x tokens in between, treat the pair as a hit. ‣ Low precision, high recall; trivial, many false positives. • Dependency parsing ‣ If a path covering certain nodes (e.g. prepositions like “in/IN” or predicates [~verbs]) connects two entities, extract that pair. ‣ Balanced precision and recall, computationally expensive. • Pattern extraction ‣ e.g.: <ORG>+ <IN> <LOC>+ ‣ High precision, low recall; cumbersome, but very common. ‣ Pattern learning can help. ! • Machine Learning ‣ Features for sentences with entities and some classifier (e.g., SVM, neural net, MaxEnt, Bayesian net, …) ‣ Highly variable milages.
 … but loads of fun in your speaker’s opinion :) 152 preposition token-distance, #tokens between the entities, tokens before/after them, etc.)
Data & Analytics

Description

The updated slides for my introductory course on text mining. The slides take you from basic Bayesian statistics over Markov chains and language models (incl. neural embeddings) to text similarity measures (Locality Sensitive Hashing, Latent Semantic Analysis, and Latent Dirichlet Allocation) and classification techniques (Naïve Bayes, MaxEnt [logistic regression]). Finally, they introduce you to shallow parsing with dynamic graphical models (HMMs, MEMMs, and CRFs) and provide you with a glimpse at dependency parsing (shift-reduce, arc-standard).

Transcript

  1. 1. 10th Madrid Summer School on
 Advanced Statistics and Data Mining ! Module C9 :: Text Mining 6th July - 10th of July 2015 ! Florian Leitner florian.leitner@upm.es License:
  2. 2. Text Mining 1 Introduction ! Madrid Summer School on Advanced Statistics and Data Mining ! Florian Leitner florian.leitner@upm.es License:
  3. 3. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining “Text mining” or
 “text analytics” The discovery of new or existing facts from text by applying natural language processing (NLP), statistical learning techniques, or both. 3 Machine Learning Inferential Statistics Computat. Linguistics RulesModels Predictions
  4. 4. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Is language understanding key to artificial intelligence? “Her” Movie, 2013 “The singularity: 2030” Ray Kurzweil
 (Google’s director of engineering) “Watson” & “CRUSH” IBM 4 “predict crimes before they happen” Criminal Reduction Utilizing Statistical History (IBM, reality) ! Precogs (Minority Report, movie) if? when? cognitive computing: “processing information more like a human than a machine” GoogleGoogle
  5. 5. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Applications of text mining and language processing (Web) Search engines Information retrieval Spam filtering Document classification Twitter brand monitoring Opinion mining Finding similar items (Amazon) Content-based recommender systems Event detection in e-mail Information extraction Spelling correction Statistical language modeling Siri (Apple) and Google Now Language understanding Website translation (Google) Machine translation “Clippy” assistant (Microsoft) Dialog systems Watson in Jeopardy! (IBM) Question answering 5 Textmining Languageprocessing
  6. 6. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Document or text
 classification and clustering 6 1st Principal Component 2ndPrincipalComponent document distance 1st Principal Component 2nd PrincipalComponent Centroid Cluster Supervised (“learning to classify from examples”, e.g., spam filtering) vs. Unsupervised (“exploratory grouping”, e.g., topic modeling)
  7. 7. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Tokens and n-grams 7 This is a sentence . This is is a a sentence sentence . This is a is a sentence a sentence . This is a sentence. { { { { { { { NB: “tokenization” Character-based, Regular Expressions, Probabilistic, … Token n-grams unigram! shingle! ! bigram! 2-shingle! ! trigram! 3-shingle all trigrams of “sentence”:
 [sen, ent, nte, ten, enc, nce] Beware: the terms “shingle”, “token” and “n-gram” are not used consistently… Character n-grams Token or Shingle
  8. 8. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The inverted index 8 Text 1: He that not wills to the end neither wills to the means. Text 2: If the mountain will not go to Moses, then Moses must go to the mountain. tokens Text 1 Text 2 end 1 0 go 0 2 he 1 0 if 0 1 means 1 0 Moses 0 2 mountain 0 2 must 0 1 not 1 1 that 1 0 the 2 2 then 0 1 to 2 2 will 2 1 unigrams T1 1 T2 p(T1) p(T2) end 1 0 0.09 0.00 go 0 2 0.00 0.13 he 1 0 0.09 0.00 if 0 1 0.00 0.07 means 1 0 0.09 0.00 Moses 0 2 0.00 0.13 mountain 0 2 0.00 0.13 must 0 1 0.00 0.07 not 1 1 0.09 0.07 that 1 0 0.09 0.00 the 2 2 0.18 0.13 then 0 1 0.00 0.07 to 2 2 0.18 0.13 will 2 1 0.18 0.07 SUM 11 15 1.00 1.00 factors, normalization (len[text]), probabilities, and n-grams bigrams Text 1 Text 2 end, neither 1 0 go, to 0 2 he, that 1 0 if, the 0 1 Moses, must 0 1 Moses, then 0 1 mountain, will 0 1 must, go 0 1 not, go 0 1 not, will 1 0 that, not 1 0 the, means 1 0 the, mountain 0 2 then, Moses 0 1 to, Moses 0 1 to, the 2 1 will, not 0 1 will, to 2 0
  9. 9. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Word vectors 9 0 1 2 3 4 5 6 7 8 9 10 10 0 1 2 3 4 5 6 7 8 9 count(Word1) count(Word2) Text1 Text2 α γ β Similarity(T1 , T2 ) := cos(T1 , T2 ) count(Word3 ) Comparing word vectors: Cosine similarity Collections of vectorized texts: Inverted index Text 1: He that not wills to the end neither wills to the means. Text 2: If the mountain will not go to Moses, then Moses must go to the mountain. tokens Text 1 Text 2 end 1 0 go 0 2 he 1 0 if 0 1 means 1 0 Moses 0 2 mountain 0 2 must 0 1 not 1 1 that 1 0 the 2 2 then 0 1 to 2 2 will 2 1 INDRI eachtoken/word isadimension! wordvector wordvector
  10. 10. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The essence of statistical learning 10 ×= y = h✓(X) XTy θ Rank, Class, Expectation, Probability, Descriptor*, … Inverted index (transposed) Parameters
 (θ) “texts”(n) n-grams (p) instances, observations variables, features per feature
  11. 11. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The essence of statistical learning 10 ×= y = h✓(X) XTy θ Rank, Class, Expectation, Probability, Descriptor*, … Inverted index (transposed) Parameters
 (θ) “texts”(n) n-grams (p) instances, observations variables, features per feature “Nonparametric” per instance
  12. 12. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The curse of
 dimensionality
 (RE Bellman, 1961) [inventor
 of dynamic programming] • p ≫ n (far more
 tokens/features than
 texts/documents) • Inverted indices are
 (discrete) sparse matrices. • Even with millions of training examples, unseen tokens will keep coming up during evaluation or in production. • In a high-dimensional hypercube, most instances are closer to the face of the cube (“nothing”, outside) than their nearest neighbor. 11
  13. 13. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Dimensionality reduction ✓ The remedy to “the curse” (aka. the “blessing of non-uniformity”) ‣ Feature extraction (compression): PCA/LDA (projection), factor analysis (regression), compression, auto-encoders (“deep learning”, “word embeddings”), … ‣ Feature selection (elimination): LASSO (regularization), SVM (support vectors), Bayesian nets (structure learning), locality sensitivity hashing, random projections, … 12
  14. 14. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Ambiguity 13 Anaphora resolution Carl and Bob were fighting: “You should shut up,” Carl told him. Part-of-Speech tagging The robot wheels out the iron. Paraphrasing Unemployment is on the rise. vs The economy is slumping. Named entity recognition Is Paris really good for you?
  15. 15. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The conditional probability for dependent events 14 Conditional Probability P(X | Y) = P(X ∩ Y) ÷ P(Y) *Independence P(X ∩ Y) = P(X) × P(Y) P(X | Y) = P(X) P(Y | X) = P(Y) ` ` Joint Probability P(X ∩ Y) = P(X, Y) = P(X × Y) The multiplication principle for dependent* events: P(X ∩ Y) = P(Y) × P(X | Y) and therefore, by using a little algebra: X Y 1/3 1/2 1 given
  16. 16. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Marginal, conditional and joint probabilities 15 Joint Probability* P(xi, yj) = P(xi) × P(yj) Marginal Probability P(yi) X=x X=x M Y= y a/n = P(x b/n = P(x (a+b)/n = P(y Y= y c/n = P(x d/n = P(x (c+d)/n = P(y M (a+c)/n = P(x (b+d)/n = P(x ∑ / n = 1 = P(X) = P(Y) Conditional Probability P(xi | yj) = P(xi, yj) ÷ P(yj) contingency table *for independent events variable/factor variable/factor margin
  17. 17. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Point-wise mutual information • Mutual information (MI) measures the degree of
 dependence of two variables: how similar is P(X,Y) to P(X)·P(Y) ? ! ! • Point-wise MI: MI of two individual events [only] ! ! ‣ e.g., neighboring words, phrases in a document, … ‣ incl. a mix of two different co-occurring event types (e.g. a word and a phrase or label) ‣ Can be normalized to a [-1,1] range: ! • Interpretation: -1: the events do not occur together; 0: the events are independent; +1: the events always co-occur 16 I(X; Y ) = X Y X X P(x, y) log2 P(x, y) P(x)P(y) PMI(w1, w2) = log2 P(w1, w2) P(w1)P(w2) PMI(w1, w2) log2 P(w1, w2) “how much you can learn about X from knowing Y”
  18. 18. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Bayes’ rule: Diachronic interpretation 17 H - Hypothesis X D - Data Y prior/belief likelihood posterior P(H|D) = P(H) ⇥ P(D|H) P(D) “normalizing constant” (law of total probability)
  19. 19. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Bayes’ rule: The Monty Hall problem 18 1 2 3 Prior p(H) 1/3 1/3 1/3 Likelihood p(D|H) 1/2 1 0 p(D) =∑ p(H)* p(D|H) 1/3×1/2 =1/6 1/3×1 =1/3 1/3×0 =0 1/6+1/3 =1/2 Posterior p(H|D) 1/6÷1/2 =1/3 1/3÷1/2 =2/3 0÷1/2 =0 P(H|D) = P(H) ⇥ P(D|H) P(D) similar case: a trickster hiding a stone in one of three cups… Images Source: Wikipedia, Monty Hall Problem, Cepheus your pick given the car is behind H=1, Monty Hall opens D=(2 or 3) H=2 ! H=3 D=3 ! D=3 Monty Hall
  20. 20. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The chain rule of
 conditional probability P(A,B,C,D) = P(A) × P(B|A) × P(C|A,B) × P(D|A,B,C) 19 P(B,Y,B) = P(B) × P(Y|B) × P(B|B,Y) 1/10 = 2/5 × 3/4 × 1/3 P(B) 2/5 P(Y|B) 3/4 P(B|B,Y) 1/3 P(w1, ..., wn) = nY i=1 P(wi|w1, ..., wi 1) = nY i=1 P(wi|wi 1 1 ) NB: the ∑ of all “trigrams” will be 1! NB: without replacement! joint conditional …to wi-1 from w1… Notation: i-1 is an index, not the power!
  21. 21. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Zipf’s law: Pareto distributions Word frequency is inversely proportional to its rank (ordered by counts) Words of lower rank “clump” within a region of a document Word frequency is inversely proportional to its length Almost all words are rare 20 f ∝ 1 ÷ r k = E[f × r] 5 10 15 20 25 0.20.40.60.81.0 Word Frequency lexical richness k Word rank This is what makes language modeling hard! the, be, to, of, … …, malarkey, quodlibet E = Expected Value the “true” mean dim. reduction Cumulativeprobabilitymass count(wi) ∝ P(wi) = pow(α, ranki) = 1/k (0, 1] “power law”
  22. 22. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Parts of Speech (PoS) • The Parts of Speech: ‣ noun: NN, verb: VB, adjective: JJ, adverb: RB, preposition: IN,
 personal pronoun: PRP, … ‣ e.g. the full Penn Treebank PoS tagset contains 48 tags: ‣ 34 grammatical tags (i.e., “real” parts-of-speech) for words ‣ one for cardinal numbers (“CD”; i.e., a series of digits) ‣ 13 for [mathematical] “SYM” and currency “$” symbols, various types of punctuation, as well as for opening/closing parenthesis and quotes 21 I ate the pizza with green peppers . PRP VB DT NN IN JJ NN . “PoS tags”
  23. 23. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Parts of Speech (2/2) • Automatic PoS tagging ➡ supervised machine learning ‣ Maximum Entropy Markov models ‣ Conditional Random Fields ‣ Convolutional Neural Networks ‣ Ensemble methods (bagging, boosting, etc.) 22 I ate the pizza with green peppers . PRP VB DT NN IN JJ NN .
  24. 24. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Linguistic morphology • [Verbal] Inflections ‣ conjugation (Indo-European languages) ‣ tense (“availability” and use varies across languages) ‣ modality (subjunctive, conditional, imperative) ‣ voice (active/passive) ‣ … ! • Contractions ‣ don’t say you’re in a man’s world…
 • Declensions • on nouns, pronouns, adjectives, determiners ‣ case (nominative, accusative, dative, ablative, genitive, …) ‣ gender (female, male, neuter) ‣ number forms (singular, plural, dual) ‣ possessive pronouns (I➞my, you➞your, she➞her, it➞its, … car) ‣ reflexive pronouns (for myself, yourself, …) ‣ … 23 not a contraction: possessive s ➡ token normalization
  25. 25. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Stemming → Lemmatization • Stemming ‣ produced by “stemmers” ‣ produces a word’s “stem” ! ‣ am ➞ am ‣ the going ➞ the go ‣ having ➞ hav ! ‣ fast and simple (pattern-based) ‣ Snowball; Lovins; Porter ! • Lemmatization ‣ produced by “lemmatizers” ‣ produces a word’s “lemma” ! ‣ am ➞ be ‣ the going ➞ the going ‣ having ➞ have ! ‣ requires: a dictionary and PoS ‣ LemmaGen; morpha; BioLemmatizer; geniatagger 24 ➡ token normalization a.k.a. token “regularization” (although that is technically the wrong wording)
  26. 26. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining PoS tagging and lemmatization for
 Named Entity Recognition (NER) 25 Token PoS Lemma NER Constitutive JJ constitutive O binding NN binding O to TO to O the DT the O peri-! NN peri-kappa B-DNA B NN B I-DNA site NN site I-DNA is VBZ be O seen VBN see O in IN in O monocytes NNS monocyte B-cell . . . O de facto standard
 PoS tagset {NN, JJ, DT, VBZ, …} Penn Treebank B-I-O chunk encoding common alternatives: I-O I-E-O B-I-E-W-O End token (unigram) Word Begin-Inside-Outside (relevant) token } chunk noun-phrase (chunk) N.B.: This is all supervised (i.e., manually annotated corpora)!
  27. 27. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String matching with regular expressions ‣ /^[^@]{1,64}@w(?:[w.-]{0,254}w)?.w{2,}$/ • (provided w has Unicode support) • http://ex-parrot.com/~pdw/Mail-RFC822-Address.html ! ‣ username@server.domain.tld ‣ florian.leitner@upm.es ‣ 123$%&-@dfa-asdf.asdf-123.wow 26 delimiters - like “quotes” in strings
 (will be omitted for clarity)
  28. 28. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Regular expressions
 quick reference 1/2 • String literals abc… ‣ abc → axc abc xca • Wild card . (any character) ‣ a.c → axc abc xca • Start ^ or end $ of string ‣ ^a.c → axc abc xca ‣ bc$ → axc abc xca ! • Word boundaries b ‣ bxc → axc abc xca ‣ bcb → axc abc xca • Character choice […] ‣ [ax][xbc][ac] →
 axc abc xca • Negations [^…] (“not”) ‣ [ax][^b][^xb] →
 axc abc xca 27 no match: …bc not at end of string (compare with word boundaries!)
  29. 29. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Regular expressions quick reference 2/2 • Groups (can be referenced for repetitions and substitutions): ‣ (…) and (…)(…)12 ‣ a(bc)1 → ac abc abcbc abcbcbc • Pattern repetitions ‣ ? “zero or one”; * “zero or more”; + “one or more”: ‣ a(bc)?d → ad abc abcd abcbcd abcbcbcd
 a(bc)*d → ad abc abcd abcbcd abcbcbcd
 a(bc)+d → ad abc abcd abcbcd abcbcbcd • Counted pattern repetitions ‣ {n} “exactly n times”, {n,} “n or more times”, {n,m} “n to m times” ‣ a(b){2}c → ac abc abbd abbbc
 ab{2,}c → ac abc abbd abbbc
 ab{0,2}c → ac abc abbd abbbc 28
  30. 30. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining An overview of free open source NLP frameworks • General Architecture for Text Engineering ‣ GATE - Java • Stanford NLP Framework ‣ CoreNLP - Java • Apache OpenNLP Framework ‣ OpenNLP (& OpenNER) - Java • Unstructured Information Management Architecture ‣ UIMA - Java • Natural Language ToolKit ‣ NLTK - Python • FreeLing NLP Suite ‣ FreeLing - C++ • The Lemur Toolkit ‣ Lemur - C++ • The Bow Toolkit ‣ Bow - C (language modeling) • Factorie Toolkit ‣ Factorie - Scala 29
  31. 31. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Sentence segmentation • Sentences are the fundamental linguistic unit ‣ Sentences are the boundaries or “constraints” for linguistic phenomena. ‣ Collocations [“United Kingdom”, “vice president”], idioms [“drop me a line”], phrases [PP: “of great fame”], clauses, statements, … all occur within a sentence. • Rule/pattern-based segmentation ‣ Segment sentences if the marker is followed by an upper-case letter ‣ Works well for “clean text” (news articles, books, papers, …) ‣ Special cases: abbreviations, digits, lower-case proper nouns (genes, “amnesty international”, …), hyphens, quotation marks, … • Supervised sentence boundary detection ‣ Use some Markov model or a conditional random field to identify possible sentence segmentation tokens ‣ Requires labeled examples (segmented sentences) 31
  32. 32. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Punkt Sentence Tokenizer (PST) 1/2 • Unsupervised sentence boundary detection • P(●|w-1) > ccpc • Determines if a marker ● is used as an abbreviation marker by comparing the conditional probability that the word w-1 before ● is followed by the marker against some (high) cutoff probability. ‣ P(●|w-1) = P(w-1, ●) ÷ P(w-1) ‣ K&S set c = 0.99 • P(w+1|w-1) > P(w+1) • Evaluates the likelihood that w-1 and w+1 surrounding the marker ● are more commonly collocated than would be expected by chance: ● is assumed an abbreviation marker (“not independent”) if the LHS is greater than the RHS. • Flength(w)×Fmarkers(w)×Fpenalty(w) ≥ cabbr • Evaluates if any of w’s morphology (length of w w/o marker characters, number of periods inside w (e.g., [“U.S.A”]), penalized when w is not followed by a ●) makes it more likely that w is an abbreviation against some (low) cutoff. • Fortho(w); Psstarter(w+1|●); … • Orthography: lower-, upper-case or capitalized word after a probable ● or not • Sentence Starter: Probability that w is found after a ● 32 Dr. Mrs. Watson U.S.A. . Therefore
  33. 33. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Punkt Sentence Tokenizer (PST) 2/2 • Unsupervised Multilingual Sentence Boundary Detection ‣ Kiss & Strunk, MIT Press 2006. ‣ Available from NLTK: nltk.tokenize.punkt (http:// www.nltk.org/api/nltk.tokenize.html) • PST is language agnostic ‣ Requires that the language uses the sentence segmentation marker as an abbreviation marker ‣ Otherwise, the problem PST solves is not present ! ! • PST factors in word length ‣ Abbreviations are relatively shorter than regular words • PST takes “internal” markers into account ‣ E.g., “U.S.A” • Main weakness: long lists of abbreviations ‣ E.g., author lists in citations ‣ Can be fixed with a pattern-based post- processing strategy • NB: a marker must be present ‣ E.g., chats or fora 33
  34. 34. Text Mining 2 Language Modeling ! Madrid Summer School on Advanced Statistics and Data Mining ! Florian Leitner florian.leitner@upm.es License:
  35. 35. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Motivation for statistical models of language Two sentences: “Colorless green ideas sleep furiously.” (from Noam Chomsky’s 1955 thesis) “Furiously ideas green sleep colorless.” Which one is (grammatically) correct? ! An unfinished sentence: “Adam went jogging with his …” What is a correct phrase to complete this sentence? 35
  36. 36. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Incentive and applications ! • Manual rule-based language processing would become cumbersome. • Word frequencies (probabilities) are easy to measure, because large amounts of texts are available to us. • Modeling language based on probabilities enables many existing applications: ‣ Spelling correction ‣ Machine translation ‣ Voice recognition ‣ Predictive keyboards ‣ Langauge generation ‣ Linguistic parsing & chunking • (analyses of the part-of-speech and grammatical structure of sentences; word semantics) 36
  37. 37. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Probabilistic language modeling ‣ Manning & Schütze. Statistical Natural Language Processing. 1999 • A sentence W is defined as a sequence of words w1, …, wn • Probability of next word wn in a sentence is: P(wn |w1, …, wn-1) ‣ a conditional probability • The probability of the whole sentence is: P(W) = P(w1, …, wn) ‣ the chain rule of conditional probability • These counts & probabilities form the language model
 [for a given document collection (=corpus)]. ‣ the model variables are discrete (counts) ‣ only needs to deal with probability mass (not density) 37
  38. 38. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Modeling the stochastic process of “generating words” using the chain rule “This is a long sentence with many words…” ➡ P(W) = P(this) × P(is | this) × P(a | this, is) × P(long | this, is, a) × P(sentence | this, is, a, long) × P(with | this, is, a, long, sentence) × P(many | this, is, a, long, sentence, with) × …. 38 n-grams for n > 5: insufficient (sparse) data (and expensive to calculate)
  39. 39. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Markov property A Markov process is a stochastic process who’s future (next) state only depends on the current state S, but not its past. 39 S1 S2S3 a token (i.e., any word, symbol, …) in S transitions with likelihood of that (next) token given the current token 3 word (S1,2,3) bigram model
  40. 40. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Modeling the stochastic process of “generating words” assuming it is Markovian ! ! • 1st Order Markov Chains ‣ Bigram Model, k=1, P(be | this) • 2nd Order Markov Chains ‣ Trigram Model, k=2, P(long | this, be) • 3rd Order Markov Chains ‣ Quadrigram Model, k=3,
 P(sentence | this, be, long) • … 40 Ti−0Ti−1 Ti−0Ti−1Ti−2Ti−3 Ti−0Ti−1Ti−2 dependencies could span over a dozen tokens, but these sizes are generally sufficient to work by Y P(wi|wi 1 1 ) ⇡ Y P(wi|wi 1 i k) Ti stochastic process: Unigram “model” NB: these are the Dynamic Bayesian Network representations of the Markov Chains (see lesson 5)
  41. 41. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining • Unigrams: • Bigrams: • N-grams (n=k+1): Calculating n-gram probabilities 41 P(wi|wi 1) = count(wi 1, wi) count(wi 1) P(wi) = count(wi) N N = total word count P(wi|wi 1 i k) = count(wi i k) count(wi 1 i k) k = n-gram size - 1 ‣ Language Model: Practical tip: transform probabilities to logs to avoid underflows and work with addition P(W) = Y P(wi|wi 1 i k) = = Y P(wi|wi k, ...wi 1)
  42. 42. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Calculating probabilities for the initial tokens • How to calculate the first/last [few] tokens in n-gram models? ‣ “This is a sentence.” ➡ P(this | ???) ‣ P(wn|wn-k, …, wn-1) • Fall back to lower-order Markov models ‣ P(w1|wn-k,…,wn-1) = P(w1); P(w2|wn-k,…,wn-1) = P(w2|w1); … • Fill positions prior to n = 1 with a generic “start token”. ‣ left and/or right padding ‣ conventionally, a strings like “<s>” and “</s>”, “*”, or “·” are used
 (but anything will do, as long as it cannot collide with a possible, real token) 42 NB: it is important to maintain sentence terminal tokens (., ?, !) to generate robust probability distributions; do not drop them!
  43. 43. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The inverted index 43 Text 1: He that not wills to the end neither wills to the means. Text 2: If the mountain will not go to Moses, then Moses must go to the mountain. tokens Text 1 Text 2 end 1 0 go 0 2 he 1 0 if 0 1 means 1 0 Moses 0 2 mountain 0 2 must 0 1 not 1 1 that 1 0 the 2 2 then 0 1 to 2 2 will 2 1 unigrams T1 1 T2 p(T1) p(T2) end 1 0 0.09 0.00 go 0 2 0.00 0.13 he 1 0 0.09 0.00 if 0 1 0.00 0.07 means 1 0 0.09 0.00 Moses 0 2 0.00 0.13 mountain 0 2 0.00 0.13 must 0 1 0.00 0.07 not 1 1 0.09 0.07 that 1 0 0.09 0.00 the 2 2 0.18 0.13 then 0 1 0.00 0.07 to 2 2 0.18 0.13 will 2 1 0.18 0.07 SUM 11 15 1.00 1.00 bigrams Text 1 Text 2 end, neither 1 0 go, to 0 2 he, that 1 0 if, the 0 1 Moses, must 0 1 Moses, then 0 1 mountain, will 0 1 must, go 0 1 not, go 0 1 not, will 1 0 that, not 1 0 the, means 1 0 the, mountain 0 2 then, Moses 0 1 to, Moses 0 1 to, the 2 1 will, not 0 1 will, to 2 0 factors, normalization (len[text]), probabilities, and n-grams REMINDER
  44. 44. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Unseen n-grams and the zero probability issue • Even for unigrams, unseen words will occur sooner or later • The longer the n-grams, the sooner unseen cases will occur • “Colorless green ideas sleep furiously.” (Chomsky, 1955) • As unseen tokens have zero probability, the probability of the whole sentence P(W) = 0 would become zero, too ! ‣ Intuition/idea: Divert a bit of the overall probability mass of each [seen] token to all possible unseen tokens • Terminology: model smoothing (Chen & Goodman, 1998) 44
  45. 45. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Additive (Lidstone) and Laplace smoothing • Add a smoothing factor α to all n-gram counts: ! ! • V is the size of the vocabulary ‣ the number of unique words in the training corpus • α ≤ 1 usually; if α =1, it is known as Add-One Smoothing • Very old: first suggested by Pierre-Simon Laplace in 1816 • But it performs poorly (compared to “modern” approaches) ‣ Gale & Church, 1994 45 P(wi|wi 1 i k) = count(wi i k) + ↵ count(wi 1 i k) + ↵V
  46. 46. Neural network models of language 46 Log-linear nodes; Training: SGD with backpropagation Input layer size: log2 V Projection layer: N ∙ D Output layer: N ∙ log2 V Input layer size: N ∙ log2 V (200) Projection layer: N ∙ D (500-20k) Output layer size: log2 V (20) N - window size (typically 10) D - projection dimensionality (50-1000) V - vocabulary size (1M unique tokens) [log2: represented as Huffmann binary tree] “generative mode” ! predict next word “descriminative mode”
 predict a word’s surrounding Trained on corpora for 40M to 6B tokens (in 300 CPU-days) word2vec - Thomas Mikolov et al. - Google - 2013
  47. 47. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Statistical models of language and polysemy • Polysemous words have multiple meanings (e.g., “bank”). ‣ This is a real problem in scientific texts because polysemy is frequent. • One idea: Create context vectors for each sense of a word (vector). ‣ MSSG - Neelakantan et al. - 2015 • Caveat: Performance isn’t much better than for the skip-gram model by Mikolov et al., while training is ~5x slower. 47
  48. 48. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Neural embeddings: Applications in TM & NLP • Opinion mining (Maas et al., 2011) • Paraphrase detection (Socher et al., 2011) • Chunking (Turian et al., 2010; Dhillon and Ungar, 2011) • Named entity recognition (Neelakantan and Collins, 2014; Passos et al., 2014; Turian et al., 2010) • Dependency parsing (Bansal et al., 2014) 48
  49. 49. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Language model evaluation • How good is the model you just trained? • Did your update to the model do any good…? • Is your model better than someone else’s? ‣ NB: You should compare on the same test set! 49
  50. 50. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Extrinsic evaluation: Error rate • Extrinsic evaluation: minimizing the error rate ‣ evaluates a model’s error frequency ‣ estimates the model’s per-word error rate by comparing the generated sequences to all true sequences (which cannot be established) using a manual classification of errors (therefore, “extrinsic”) ‣ time consuming, but can evaluate non-probabilistic approaches, too 50 a “perfect prediction” would evaluate to zero
  51. 51. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Intrinsic evaluation: Cross-entropy • Intrinsic evaluation: minimizing perplexity (Rubinstein, 1997) ‣ Compares a model’s probability distribution to a “perfect” model ‣ Estimates a distance based on cross-entropy (Kullback-Leibler divergence; explained next) between the generated word distribution and the true distribution (which cannot be observed) using the empirical distribution as a proxy ‣ Efficient, but can only evaluate probabilistic language models and is only an approximation of the model quality 51 again, a “perfect prediction” would evaluate to zero perplexity: roughly, “confusion”
  52. 52. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining • Answers the questions: ‣ “How much information (bits) will I gain when I see wn?” ‣ “How predictable is wn from its past?” ! • Each outcome provides -log2 P bits of information (“surprise”). ‣ Claude E. Shannon, 1948 • The more probable an event (outcome), the lower its entropy. • A certain event (p=1 or 0) has zero entropy (“no surprise”). ! • Therefore, the entropy H in our model P for a sentence W is: ‣ H = 1/N × -∑ P(wn|w1, …, wn-1) log2 P(wn|w1, …, wn-1) Shannon entropy 52 H(X) = P(X)log2[P(X)] (1 P(X))log2[1 P(X)]Bernoulli process:
  53. 53. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining From cross-entropy to model perplexity • Cross-entropy then compares the model probability distribution P to the true distribution PT: ‣ H(PT, P, W) = 1/N × -∑ PT(wn|wn-k, …, wn-1) log2 P(wn|wn-k, …, wn-1) • CE can be simplified if the “true” distribution is a “stationary, ergodic process”: ‣ H(P, W) = 1/N × -∑ log2 P(wn|wn-k, …, wn-1) • Then, the relationship between perplexity PPX and cross- entropy is defined as: ‣ PPX(W) = 2H(P, W) = P(W)1/N • where W is the sentence, P(W) is the Markov model, and N is the number of tokens in it 53 (an “unchanging” language, i.e., a naïve assumption) our “surprise” for the observed sentence given the true model
  54. 54. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Interpreting perplexity • The lower the perplexity, the better the model (“less surprise”) • Perplexity is an indicator of the number of equiprobable choices at each step ‣ PPX = 26 for a model generating an infinite random sequence of Latin letters • An unigram Markov model having equal transition probabilities to each letter ‣ Perplexity produces “big numbers” rather than cross-entropy’s “small bits” • Typical (bigram) perplexities in English texts range from 50 to almost 1000 corresponding to a cross- entropy from about 5.6 to 10 bits/word. ‣ Chen & Goodman, 1998 ‣ Manning & Schütze, 1999 54
  55. 55. Text Mining 3 Text Similarity ! Madrid Summer School on Advanced Statistics and Data Mining ! Florian Leitner florian.leitner@upm.es License:
  56. 56. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Incentive and applications • Goals of string similarity matching: ‣ Detecting syntactically or semantically similar words ! • Grouping/clustering similar items ‣ Content-based recommender systems; plagiarism detection • Information retrieval ‣ Ranking/searching for [query-specific] documents • Entity grounding ‣ Recognizing entities from a collection of strings (a “gazetteer” or dictionary) 56
  57. 57. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining • Finding similarly spelled or misspelled words • Finding “similar” texts/documents ‣ N.B.: no semantics (yet…) • Detecting entries in a gazetteer ‣ a list of domain-specific words • Detecting entities in a dictionary ‣ a list of words, each mapped to some URI ‣ N.B.: “entities”, not “concepts” (no semantics…) String matching 57
  58. 58. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Jaccard’s set similarity
 (Jaccard’s sim. coeff.) 58 “words” “woody” w o r s d y J(A, B) = |A B| |A [ B| = 3 7 = 0.43 vs o
  59. 59. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Jaccard’s set similarity
 (Jaccard’s sim. coeff.) 58 “words” “woody” w o r s d y J(A, B) = |A B| |A [ B| = 3 7 = 0.43 vs o 6 o.5 ABC vs. ABCABCABC
  60. 60. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String similarity measures • Edit Distance Measures ‣ Hamming Distance [1950] ‣ Levenshtein-Damerau Distance [1964/5] ‣ Needelman-Wunsch [1970] and
 Smith-Waterman [1981] Distance • also align the strings (“sequence alignment”) • use dynamic programming • Modern approaches: BLAST [1990], BWT [1994] • Other Similarity Metrics ‣ Jaro-Winkler Similarity [1989/90] • coefficient of matching characters within a dynamic window minus transpositions ‣ Soundex (➞ homophones; spelling!) ‣ … • Basic Operations: “indels” ‣ Insertions • ac ➞ abc ‣ Deletions • abc ➞ ac ! • “Advanced” Operations ‣ Require two “indels” ‣ Substitutions • abc ➞ aBc ‣ Transpositions • ab ➞ ba 59
  61. 61. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef 60
  62. 62. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 60
  63. 63. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 • Damerau-Levenshtein D. ‣ also allows transpositions ‣ has quadratic complexity ‣ karlo ⬌ carol = 2 ‣ karlos ⬌ carol = 3 60
  64. 64. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 • Damerau-Levenshtein D. ‣ also allows transpositions ‣ has quadratic complexity ‣ karlo ⬌ carol = 2 ‣ karlos ⬌ carol = 3 60 typos!
  65. 65. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 • Damerau-Levenshtein D. ‣ also allows transpositions ‣ has quadratic complexity ‣ karlo ⬌ carol = 2 ‣ karlos ⬌ carol = 3 • Jaro Similarity (a, b) ‣ calculates (m/|a| + m/|b| + (m-t)/m) / 3 ‣ 1. m, the # of matching characters ‣ 2. t, the # of transpositions ‣ window: !max(|a|, |b|) / 2" - 1 chars ‣ karlos ⬌ carol = 0.74 ‣ (4 ÷ 6 + 4 ÷ 5 + 3 ÷ 4) ÷ 3 60 typos!
  66. 66. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 • Damerau-Levenshtein D. ‣ also allows transpositions ‣ has quadratic complexity ‣ karlo ⬌ carol = 2 ‣ karlos ⬌ carol = 3 • Jaro Similarity (a, b) ‣ calculates (m/|a| + m/|b| + (m-t)/m) / 3 ‣ 1. m, the # of matching characters ‣ 2. t, the # of transpositions ‣ window: !max(|a|, |b|) / 2" - 1 chars ‣ karlos ⬌ carol = 0.74 ‣ (4 ÷ 6 + 4 ÷ 5 + 3 ÷ 4) ÷ 3 60 [0,1] range typos!
  67. 67. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining String distance measures • Hamming Distance ‣ only counts substitutions ‣ requires equal string lengths ‣ karolin ⬌ kathrin = 3 ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = undef • Levenshtein Distance ‣ counts all but transpositions ‣ karlo ⬌ carol = 3 ‣ karlos ⬌ carol = 4 • Damerau-Levenshtein D. ‣ also allows transpositions ‣ has quadratic complexity ‣ karlo ⬌ carol = 2 ‣ karlos ⬌ carol = 3 • Jaro Similarity (a, b) ‣ calculates (m/|a| + m/|b| + (m-t)/m) / 3 ‣ 1. m, the # of matching characters ‣ 2. t, the # of transpositions ‣ window: !max(|a|, |b|) / 2" - 1 chars ‣ karlos ⬌ carol = 0.74 ‣ (4 ÷ 6 + 4 ÷ 5 + 3 ÷ 4) ÷ 3 • Jaro-Winkler Similarity ‣ adds a bonus for matching prefixes 60 [0,1] range typos!
  68. 68. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Gazetteers:
 Dictionary matching • Finding all tokens that match the entries ‣ hash table lookups: constant complexity - O(1) • Exact, single token matches ‣ regular hash table lookup (e.g., MURMUR3) • Exact, multiple tokens ‣ prefix tree of hash tables (each node being a token) • Approximate, single tokens ‣ use some string metric - but do not compare all n-to-m cases… • Approximate, multiple tokens ‣ a prefix tree of whatever the single token lookup strategy… 61 LSH (next) hash table hash table hash table default/traditional approach: character n-gram similarity (e/g. databases)
  69. 69. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Locality Sensitive Hashing (LSH) 1/2 • A hashing approach to group near neighbors. • Map similar items into the same [hash] buckets. • LSH “maximizes” (instead of minimizing) hash collisions. • It is another dimensionality reduction technique. • For documents, texts or words, minhashing can be used. ‣ Approach from Rajaraman & Ullman, Mining of Massive Datasets, 2010 • http://infolab.stanford.edu/~ullman/mmds/ch3a.pdf 62
  70. 70. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Locality Sensitive Hashing (LSH) 2/2 63 M Vogiatzis. micvog.com 2013.
  71. 71. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Minhash signatures (1/2) 65 shingleorn-gramID Create character n-gram × token or word k-shingle × document matrix (likely very sparse!) Lemma: Two texts will have the same first “true” shingle/n-gram when looking from top to bottom with a probability equal to their Jaccard (Set) Similarity. ! Idea: Create sufficient permutations of the row (shingle/n-gram) ordering so that the Jaccard Similarity can be approximated by comparing the number of coinciding vs. differing rows. 0 1 2 3 4 T T F F T F T F F T F F T F T F T T T T F T T F h 1 2 3 4 0 h 1 4 2 0 3 a family of hash functions hi h1(x) = (x+1)%n ! h2(x) = (3x+1)%n ! n=5 T: shingle/n-gram in Ti F: shingle/n-gram not in Ti “permuted” row IDs
  72. 72. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Locality Sensitive Hashing (LSH) 2/2 66 M Vogiatzis. micvog.com 2013.
  73. 73. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Minhash signatures (2/2) 67 shingleorn-gramID S T T T T h h 0 T F F T 1 1 1 F F T F 2 4 2 F T F T 3 2 3 T F T T 4 0 4 F F T F 0 3 h1(x) = (x+1)%n ! h2(x) = (3x+1)%n ! n=5 M T T T T h ∞ ∞ ∞ ∞ h ∞ ∞ ∞ ∞ init matrix M = ∞ for each shingle c, hash h, and text t: if S[t,c] and M[t,h] > h(c): M[t,h] = h(c) perfectly map-reduce-able and embarrassingly parallel!
  74. 74. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Minhash signatures (2/2) 67 shingleorn-gramID S T T T T h h 0 T F F T 1 1 1 F F T F 2 4 2 F T F T 3 2 3 T F T T 4 0 4 F F T F 0 3 h1(x) = (x+1)%n ! h2(x) = (3x+1)%n ! n=5 M T T T T h ∞ ∞ ∞ ∞ h ∞ ∞ ∞ ∞ init matrix M = ∞ for each shingle c, hash h, and text t: if S[t,c] and M[t,h] > h(c): M[t,h] = h(c) perfectly map-reduce-able and embarrassingly parallel! c=0 T T T T h ∞ ∞ ∞ ∞ h ∞ ∞ ∞ ∞ c=1 T T T T h 1 ∞ ∞ 1 h 1 ∞ ∞ 1
  75. 75. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Minhash signatures (2/2) 67 shingleorn-gramID S T T T T h h 0 T F F T 1 1 1 F F T F 2 4 2 F T F T 3 2 3 T F T T 4 0 4 F F T F 0 3 h1(x) = (x+1)%n ! h2(x) = (3x+1)%n ! n=5 M T T T T h ∞ ∞ ∞ ∞ h ∞ ∞ ∞ ∞ init matrix M = ∞ for each shingle c, hash h, and text t: if S[t,c] and M[t,h] > h(c): M[t,h] = h(c) perfectly map-reduce-able and embarrassingly parallel! c=0 T T T T h ∞ ∞ ∞ ∞ h ∞ ∞ ∞ ∞ c=1 T T T T h 1 ∞ ∞ 1 h 1 ∞ ∞ 1 c=2 T T T T h 1 ∞ 2 1 h 1 ∞ 4 1 c=3 T T T T h 1 3 2 1 h 1 2 4 1 c=4 T T T T h 1 3 2 1 h 0 2 0 0 M T T T T h 1 3 0 1 h 0 2 0 0
  76. 76. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Locality Sensitive Hashing (LSH) 2/2 68 M Vogiatzis. micvog.com 2013.
  77. 77. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining T T T T T T T T … h 1 0 2 1 7 1 4 5 h 1 2 4 1 6 5 5 6 h 0 5 6 0 6 4 7 9 h 4 0 8 8 7 6 5 7 h 7 7 0 8 3 8 7 3 h 8 9 0 7 2 4 8 2 h 8 5 4 0 9 8 4 7 h 9 4 3 9 0 8 3 9 h 8 5 8 0 0 6 8 0 … Banded locality sensitive minhashing 69 T T T T T T T T … h 1 0 2 1 7 1 4 5 h 1 2 4 1 6 5 5 6 h 0 5 6 0 6 4 7 9 h 4 0 8 8 7 6 5 7 h 7 7 0 8 3 8 7 3 h 8 9 0 7 2 4 8 2 h 8 5 4 0 9 8 4 7 h 9 4 3 9 0 8 3 9 h 8 5 8 0 0 6 8 0 … Bands 1 2 3 … Bands b ∝ pagreement Hashes/Band r ∝ 1/pagreement pagreement = 1 - (1 - sr )b s = Jaccard(A,B) (in at least one band) typical: r=10, b=30
  78. 78. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Document similarity • Similarity measures ✓Cosine similarity (of document/text vectors) ‣ Correlation coefficients • Word vector normalization ‣ TF-IDF • Dimensionality Reduction/Clustering ✓Locality Sensitivity Hashing ‣ Latent semantic indexing ‣ Latent Dirichlet allocation (tomorrow) 70
  79. 79. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Word vectors 71 0 1 2 3 4 5 6 7 8 9 10 10 0 1 2 3 4 5 6 7 8 9 count(Word1) count(Word2) Text1 Text2 α γ β Similarity(T1 , T2 ) := cos(T1 , T2 ) count(Word3 ) Comparing word vectors: Cosine similarity Collections of vectorized texts: Inverted index Text 1: He that not wills to the end neither wills to the means. Text 2: If the mountain will not go to Moses, then Moses must go to the mountain. tokens Text 1 Text 2 end 1 0 go 0 2 he 1 0 if 0 1 means 1 0 Moses 0 2 mountain 0 2 must 0 1 not 1 1 that 1 0 the 2 2 then 0 1 to 2 2 will 2 1 INDRI eachtoken/word isadimension! wordvector wordvector REMINDER
  80. 80. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Cosine similarity • Define a similarity score between two document vectors
 (or the query vector in Information Retrieval) • Euclidian vector distance is length dependent • The cosine [angle] between two vectors is not 72 sim(~x, ~y) = cos(~x, ~y) = ~x · ~y |~x||~y| = P xiyi pP x2 i pP y2 i sim(~x, ~y) = cos(~x, ~y) = ~x · ~y |~x||~y| = P xiyi pP x2 i pP y2 i can be dropped if using unit vectors (“length-normalized” a.k.a. “cosine normalization”) only dot-product is now left: extremely efficient ways to compute
  81. 81. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Alternative similarity coefficients • Spearman’s rank correlation coefficient ρ (r[ho]) ‣ Ranking is done by term frequency (TF; count) ‣ Critique: sensitive to ranking differences that are likely to occur with high- frequency words (e.g., “the”, “a”, …) ➡ use the log of the term count, rounded to two significant digits • NB that this is not relevant when only short documents (e.g. titles) with low TF counts are compared • Pearson’s chi-square test χ2 ‣ Directly on the TFs (counts) - intuition:
 Are the TFs “random samples” from the same base distribution? ‣ Usually, χ2 should be preferred over ρ (Kilgarriff & Rose, 1998) • NB that both measures have no inherent normalization of document size ‣ preprocessing might be necessary! 73
  82. 82. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Term Frequency times Inverse Document Frequency (TF-IDF) • Motivation and background • The problem ‣ Frequent terms contribute most to a document vector’s direction, but not all terms are relevant (“the”, “a”, …). • The goal ‣ Separate important terms from frequent, but irrelevant terms in the collection. • The idea ‣ Frequent terms appearing in all documents tend to be less important versus frequent terms in just a few documents. • Also dampens the effect of topic-specific noun phrases or an author’s bias for a specific set of adjectives 74 Zipf’s Law!
  83. 83. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Term Frequency times Inverse Document Frequency (TF-IDF) ‣ tf.idf(w) := tf(w) × idf(w) • tf: (document-specific) term frequency • idf: inverse (global) document frequency ! ! ‣ tfnatural(w) := count(w) • tfnatural: n. of times term w occurs in a document ‣ tflog(w) := log(count(w) + 1) • tflog: the TF is smoothed by taking its log ! ! ! ! ! ‣ idfnatural(w) := N / ∑N {wi > 0} • idfnatural: n. documents divided by n. documents in which term w occurs ‣ idflog(w) := log(N / ∑N {wi > 0}) • idflog: the IDF is smoothed by taking its log • where N is the number of documents,
 wi the count of word w in document i, and {wi>0} is 1 if document i has word w or 0 otherwise 75
  84. 84. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining TF-IDF in
 information retrieval • Document vectors = tflog • Query vector = tflog idflog ‣ Terms are counted on each individual document & the query • Cosine vector length normalization for TF-IDF scores: ‣ Document W normalization ! ‣ Query Q normalization ! • IDF is calculated over the indexed collection of all documents 76 i.e. the DVs do not use any IDF weighting (simply for efficiency: QV already has IDF
 that gets multiplied with DV values) s X w2W tflog(w)2 sX q2Q (tflog(q) ⇥ idflog(q))2
  85. 85. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining TF-IDF query score:
 An example 77 Collection Query Q Document D Similarity Term df idf tf tf tf.idf norm tf tf tf.1 cos(Q,D) best 3.5E+05 1.46 1 0.30 0.44 0.21 0 0.00 0.00 0.00 text 2.4E+03 3.62 1 0.30 1.09 0.53 10 1.04 0.06 0.03 mining 2.8E+02 4.55 1 0.30 1.37 0.67 8 0.95 0.06 0.04 tutorial 5.5E+03 3.26 1 0.30 0.98 0.48 3 0.60 0.04 0.02 data 9.2E+05 1.04 0 0.00 0.00 0.00 10 1.04 0.06 0.00 … … … … ! … ! 0.00 0.00 … ! 16.00 … ! 0.00 Sums 1.0E+07 4 2.05 ~355 16.11 0.09 3 out of hundreds of unique words match (Jaccard < 0.03) √ of ∑ of 2 Example idea from: Manning et al. Introduction to Information Retrieval. 2009 free PDF! √ of ∑ of 2 ÷÷ × ×
  86. 86. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining From syntactic to
 semantic similarity Cosine Similarity, χ2 , Spearman’s ρ, LSH, etc. all compare equal tokens. But what if you are talking about “automobiles” and I am lazy, calling it a “car”? We can solve this with Latent Semantic Indexing! 78
  87. 87. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Semantic Analysis (LSI 1/3) • a.k.a. Latent Semantic Indexing (in Text Mining):
 dimensionality reduction for semantic inference • Linear algebra background ‣ Singular value decomposition of a matrix Q: Q = UΣVT ! ! ! ! ! • SVD in text mining ‣ Inverted index = doc. eigenvectors × singular values × term eigenvectors 79 singular values:
 scaling factor orthonormal factors of Q (QQT and QT Q) the factors “predict” Q in terms of similarity (Frobenius
 norm) using as many factors as the lower dimension of Q Q P1 P2 P3 G1 G2 G3 G4 P1 P2 P3Players U G1 G2 G3 G4 Â Â’ Â’’ Games avrggamescore player ability avrgscore
 deltas player ability deltas = × S S S scaling factors ! ! ! ! (U and V are eigenvectors) ×
  88. 88. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Semantic Analysis (LSI 2/3) • Image taken from: Manning et al. An Introduction to IR. 2009 80 ‣ Inverted index = doc. eigenvectors × singular values × term eigenvectors docs terms
  89. 89. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Semantic Analysis (LSI 2/3) • Image taken from: Manning et al. An Introduction to IR. 2009 80 ‣ Inverted index = doc. eigenvectors × singular values × term eigenvectors docs terms C = DimRed by selecting only the largest n eigenvaluesˆ
  90. 90. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Semantic Analysis (LSI 3/3) 81 From: Landauer et al. An Introduction to LSA. 1998 C Cˆ top 2 dim [Spearman’s] rho(human, user) = -0.38 rho(human, minors) = -0.29 rho(human, user) = 0.94 rho(human, minors) = -0.83 test # dim to use via synonyms or missing words
  91. 91. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Principal Component vs. Latent Semantic Analysis • LSA seeks for the best linear subspace in Frobenius norm, while PCA aims for the best affine linear subspace. • LSA (can) use TF-IDF weighting as preprocessing step. • PCA requires the (square) covariance matrix of the original matrix as its first step and therefore can only compute term-term or doc-doc similarities. • PCA matrices are more dense (zeros occur only when true independence is detected). 82 best Frobenius norm: minimize “std. dev.” of matrix best affine subspace: minimize dimensions while maintaing the form
  92. 92. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining From similarity to labels • So far, we have seen how to establish if two documents are syntactically (kNN/LSH) and even semantically (LSI) similar. ! • But how do we now assign a label (a “class”) to a document? ‣ E.g., relevant/not relevant; polarity (positive, neutral, negative);
 a topic (politics, sport, people, science, healthcare, …) ‣ We could use the distances (e.g., from LSI) to cluster the documents ‣ Instead, let’s look at supervised methods next. 83
  93. 93. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Text classification approaches • Multinomial naïve Bayes* • Nearest neighbor classification (ASDM Course) ‣ incl. locality sensitivity hashing* (already seen) • Latent semantic indexing* (already seen) • Cluster analysis (ASDM Course) • Maximum entropy classification* • Latent Dirichlet allocation* • Random forests • Support vector machines (ASDM Course) • Artificial neural networks (ASDM Course) 84 efficient/fasttraininghighaccuracy * this course
  94. 94. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Three text classifiers • Multinomial naïve Bayes • Maximum entropy (multinomial logistic regression) • Latent Dirichlet allocation unsupervised! 85
  95. 95. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum A Posterior (MAP) estimator • Issue: Predict the class c ∈ C for a given document d ∈ D • Solution: MAP, a “perfect” Bayesian estimator: ! ! ! • Problem: d is really the set {w1, …, wn} of dependent words W ‣ exponential parameterization: one for each possible combination of W and C 86 CMAP (d) = argmax c2C P(c|d) = argmax c2C P(d|c)P(c) P(d) redundantthe posterior
  96. 96. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Multinomial naïve Bayes classification • A simplification of the MAP Estimator ‣ count(w) is a discrete, multinomial variable (unigrams, bigrams, etc.) ‣ Reduce space by making a strong independence assumption (“naïve”) ! ! • Easy parameter estimation ! ! ‣ V is the entire vocabulary (collection of unique words/n-grams/…) in D ‣ uses Laplacian/add-one smoothing 87 independence assumption: “each word is on its own” “bag of words/features” ˆP(wi|c) = count(wi, c) + 1 |V | + P w2V count(w, c) CMAP (d) = argmax c2C P(d|c)P(c) ⇡ argmax c2C P(c) Y w2W P(w|c) count(wi, c): the total count of word i in all documents of class c [in our training set]
  97. 97. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Multinomial naïve Bayes: Practical aspects • Can gracefully handle unseen words • Has low space requirements: |V| + |C| floats • Irrelevant (“stop”) words cancel each other out • Opposed to SVM or Nearest Neighbor, it is very fast ‣ (Locality Sensitivity Hashing was another very efficient approach we saw) ‣ But fast approaches tend to result in lower accuracies (➡ good “baselines”) • Each class has its own n-gram language model • Logarithmic damping (log(count)) might improve classification 88 sum ∏ using logs! ˆP(wi|c) = log(count(wi, c) + 1) log(|V | + P w2V count(w, c))
  98. 98. Text Mining 4 Text Classification ! Madrid Summer School on Advanced Statistics and Data Mining ! Florian Leitner florian.leitner@upm.es License:
  99. 99. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Incentive and applications • Assign one or more “labels” to a collection of “texts”. ! • Spam filtering • Marketing and politics (opinion mining) • Topic clustering • … 90
  100. 100. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Generative vs. discriminative models • Generative models describe how the [hidden] labels “generated” the [observed] input as joint probabilities: P(class, data) ‣ They learn the distributions of each individual class. ‣ Examples: Markov Chain, Naïve Bayes, Latent Dirichlet Allocation, Hidden Markov Model, … ‣ Graphical models for detecting outliers or when there is a need to update models (change) • Discriminative models predict (“discriminate”) the [hidden] labels conditioned on the [observed] input: P(class | data) ‣ They (“only”) learn the boundaries between classes. ‣ Ex.: Logistic Regression, Support Vector Machine, Conditional Random Field, Random Forest, … • Both can identify the most likely labels and their likelihoods • Only generative models: ‣ Most likely input value[s] and their likelihood[s] ‣ Likelihood of input value[s] for some particular label[s] 91 D D C D D D C D P(H|D) = P(H) ⇥ P(D|H) P(D)
  101. 101. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum entropy (MaxEnt) intuition 92 go to up outside home out { w ∈W ∑ w∈ W P(w |go)= 1 1/5 1/5 1/5 1/5 1/5 The principle of maximum entropy Observations: 1/6 1/6 1/6 1/4 1/4 P(out|go)+ P(hom e|go)= 0.5 ?? ?? ?? ?? ?? P(to |go)+ P(hom e|go)= 0.75
  102. 102. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Supervised MaxEnt classification • a.k.a. multinomial logistic regression • Does not assume independence between the features • Can model mixtures of binary, discrete, and real features • Training data are per-feature-label probabilities: P(F, L) ‣ I.e., count(fi, li) ÷ ∑N i=1 count(fi, li) ➡ words → very sparse training data (zero or few examples) • Model parameters are commonly learned using gradient descent ‣ Expensive if compared to Naïve Bayes, but efficient optimizers exist (L-BFGS) 93 logistic function p p(x) = 1 1 + exp( ( 0 + 1x)) ln p(x) 1 p(x) = 0 + 1x p(x) 1 p(x) = exp( 0 + 1x)odds-ratio! ln e Image Source: WikiMedia Commons, Qef
  103. 103. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Example feature functions for MaxEnt classifiers • Examples of indicator functions (a.k.a. feature functions) ‣ Assume we wish to classify the general polarity (positive, negative) of product reviews: • f(c, w) := {c = POSITIVE ∧ w = “great”} ‣ Equally, for classifying words in a text, say to detect proper names, we could create a feature: • f(c, w) := {c = NAME ∧ isCapitalized(w)} • Note that while we can have multiple classes, we cannot require more than one class in the whole match condition of a single indicator (feature) function. 94 NB: typical text mining models can have a million or more features: unigrams + bigrams + trigrams + counts + dictionary matchs + …
  104. 104. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximizing the
 conditional entropy • The conditioned (on X) version of Shannon’s entropy H: ! ! ! ! ! • MaxEnt training then is about selecting the model p* that maximizes H: 95 H(Y |X) = X x2X P(x) H(Y |X = x) = X x2X P(x) X y2Y P(y|x) log2 P(y|x) = X x,y2X,Y P(x, y) log2 P(x) P(x, y) (swapped nom/denom to remove the minus) p⇤ = argmax p2P H(P) = argmax p2P H(Y |X) P(x, y) = P(x) P(y|x) NB: the chain rule
  105. 105. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum entropy (MaxEnt 1/2) • Some definitions: ‣ The observed probability of y (the class) with x (the words) is: ! ‣ An indicator function (“feature”) is defined as a binary valued function that returns 1 iff class and data match the indicated requirements (constraints): ! ! ! ‣ The probability of a feature with respect to the observed distribution is: 96 f(x, y) = ( 1 if y = ci ^ x = wi 0 otherwise ˆP(x, y) = count(x, y) ÷ N ˆP(fi, X, Y ) = E ˆP [fi] = X ˆP(x, y)fi(x, y) real/discrete/binary features now are all the same!
  106. 106. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Getting lost? Reality check: • I have told you: ‣ MaxEnt is about maximizing “conditional entropy”: ‣ By multiplying binary (0/1) feature functions for observations with the joint (observation, class) probabilities, we can calculate the conditional probability of a class given its observations H(Y=y|X=x) • We will still have to do: ‣ Find weights (i.e., parameters) for each feature [function] that lead to the best model of the [observed] class probabilities. • And you want to know: ‣ How do we use all this to actually classify new input data? 97
  107. 107. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum entropy (MaxEnt 2/2) ‣ In a linear model, we’d use weights (“lambdas”) that identify the most relevant features of our model, i.e., we use the following MAP to select a class: ! ! ! ‣ To do multinomial logistic regression, expand with a linear combination: ! ! ! ‣ Next: Estimate the λ weights (parameters) that maximize the conditional likelihood of this logistic model (MLE) 98 “exponential model”argmax y2Y exp( P ifi(X, y)) P y2Y exp( P ifi(X, y)) argmax y2Y X ifi(X, y)
  108. 108. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum entropy (MaxEnt 2/2) ‣ In summary, MaxEnt is about selecting the “maximal” model p*: ! ! ! ‣ That obeys the following conditional equality constraint: ! ! ! ‣ Next: Using, e.g., Langrange multipliers, one can
 establish the optimal λ parameters of the model that
 maximize the entropy of this probability: 99 X x2X P(x) X y2Y P(y|x) f(x, y) = X x2X,y2Y P(x, y) f(x, y) p⇤ = argmax p2P X x2X p(x) X y2Y p(y|x) log2 p(y|x) …using a conditional model that matches the (observed) joint probabilities select some model that maximizes the conditional entropy… [again] Image Source: WikiMedia Commons, Nexcis p⇤ (y|X) = exp( P ifi(X, y)) P y2Y exp( P ifi(X, y))
  109. 109. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Newton’s method for paramter optimization • Problem: find the λ parameters ‣ an “optimization problem” • MaxEnt surface is concave ‣ one single maximum • Using Newton’s method ‣ iterative, hill-climbing search for max. ‣ the first derivative f´ is zero at the [global] maximum (the “goal”) ‣ the second derivative f´´ indicates rate of change: ∆λi (search direction) ‣ takes the most direct route to the maximum • Using L-BFGS ‣ a heuristic to simplify Newton’s method ‣ L-BFGS: limited memory Broyden– Fletcher–Goldfarb–Shanno ‣ normally, the partial second derivatives would be stored in the Hessian, a matrix that grows quadratically with respect to the number of features ‣ only uses the last few [partial] gradients to approximate the search direction 100 it is said to be “quasi-Newtonian” as opposed to gradient descent, which will follow a possibly curved path to the optimum
  110. 110. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining MaxEnt vs. naïve Bayes • P(w) = 6/7 • P(r|w) = 1/2 • P(g|w) = 1/2 101 Note that the example has dependent features: the two stoplights! MaxEntmodel (asobserved) NaïveBayesmodel MaxEnt adjusts the Langrange multipliers (weights) to model the correct (observed) joint probabilities. • P(r,r,b) = (1/7)(1)(1) = 4/28 • P(r,g,b) = P(g,r,b) = P(g,g,b) = 0 • P(*,*,w) = (6/7)(1/2)(1/2) = 6/28 • P(b) = 1/7 • P(r|b) = 1 • P(g|b) = 0 P(g,g,w) = 6/28??? Image Source: Klein & Manning. Maxent Models, Conditional Estimation, and Optimization. ACL 2003 Tutorial
  111. 111. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining But even MaxEnt cannot detect feature interaction 102 A, B a a b 1 3 b 3 0 Klein & Manning. MaxEnt Models, Conditional Estimation and Optimization. ACL 2003 Empirical (joint) observations Correct (target) distribution A, B a a b 1/7 3/7 b 3/7 0 2 feature model: A=r or B=r observed A, B a a b 16/49 12/49 b 12/49 9/49 A, B a a b b 4 feature model: any a,b observed A, B a a b 1/7 3/7 b 3/7 0 A, B a a b b A, B a a b 4/14 3/14 b 4/14 3/14 A, B a a b 4/14 4/14 b 3/14 3/14 only A=r only B=r
  112. 112. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining A first look at probabilistic graphical models • Latent Dirichlet Allocation: LDA ‣ Blei, Ng, and Jordan. Journal of Machine Learning Research 2003 ‣ For assigning “topics” to “documents” ‣ An unsupervised, generative model 103 i.e., for text classification
  113. 113. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Dirichlet Allocation (LDA 1/3) • Intuition for LDA • From: Edwin Chen. Introduction to LDA. 2011 ‣ “Document Collection” • I like to eat broccoli and bananas. • I ate a banana and spinach smoothie for breakfast. • Chinchillas and kittens are cute. • My sister adopted a kitten yesterday. • Look at this cute hamster munching on a piece of broccoli. ! ! 104 ➡ Topic A ➡ Topic B ➡ Topic 0.6A + 0.4B Topic A: 30% broccoli, 15% bananas, 10% breakfast, 10% munching, … ! Topic B: 20% chinchillas, 20% kittens, 20% cute, 15% hamster, …
  114. 114. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Dirichlet process • A Dirichlet is a [possibly continuos] distribution over [discrete/multinomial] distributions (probability masses). ! ! ! • The Dirichlet Process samples multiple independent, discrete distributions θi with repetition from θ (“statistical clustering”). 105 D(✓, ↵) = ( P ↵i) Q (↵i) Y ✓↵i 1 i Xnα N A Dirichlet process is like drawing from an (infinite) ”bag of dice“ (with finite faces). 1. Draw a new distribution X from D(θ, α) 2. With probability α ÷ (α + n - 1) draw a new X
 With probability n ÷ (α + n - 1), (re-)sample an Xi from X ∑ i = 1; a Probability Mass Function Gamma function -> a “continuous” factorial [!] Dirichlet prior: ∀ i ∈ : i > 0
  115. 115. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Dirichlet prior α 106 bluered green Frigyik et al. Introduction to the Dirichlet Distribution and Related Processes. 2010 ⤳ equal, =1 ➡ uniform distribution ⤳ equal, <1 ➡ marginal distrib. (”choose few“) ⤳ equal, >1 ➡ symmetric, mono-modal distrib. ⤳ not equal, >1 ➡ non-symmetric distribution Documents and topic distributions (N=3)
  116. 116. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Dirichlet Allocation (LDA 2/3) • α - per-document Dirichlet prior • θd - topic distribution of document d • zd,n - word-topic assignments • wd,n - observed words • βk - word distrib. of topic k • η - per-topic Dirichlet prior 107 βkwd,nzd,nθdα η ND K Documents Words Topics P(B, ⇥, Z, W) = KY k P( k|⌘) ! DY d P(✓d|↵) NY n P(zd,n|✓d)P(wd,n| 1:K, zd,n) ! P(Topics) P(Document-T.) P(Word-T. | Document-T.) P(Word | Topics, Word-T.) Joint Probability termscorek,n = ˆk,n log ˆk,n ⇣QK j ˆj,n ⌘1/K dampens the topic-specific score of terms assigned to many topics What Topics is a Word assigned to?
  117. 117. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Latent Dirichlet Allocation (LDA 3/3) • LDA inference in a nutshell ‣ Calculate the posterior probability that Topic t generated Word w. ‣ Initialization: Choose K, the number of Topics, and randomly assign one out of the K Topics to each of the N Words in each of the D Documents. • The same word can have different Topics at different positions in the Document. ‣ Then, for each Topic:
 And for each Word in each Document: 1. Compute P(Word-Topic | Document): the proportion of [Words assigned to] Topic t in Document d 2. Compute P(Word | Topics, Word-Topic): the probability a Word w is assigned a Topic t (using the general distribution of Topics and the Document-specific distribution of [Word-] Topics) • Note that a Word can be assigned a different Topic each time it appears in a Document. 3. Given the prior probabilities of a Document’s Topics and that of Topics in general, reassign
 P(Topic | Word) = P(Word-Topic | Document) * P(Word | Topics, Word-Topic) ‣ Repeat until P(Topic | Word) stabilizes (e.g., MCMC Gibbs sampling, Course 04) 108
  118. 118. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Evaluation metrics for classification tasks Evaluations should answer questions like: ! How to measure a change to an approach? Did adding a feature improve or decrease performance? Is the approach good at locating the relevant pieces or good at excluding the irrelevant bits? How do two or more different methods compare? 109
  119. 119. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Essential evaluation metrics: Accuracy, F-Measure, MCC Score • True/False
 Positive/Negative ‣ counts; TP, TN, FP, FN • Precision (P) ‣ correct hits [TP] ÷
 all hits [TP + FP] • Recall (R; Sensitivity, TPR) ‣ correct hits [TP] ÷
 true cases [TP + FN] • Specificity (True Negative Rate) ‣ correct misses [TN] ÷
 negative cases [FP + TN] ! • Accuracy ‣ correct classifications [TP + TN] ÷
 all cases [TP + TN + FN + FP]) ‣ highly sensitive to class imbalance • F-Measure (F-Score) ‣ the harmonic mean between P & R
 = 2 TP ÷ (2 TP + FP + FN)
 = (2 P R) ÷ (P + R) ‣ does not require a TN count • MCC Score (Mathew’s Correlation Coefficient) ‣ χ2 -based: (TP TN - FP FN) ÷
 sqrt[(TP+FP)(TP+FN)(TN+FP)(TN+FN)] ‣ robust against class imbalance 110
  120. 120. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Essential evaluation metrics: Accuracy, F-Measure, MCC Score • True/False
 Positive/Negative ‣ counts; TP, TN, FP, FN • Precision (P) ‣ correct hits [TP] ÷
 all hits [TP + FP] • Recall (R; Sensitivity, TPR) ‣ correct hits [TP] ÷
 true cases [TP + FN] • Specificity (True Negative Rate) ‣ correct misses [TN] ÷
 negative cases [FP + TN] ! • Accuracy ‣ correct classifications [TP + TN] ÷
 all cases [TP + TN + FN + FP]) ‣ highly sensitive to class imbalance • F-Measure (F-Score) ‣ the harmonic mean between P & R
 = 2 TP ÷ (2 TP + FP + FN)
 = (2 P R) ÷ (P + R) ‣ does not require a TN count • MCC Score (Mathew’s Correlation Coefficient) ‣ χ2 -based: (TP TN - FP FN) ÷
 sqrt[(TP+FP)(TP+FN)(TN+FP)(TN+FN)] ‣ robust against class imbalance 110 NB: no result order Patient! Doctor has cancer is healthy diagnose cancer TP FN detects nothing FP TN
  121. 121. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Ranked evaluation results: AUC ROC and PR . 111 Image Source: WikiMedia Commons, kku (“kakau”, eddie) Area Under the Curve Receiver-Operator Characteristic Precision-Recall TPR / Recall! TP ÷ (TP + FN) ! FPR! FP ÷ (TN + FP) ! Precision! TP ÷ (TP + FP) (aka. Sensitivity) (not Specificity!) Davis & Goadrich.
 ICML 2006 toplast
  122. 122. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining To ROC or to PR? 112 • Davis & Goadrich. The Relationship Between PR and ROC Curves. ICML 2006 • Landgrebe et al. Precision-recall operating characteristic (P-ROC) curves in imprecise environments. Pattern Recognition 2006 • Hanczar et al. Small-Sample Precision of ROC-Related Estimates. Bioinformatics 2010 “An algorithm which optimizes the area under the ROC curve is not guaranteed to optimize the area under the PR curve.” Davis & Goadrich, 2006 Curve I: 10 hits in the top 10, and 10 hits spread over the next 1500 results. ! AUC ROC 0.813 Curve II: Hits spread evenly over the first 500 results. ! AUC ROC 0.875 Results: 20 T ≪ 1980 N → Use (AUC) PR in imbalanced scenarios!
  123. 123. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Sentiment Analysis as an example domain for text classification (only if there is time left after the exercises) ! 113 Cristopher Potts. Sentiment Symposium Tutorial. 2011 http://sentiment.christopherpotts.net/index.html
  124. 124. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Opinion/Sentiment Analysis • Harder than “regular” document classification ‣ irony, neutral (“non-polar”) sentiment, negations (“not good”),
 syntax is used to express emotions (“!”), context dependent • Confounding polarities from individual aspects (phrases) ‣ e.g., a car company’s “customer service” vs. the “safety” of their cars • Strong commercial interest in this topic ‣ “Social” (commercial?) networking sites (FB, G+, …; advertisement) ‣ Reviews (Amazon, Google Maps), blogs, fora, online comments, … ‣ Brand reputation and political opinion analysis 114
  125. 125. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Polarity of Sentiment Keywords in IMDB 115 Cristopher Potts. On the negativity of negation. 2011 Note: P(rating | word) = P(word | rating) ÷ P(word) count(w, r) ÷ ∑ count(w, r) “not good”
  126. 126. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining 5+1 Lexical Resources for Sentiment Analysis 116 Disagree- ment Opinion Lexicon General Inquirer SentiWordNet LIWC Subjectivity Lexicon 33/5402 (0.6%) 49/2867 (2%) 1127/4214 (27%) 12/363 (3%) Opinion Lexicon 32/2411 (1%) 1004/3994 (25%) 9/403 (2%) General Inquirer 520/2306 (23%) 1/204 (0.5%) SentiWord
 Net 174/694 (25%) MPQA Subjectivity Lexicon: http://mpqa.cs.pitt.edu/ Liu’s Opinion Lexicon: http://www.cs.uic.edu/~liub/FBS/sentiment-analysis.html General Inquirer: http://www.wjh.harvard.edu/~inquirer/ SentiWordNet: http://sentiwordnet.isti.cnr.it/ LIWC (commercial, $90): http://www.liwc.net/ NRC Emotion Lexicon (+1): http://www.saifmohammad.com/ (➡Publications & Data) Cristopher Potts. Sentiment Symposium Tutorial. 2011
  127. 127. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Detecting the Sentiment of Individual Aspects • Goal: Determine the sentiment for a particular aspect or establish their polarity. ‣ An “aspect” here is a phrase or concept, like “customer service”. ‣ “They have a great+ customer service team, but the delivery took ages-.” • Solution: Measure the co-occurrence of the aspect with words of distinct sentiment or relative co-occurrence with words of the same polarity. ‣ The “sentiment” keywords are taken from some lexical resource. 117
  128. 128. Google’s Review Summaries 118
  129. 129. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Using PMI to Detect Aspect Polarity • Polarity(aspect) := PMI(aspect, pos-sent-kwds) - PMI(aspect, neg-sent-kwds) ‣ Polarity > 0 = positive sentiment ‣ Polarity < 0 = negative sentiment • Google’s approach: ! ! ! ! ! • Blair-Goldensohn et al. Building a Sentiment Summarizer for Local Service Reviews. WWW 2008 119 nouns and/or noun phrases keyword gazetteer
  130. 130. Text Mining 5 Information Extraction ! Madrid Summer School on Advanced Statistics and Data Mining ! Florian Leitner florian.leitner@upm.es License:
  131. 131. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Retrospective We have seen how to… • Design generative models of natural language. • Segment, tokenize, and compare text and/or sentences. • [Multi-] labeling whole documents or chunks of text. ! Some open questions… • How to assign labels to individual tokens in a stream? ‣ without using a dictionary/gazetteer: sequence taggers • How to detect semantic relationships between tokens? ‣ dependency parsers 121
  132. 132. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Incentive and applications ➡ Statistical analyses of [token] sequences ! • Part-of-Speech (PoS) tagging & chunking ‣ noun, verb, adjective, … & noun/verb/preposition/… phrases • Named Entity Recognition (NER) ‣ organizations, persons, places, genes, chemicals, … • Information extraction ‣ locations/times, phys. constants & chem. formulas, entity linking, event extraction, entity-relationship extraction, … 122
  133. 133. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Probabilistic graphical models • Graphs of hidden (blank) and observed (shaded) variables (vertices/nodes). • The edges depict dependencies, and if directed, show [ideally causal] relationships between nodes. 123 H O S3S2S1 directed ➡ Bayesian Network (BN) undirected ➡ Markov Random Field (MRF) mixed ➡ Mixture Models Koller & Friedman. Probabilistic Graphical Models. 2009
  134. 134. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Hidden vs. observed state and statistical parameters Rao. A Kalman Filter Model of the Visual Cortex. Neural Computation 1997 124
  135. 135. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining A Bayesian network for the Monty Hall problem 125 Choice 1 Choice 2 Goat Winner Car
  136. 136. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Markov random field 126 normalizing constant (partition function Z) factor (clique potential) A D B C θ(A, B) θ(B, C) θ(C, D) θ(D, A) a b 30 b c 100 c d 1 d a 100 a b 5 b c 1 c d 100 d a 1 a b 1 b c 1 c d 100 d a 1 a b 10 b c 100 c d 1 d a 100 P(a1, b1, c0, d1) = 10·1·100·100 ÷ 7’201’840 = 0.014 factor table factor graph P(X = ~x) = Q cl2~x cl(cl) P ~x2X Q cl2~x cl(cl) cl … [maximal] clique; a subset of factors
 in the graph where every pair is connected History class: Ising developed a linear field to model (binary) atomic spin states (Ising, 1924); the 2-dim. model problem then was solved by Onsager in 1944.
  137. 137. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Probabilistic models for sequential data • a.k.a. Temporal or dynamic Bayesian networks ‣ Static process w/ constant model ➡ temporal process w/ dynamic model ‣ Model structure and parameters are [still] constant ‣ The model topology within a [constant] “time slice” is depicted • Markov Chain (MC; Markov. 1906) • Hidden Markov Model (HMM; Baum et al. 1970) • MaxEnt Markov Model (MEMM; McCallum et al. 2000) • [Markov] Conditional Random Field (CRF; Lafferty et al. 2001) ‣ Naming: all four models make the Markov assumption (see part 2) 127 generativediscriminative
  138. 138. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining From a Markov chain to a Hidden Markov Model (HMM) 128 WW’ SS’ W hidden states observed state S1S0 W1 S2 W2 S3 W3 “unrolled” (for 3 words) “time-slice” W depends on S and S in turn depends on S’ P(W | W’) P(W | S) P(S | S’)
  139. 139. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining A language-based intuition for HMMs • A Markov Chain: P(W) = ∏ P(w | w’) ‣ assumes the observed words are in and of themselves the cause of the observed sequence. • A HMM: P(S, W) = ∏ P(s | s’) P(w | s) ‣ assumes the observed words are emitted by a hidden (not observable) sequence, for example the chain of part-of-speech-states. 129 S DT NN VB NN . The dog ran home ! again, this is the “unrolled” model that does not depict the conditional dependencies
  140. 140. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The two matrices of a HMM 130 P(s | s’) DT NN VB … DT 0.03 0.7 0 NN 0 0 0.5 VB 0 0.5 0.2 … P(w | s) word word word … DT 0.3 0 0 NN 0.0001 0.002 0 VB 0 0 0.001 … SS’ W very sparse (W is large) ➡ Smoothing! Transition Matrix Observation Matrix underflow danger ➡ use “log Ps”! a.k.a. “CPDs”: Conditional Probability Distributions (measured as discrete factor tables from annotated PoS corpora)
  141. 141. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Three tasks solved by HMMs Evaluation: Given a HMM, infer the P of the observed sequence (because a HMM is a generative model). Solution: Forward Algorithm Decoding: Given a HMM and an observed sequence, predict the hidden states that lead to this observation. Solution: Viterbi Algorithm Training: Given only the graphical model and an observation sequence, learn the best [smoothed] parameters. Solution: Baum-Welch Algorithm 131 all three algorithms are are implemented using dynamic programming in Bioinformatics: Likelihood of a particular DNA element in Statistical NLP: PoS annotation
  142. 142. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Three limitations of HMMs Markov assumption: The next state only depends on the current state. Example issue: trigrams Output assumption: The output (observed value) is independent of all previous outputs (given the current state). Example issue: word morphology Stationary assumption: Transition probabilities are independent of the actual time when they take place. Example issue: position in sentence 132 (label bias problem, see next!) (long-range dependencies!) (inflection, declension!) MEMMCRF“unsolved” (CRF)
  143. 143. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining From generative to discriminative Markov models 133 SS’ W S’ S W S’ S W Hidden Markov Model Maximum Entropy Markov Model Conditional Random
 Field this “clique” makes CRFs expensive to compute generative model; lower bias is beneficial for small training sets (linear chain version)(first oder version) P(S, W) P(S | S’, W) NB boldface W: all words! (first oder version) P(S | S’, W)
  144. 144. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum entropy (MaxEnt 2/2) ‣ In summary, MaxEnt is about selecting the “maximal” model p*: ! ! ! ‣ That obeys the following conditional equality constraint: ! ! ! ‣ Next: Using, e.g., Langrange multipliers, one can
 establish the optimal λ parameters of the model that
 maximize the entropy of this probability: 134 X x2X P(x) X y2Y P(y|x) f(x, y) = X x2X,y2Y P(x, y) f(x, y) p⇤ = argmax p2P X x2X p(x) X y2Y p(y|x) log2 p(y|x) …using a conditional model that matches the (observed) joint probabilities select some model that maximizes the conditional entropy… [again] Image Source: WikiMedia Commons, Nexcis p⇤ (y|X) = exp( P ifi(X, y)) P y2Y exp( P ifi(X, y)) REMINDER “Exponential Model”
  145. 145. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Maximum Entropy Markov Models (MEMM) Simplify training of P(s | s’, w)
 by splitting the model into |S| separate transition functions Ps’(s | w) for each s’ 135 P(S | S’, W) S’ S W Ps0 (s|w) = exp ( P ifi(w, s)) P s⇤2S exp ( P ifi(w, s⇤)) P(s | s’, w) = Ps’(s | w) (The MaxEnt slide had {x, y} which here are {w, s}.)
  146. 146. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The label bias problem of directional Markov models 136 The robot wheels are round. The robot wheels Fred around. The robot wheels were broken. DT NN VB NN RB DT NN NN VB JJ DT NN ?? — — yet unseen! Wallach. Efficient Training of CRFs. MSc 2002 because of their directionality constraints, MEMMs & HMMs suffer from the label bias problem S’ S W MEMM HMM SS’ W
  147. 147. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Conditional Random Field 137 SS’ W w1, …, wn Models a per-state exponential function of joint probability over the entire observed sequence W. (max.) clique MRF: The label bias problem is “solved” by conditioning the MRF Y-Y’ on the entire observed sequence. CRF: note W (upper-case/bold), not w (lower-case): all words are used in each step! P(X = ~x) = Q cl2~x cl(cl) P ~x2X Q cl2~x cl(cl) P(Y = ~y |X = ~x) = Q y2~y cl(y0 , y, ~x) P ~y2Y Q y2~y cl(y0, y, ~x) P(S|W) = exp ( P ifi(W, s0 , s)) P s⇤2S exp ( P ifi(W, s0⇤, s⇤)) Wallach. Conditional Random Fields: An introduction. TR 2004
  148. 148. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Parameter estimation and L2 regularization of CRFs • For training {Y(n), X(n)}N n=1 sequence pairs with K features • Parameter estimation using conditional log-likelihood ! ! • Substitute log P(Y(n) | X(n)) with log exponential model ! ! • Add a penalty for parameters with a to high L2-norm 138 free regularization parameter `( ) = NX n=1 X y2Y (n) KX i=1 ifi(y0 , y, X(n) ) NX n=1 log Z(X(n) ) `( ) = NX n=1 X y2Y (n) KX i=1 ifi(y0 , y, X(n) ) NX n=1 log Z(X(n) ) KX i=1 2 i 2 2 (regularization reduces the effects of overfitting) normalizing constant (partial function Z) = argmax 2⇤ NX n log P(Y (n) |X(n) ; )
  149. 149. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Parameter estimation and L2 regularization of CRFs • For training {Y(n), X(n)}N n=1 sequence pairs with K features • Parameter estimation using conditional log-likelihood ! ! • Substitute log P(Y(n) | X(n)) with log exponential model ! ! • Add a penalty for parameters with a to high L2-norm 138 free regularization parameter `( ) = NX n=1 X y2Y (n) KX i=1 ifi(y0 , y, X(n) ) NX n=1 log Z(X(n) ) `( ) = NX n=1 X y2Y (n) KX i=1 ifi(y0 , y, X(n) ) NX n=1 log Z(X(n) ) KX i=1 2 i 2 2 (regularization reduces the effects of overfitting) normalizing constant (partial function Z) = argmax 2⇤ NX n log P(Y (n) |X(n) ; ) L2: Euclidian norm (∑ of squared errors) k⇤k2 2 2 2
  150. 150. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Model summaries:
 HMM, MEMM, CRF • A HMM ‣ generative model ‣ efficient to learn and deploy ‣ trains with little data ‣ generalizes well (low bias) • A MEMM ‣ better labeling performance ‣ modeling of features ‣ label bias problem ! • CRF ‣ conditioned on entire observation ‣ complex features over full input ‣ training time scales exponentially • O(NTM2 G) • N: # of sequence pairs;
 T: E[sequence length];
 M: # of (hidden) states;
 G: # of gradient computations for parameter estimation 139 a PoS model w/45 states and 1 M words can take a week to train… Sutton & McCallum. An Introduction to CRFs for Relational Learning. 2006
  151. 151. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Information extraction: Application of dynamic graphical models 140
  152. 152. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The Parts of Speech • Corpora for the [supervised] training of PoS taggers ‣ Brown Corpus (AE from ~1961) ‣ British National Corpus: BNC (20th century British) ‣ Wall Street Journal Corpus: WSJ Corpus (AE from the 80s) ‣ American National Corpus: ANC (AE from the 90s) ‣ Lancaster Corpus of Mandarin Chinese: LCMC (Books in Mandarin) ‣ The GENIA corpus (Biomedical abstracts from PubMed) ‣ NEGR@ (German Newswire from the 90s) ‣ Spanish and Arabian corpora should be (commercially…) available… ??? 141 I ate the pizza with green peppers . PRP VB DT NN IN JJ NN . ! Best tip: Ask on the “corpora list” mailing list!
  153. 153. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Noun and verb phrase chunking with BIO-encoded labels 142 The brown fox quickly jumps over the lazy dog . a pangram (hint: check the letters) DT JJ NN RB VBZ IN DT JJ NN . B-N I-N I-N B-V I-V O B-N I-N I-N O Performance (2nd order CRF) ~ 94% Main problem: embedded & chained NPs (N of N and N) ! Chunking is “more robust to the highly diverse corpus of text on the Web” and [exponentially] faster than [deep] parsing. Banko et al. Open Information Extraction from the Web. IJCAI 2007 a paper with over 700 citations Wermter et al. Recognizing noun phrases in biomedical text. SMBM 2005 error sources “shallow parsing”
  154. 154. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Word Sense Disambiguation (WSD) • Basic Example: hard [JJ] ‣ physically hard (a hard stone) ‣ difficult [task] (a hard task) ‣ strong/severe (a hard wind) ‣ dispassionate [personality] (a hard bargainer) • Entity Disambig.: bank [NN] ‣ finance (“bank account”) ‣ terrain (“river bank”) ‣ aeronautics (“went into bank”) ‣ grouping (“a bank of …”) ! • SensEval ‣ http://www.senseval.org/ ‣ SensEval/SemEval Challenges ‣ Provides corpora where every word is tagged with its sense • WordNet ‣ http://wordnet.princeton.edu/ ‣ A labeled graph of word senses • Applications ‣ Named entity recognition ‣ Machine translation ‣ Language understanding 143 Note the PoS-tag “dependency”: otherwise, the two examples would have even more senses!
  155. 155. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Word vector representations: Unsupervised WSD • Idea 1: Words with similar meaning have similar environments. • Use a word vector to count a word’s surrounding words. • Similar words now will have similar word vectors. ‣ See lecture 2, neural network models of language and lecture 4, cosine similarity ‣ Visualization: Principal Component Analysis ! • Idea 2: Words with similar meaning have similar environments. • Use the surrounding of unseen words to “smoothen” language models (i.e., the correlation between word wi and its context cj). ‣ see Text Mining 4: TF-IDF weighting, Cosine similarity and point-wise MI ‣ Levy & Goldberg. Linguistic Regularities in Sparse and Explicit Word Representations. CoNLL 2014 144 Levy & Goldberg took two words on each side to “beat” a neural
 network model with a four word window! Turian et al. Word representations. ACL 2010
  156. 156. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Named Entity Recognition (NER) 145 Date Location Money Organization Percentage Person ➡ Conditional Random Field ➡ Ensemble Methods; +SVM, HMM, MEMM, … ➡ pyensemble
 NB these are corpus-based approaches (supervised) CoNLL03: http://www.cnts.ua.ac.be/conll2003/ner/ ! How much training 
 data do I need? “corpora list” Image Source: v@s3k [a GATE session; http://vas3k.ru/blog/354/]
  157. 157. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining PoS tagging and lemmatization for
 Named Entity Recognition (NER) 146 Token PoS Lemma NER Constitutive JJ constitutive O binding NN binding O to TO to O the DT the O peri-! NN peri-kappa B-DNA B NN B I-DNA site NN site I-DNA is VBZ be O seen VBN see O in IN in O monocytes NNS monocyte B-cell . . . O de facto standard
 PoS tagset {NN, JJ, DT, VBZ, …} Penn Treebank B-I-O chunk encoding common alternatives: I-O I-E-O B-I-E-W-O End token (unigram) Word Begin-Inside-Outside (relevant) token } chunk noun-phrase (chunk) N.B.: This is all supervised (i.e., manually annotated corpora)! REMINDER
  158. 158. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining The next step: Relationship extraction Given this piece of text: The fourth Wells account moving to another agency is the packaged paper-products division of Georgia-Pacific Corp., which arrived at Wells only last fall. Like Hertz and the History Channel, it is also leaving for an Omnicom-owned agency, the BBDO South unit of BBDO Worldwide. BBDO South in Atlanta, which handles corporate advertising for Georgia-Pacific, will assume additional duties for brands like Angel Soft toilet tissue and Sparkle paper towels, said Ken Haldin, a spokesman for Georgia-Pacific in Atlanta. Which organizations operate in Atlanta? (BBDO S., G-P) 147
  159. 159. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Tesnière’s dependency relations (1959) 148 He ate pizza with anchovies. He ate pizza with friends. ate(he, pizza with anchovies) ate(he, pizza) ate(he, with friends) Relationships ate(he, with anchovies)
  160. 160. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Dependency parsing 1/2 • Transition-based, arc-standard, shift-reduce, greedy parsing. • The default approach to dependency parsing today in O(n). ‣ Transition-based: Move from one token to the next. ‣ Arc-standard: assign arcs when the dependent token (arrowhead) is fully resolved (alternative: arc-eager → assign the arcs immediately). ‣ Shift-reduce: A stack of words and a stream buffer: either shift next word from the buffer to the stack or reduce a word from the stack by “arcing”. ‣ Greedy: Make locally optimal transitions (assume independence of arcs). 149
  161. 161. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Buffer A shift-reduce parse Stack 150 ROOT Economic marketsfinancialoneffectlittlenews had . ROOT Economic marketsfinancialoneffectlittlenews had . (left-arc, right-arc) Dependency Parsing. Kübler et al., 2009
  162. 162. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Buffer A shift-reduce parse Stack 150 ROOT marketsfinancial . ROOT Economic marketsfinancialoneffectlittlenews had . Shift: Economic Shift: news Left-arc: Economic←news Shift: had Left-arc: news←had Shift: little Shift: effect Left-arc: little←effect had effect on Shift: on (left-arc, right-arc) Dependency Parsing. Kübler et al., 2009
  163. 163. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Buffer A shift-reduce parse Stack 150 ROOT ROOT Economic marketsfinancialoneffectlittlenews had . Shift: Economic Shift: news Left-arc: Economic←news Shift: had Left-arc: news←had Shift: little Shift: effect Left-arc: little←effect Shift: on Shift: financial Shift: markets Shift: . Left-arc: financial←markets Right-arc: on→markets Right-arc: effect→on Right-arc: had→effect Right-arc: had→. Right-arc: ROOT→had (left-arc, right-arc) Dependency Parsing. Kübler et al., 2009
  164. 164. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Dependency parsing 2/2 • (Arc-standard) Transitions: shift or reduce (left-arc, right-arc) • Transitions are chosen using some classifier ‣ Maximum entropy classifier, support vector machine, single-layer perceptron, perceptron with one hidden layer (→ Stanford parser, 2014 edition) • Main issues: ‣ Few large, well annotated training corpora (“dependency treebanks”).
 Biomedical domain: GENIA; Newswire: WSJ, Prague, Penn, … ‣ Non-projective trees (i.e., trees with arcs crossing each other; common in a number of other languages) with arcs that have to be drawn between nodes that are not adjacent on the stack. 151
  165. 165. Florian Leitner <florian.leitner@upm.es> MSS/ASDM: Text Mining Four approaches to relationship extraction • Co-mention window ‣ E.g.: if ORG and LOC entity within same sentence and no more than x tokens in between, treat the pair as a hit. ‣ Low precision, high recall; trivial, many false positives. • Dependency parsing ‣ If a path covering certain nodes (e.g. prepositions like “in/IN” or predicates [~verbs]) connects two entities, extract that pair. ‣ Balanced precision and recall, computationally expensive. • Pattern extraction ‣ e.g.: <ORG>+ <IN> <LOC>+ ‣ High precision, low recall; cumbersome, but very common. ‣ Pattern learning can help. ! • Machine Learning ‣ Features for sentences with entities and some classifier (e.g., SVM, neural net, MaxEnt, Bayesian net, …) ‣ Highly variable milages.
 … but loads of fun in your speaker’s opinion :) 152 preposition token-distance, #tokens between the entities, tokens before/after them, etc.)
Data & Analytics
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