Over fitting &Transformation Based Learning CS 371: Spring 2012
Machine Learning• Machines can learn from examples – Learning modifies the agents decision mechanisms to improve performance• Given training data, machines analyze the data, and learn rules which generalize to new examples – Can be sub-symbolic (rule may be a mathematical function) – Or it can be symbolic (rules are in a representation that is similar to representation used for hand-coded rules)• In general, machine learning approaches allow for more tuning to the needs of a corpus, and can be reused across corpora
Training data example• Inductive learning Empirical error function: E(h) = x distance[h(x; ) , f] Empirical learning = finding h(x), or h(x; ) that minimizes E(h)• Note an implicit assumption: – For any set of attribute values there is a unique target value – This in effect assumes a “no-noise” mapping from inputs to targets • This is often not true in practice (e.g., in medicine).
Learning Boolean Functions• Given examples of the function, can we learn the function?• 2 to the power of 2d different Boolean functions can be defined on d attributes – This is the size of our hypothesis space• Observations: – Huge hypothesis spaces –> directly searching over all functions is impossible – Given a small data (n pairs) our learning problem may be underconstrained • Ockham’s razor: if multiple candidate functions all explain the data equally well, pick the simplest explanation (least complex function) • Constrain our search to classes of Boolean functions, e.g., – decision trees
Decision Tree Learning• Constrain h(..) to be a decision tree
Major issuesQ1: Choosing best attribute: what quality measure to use?Q2: Handling training data with missing attribute valuesQ3: Handling training data with noise, irrelevant attributes - Determining when to stop splitting: avoid overfitting
Major issuesQ1: Choosing best attribute: different quality measures. Information gain, gain ratio …Q2: Handling training data with missing attribute values: blank value, most common value, or fractional countQ3: Handling training data with noise, irrelevant attributes: - Determining when to stop splitting: ????
Assessing PerformanceTraining data performance is typically optimistic e.g., error rate on training dataReasons? - classifier may not have enough data to fully learn the concept (but on training data we don’t know this) - for noisy data, the classifier may overfit the training dataIn practice we want to assess performance “out of sample” how well will the classifier do on new unseen data? This is the true test of what we have learned (just like a classroom)With large data sets we can partition our data into 2 subsets, train and test - build a model on the training data - assess performance on the test data
Example of Test PerformanceRestaurant problem - simulate 100 data sets of different sizes - train on this data, and assess performance on an independent test set - learning curve = plotting accuracy as a function of training set size - typical “diminishing returns” effect
How Overfitting affects PredictionPredictive Error Error on Training Data Model Complexity
How Overfitting affects PredictionPredictive Error Error on Test Data Error on Training Data Model Complexity
How Overfitting affects Prediction Underfitting OverfittingPredictive Error Error on Test Data Error on Training Data Model Complexity Ideal Range for Model Complexity
Training and Validation DataFull Data Set Idea: train each Training Data model on the “training data” and then test each model’s Validation Data accuracy on the validation data
The v-fold Cross-Validation Method• Why just choose one particular 90/10 “split” of the data? – In principle we could do this multiple times• “v-fold Cross-Validation” (e.g., v=10) – randomly partition our full data set into v disjoint subsets (each roughly of size n/v, n = total number of training data points) • for i = 1:10 (here v = 10) – train on 90% of data, – Acc(i) = accuracy on other 10% • end • Cross-Validation-Accuracy = 1/v i Acc(i) – choose the method with the highest cross-validation accuracy – common values for v are 5 and 10 – Can also do “leave-one-out” where v = n
Disjoint Validation Data SetsFull Data Set Validation Data Training Data 1st partition
Disjoint Validation Data SetsFull Data Set Validation Data Validation Data Training Data 1st partition 2nd partition
More on Cross-Validation• Notes – cross-validation generates an approximate estimate of how well the learned model will do on “unseen” data – by averaging over different partitions it is more robust than just a single train/validate partition of the data – “v-fold” cross-validation is a generalization • partition data into disjoint validation subsets of size n/v • train, validate, and average over the v partitions • e.g., v=10 is commonly used – v-fold cross-validation is approximately v times computationally more expensive than just fitting a model to all of the data
Problem Domain: POS Tagging What is text tagging? – Some sort of markup, enabling understanding of language. – Can be word tags: He will race/VERB the car. He will not race/VERB the truck. When will the race/NOUN end?
Why do we care? Sometimes, meaning changes a lot – Transcribed speech lacks clear punctuation: “I called, John and Mary are there.” → I called John and Mary are there. (I called John) and (Mary are there.) ?? I called ((John and Mary) are there.) – We can tell, but can a computer? Here, needs to know about verb forms and collections – Can be important! Quick! Wrap the bandage on the table around her leg! Imagine a robotic medical assistant with this one . . .
Where is this used?• Any natural language task! – Translators: word-by-word translation does not always work, sentences need re-arranging. – It can help with OCR or voice transcription “I need to writer. Im a good write her.” “to writer”?? “a good write”?→ “I need to write her. Im a good writer.
Some terms Corpus – Big body of text, annotated (expert-tagged) or not Dictionary – List of known words, and all possible parts of speech Lexical/Morphological vs. Contextual – Is it a word property (spelling) or surroundings (neighboring parts of speech)? Semantics vs Syntax – Meaning (definition) vs. Structure (phrases, parsing) Tokenizer – Separates text into words or other sized blocks (idioms,phrases . . . ) Disambiguator – Extra pass to reduce possible tags to a single one.
Some problems we faceClassification challenges: – Large number of classes: English POS: varying tagsets, 48 to 195 tags – Often ambiguous, varying with use/context POS: There must be a way to go there; I know a person from there – see that guy there? (pron., adv., n.) – Varying number of relevant features Spelling, position, surrounding words, paragraph position, article topic . . .
TBL: A Symbolic Learning Method• A method called error-driven Transformation-Based Learning (TBL) (Brill algorithm) can be used for symbolic learning – The rules (actually, a sequence of rules) are learned from an annotated corpus – Performs about as accurately as other statistical approaches• Can have better treatment of context compared to HMMs (as we’ll see) – rules which use the next (or previous) POS • HMMs just use P(Ti| Ti-1) or P(Ti| Ti-2 Ti-1) – rules which use the previous (next) word • HMMs just use P(Wi|Ti)
What does it do? Transformation-Based Error-Driven Learning: – First, a dictionary tags every word with its most common POS. So, “run” is tagged as a verb in both: “The run lasted 30 minutes” and “We run 3 miles every day” – Unknown capitalized words are assumed to be proper nouns, and remaining unknown words are assigned the most common tag for their three-letter ending. → “blahblahous” is probably an adjective. – Finally, the tags are updated by a set of “patches,” with the form “Change tag a to b if:” – The word is in context C (eg, the pattern of surrounding tags) – The word or one in a region R has lexical property P (eg, capitalization)
Rule Templates• Brill’s method learns transformations which fit different templates – Template: Change tag X to tag Y when previous word is W • Transformation: NN VB when previous word = to – Change tag X to tag Y when previous tag is Z Ex: – The can rusted. → The (determiner) can (modal verb) rusted (verb) . (.) – Transformation: Modal Noun when previous tag = DET → The (determiner) can (noun) rusted (verb) . (.) – Change tag X to tag Y when previous 1st, 2nd, or 3rd word is W • VBP VB when one of previous 3 words = has• The learning process is guided by a small number of templates (e.g., 26) to learn specific rules from the corpus• Note how these rules sort of match linguistic intuition
Brill Algorithm (Overview) • Assume you are given a 1. Initial-state annotator: training corpus G (for gold Label every word token standard) in V with most likely tag for that word type from • First, create a tag-free G. version V of it … then do 2. Consider every possible steps 1-4 transformational rule: • Notes: select the one that leads to the most – As the algorithm improvement in V using proceeds, each G to measure the error successive rule covers 3. Retag V based on this fewer examples, but rule potentially more 4. Go back to 2, until there accurately is no significant – Some later rules may improvement in accuracy change tags changed over previous iteration by earlier rules
Error-driven method• How does one learn the rules?• The TBL method is error-driven – The rule which is learned on a given iteration is the one which reduces the error rate of the corpus the most, e.g.: – Rule 1 fixes 50 errors but introduces 25 more net decrease is 25 – Rule 2 fixes 45 errors but introduces 15 more net decrease is 30 Choose rule 2 in this case• We set a stopping criterion, or threshold once we stop reducing the error rate by a big enough margin, learning is stopped
Example of Error Reduction From Eric Brill (1995): Computational Linguistics, 21, 4, p. 7
Rule ordering• One rule is learned with every pass through the corpus. – The set of final rules is what the final output is – Unlike HMMs, such a representation allows a linguist to look through and make more sense of the rules• Thus, the rules are learned iteratively and must be applied in an iterative fashion. – At one stage, it may make sense to change NN to VB after to – But at a later stage, it may make sense to change VB back to NN in the same context, e.g., if the current word is school
Example of Learned Rule Sequence• 1. NN VB PREVTAG TO – to/TO race/NN->VB• 2. VBP VB PREV1OR20R3TAG MD – might/MD vanish/VBP-> VB• 3. NN VB PREV1OR2TAG MD – might/MD not/RB reply/NN -> VB• 4. VB NN PREV1OR2TAG DT – the/DT great/JJ feast/VB->NN• 5. VBD VBN PREV1OR20R3TAG VBZ – He/PP was/VBZ killed/VBD->VBN by/IN Chapman/NNP
Insights on TBL• TBL takes a long time to train, but is relatively fast at tagging once the rules are learned• The rules in the sequence may be decomposed into non- interacting subsets, i.e., only focus on VB tagging (need to only look at rules which affect it)• In cases where the data is sparse, the initial guess needs to be weak enough to allow for learning• Rules become increasingly specific as you go down the sequence. – However, the more specific rules generally don’t overfit because they cover just a few cases
DT and TBLDT is a subset of TBL 1. Label with S 2. If X then S A 3. S B
DT is a proper subset of TBL• There exists a problem that can be solved by TBL but not a DT, for a fixed set of primitive queries.• Ex: Given a sequence of characters – Classify a char based on its position • If pos % 4 == 0 then “yes” else “no” – Input attributes available: previous two chars
• Transformation list: – Label with S: A/S A/S A/S A/S A/S A/S A/S – If there is no previous character, then S F A/F A/S A/S A/S A/S A/S A/S – If the char two to the left is labeled with F, then S F A/F A/S A/F A/S A/F A/S A/F – If the char two to the left is labeled with F, then FS A/F A/S A/S A/S A/F A/S A/S – F yes – S no
DT and TBL• TBL is more powerful than DT• Extra power of TBL comes from – Transformations are applied in sequence – Results of previous transformations are visible to following transformations.
Brill Algorithm (More Detailed) • 1. Label every word token with its most likely tag (based on lexical generation Most likely tag: probabilities). P(NN|race) = .98 • 2. List the positions of tagging errors and their counts, by comparing with “truth” (T) P(VB|race) = .02 • 3. For each error position, consider each Is/VBZ expected/VBN to/TO instantiation I of X, Y, and Z in Rule race/NN tomorrow/NN template. – If Y=T, increment improvements[I], Rule template: Change a word from else increment errors[I]. tag X to tag Y when previous tag is • 4. Pick the I which results in the greatest Z error reduction, and add to output Rule Instantiation for above example: – VB NN PREV1OR2TAG DT improves NN VB PREV1OR2TAG TO on 98 errors, but produces 18 new errors, so net decrease of 80 errors Applying this rule yields: • 5. Apply that I to corpus Is/VBZ expected/VBN to/TO • 6. Go to 2, unless stopping criterion is race/VB tomorrow/NN reached
Handling Unknown Words• Can also use the Brill Example Learned Rule Sequence method to learn how to tag for Unknown Words unknown words• Instead of using surrounding words and tags, use affix info, capitalization, etc. – Guess NNP if capitalized, NN otherwise. – Or use the tag most common for words ending in the last 3 letters. – etc.• TBL has also been applied to some parsing tasks