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http://www.summerschool.websci.net/

WebScience Summer School Southampton

Data Science 2014

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- 1. Dr. ClaudiaWagner http://claudiawagner.info/ Web Science Summer SchoolWS3 , Southampton, UK , 21th July 2014
- 2. source: Twitter 2
- 3. Statistical computing is very central , but data science is more than statistics Activities of data scientists: collection and generation, preparation, analysis, visualization, management and preservation of large collections of data Jeffrey Stanton, Introduction to Data Science, free e-book 3
- 4. Ask interesting question Why is it important?Which number answers your question? Get or generate the data Which data will help answering you question? How is the data generated? Are their any sampling biases? Ethical issues? Analyze the data Are there any anomalies or regularities? Which hidden process has generated the data? Fit a model to the data and validate it Visualize and communicate results What does 75% probability mean? Preserve and share the data to make results reproducible 4
- 5. Data is a collection of facts Facts can be numbers, words, measurements, observations or even just descriptions of things Qualitative data (e.g., “it was great”) Quantitative data Discrete (e.g., 5) Continuous (e.g., 3.723) 5
- 6. 6 Stevens, S. S. (1946). "On theTheory of Scales of Measurement". Science 103 (2684): 677–680. Nominal (e.g., ethnic group, sex, nationality) Ordinal (e.g., status) Interval (e.g., temperature in Celsius) Ratio (e.g., weight) Observations are only named Observations can be ordered Distance is meaningful Absolute zero
- 7. 7
- 8. Random sample of Twitter users Random sample of tweets from the public timeline More active users are more likely to be included Friendship Paradox Select a random sample of people and ask them to list the people they know. Contact a sample of the listed friends and repeat the survey. Sampling bias: people with more friends are more likely to show up in the friend lists which we generate at the first stage 8
- 9. A study found that the profession with the lowest average age of death was student. Being a student does not cause you to die at an early age. Being a student means you are young.This is what makes the average of those that die so low. Amount of ice cream consumed per day is highly correlated with number of drownings per day Both variables are correlated with the daily temperature 9 "Teaching Statistics:A Bag ofTricks," by Gelman and Nolan (2002)
- 10. A study found that only 1.5% of drivers in accidents reported that they were using a cell phone, whereas 10.9% reported that they were distracted by another occupant in the car. Can we conclude that using a cell phone safer than speaking with another occupant? P(cellphone | accident) != P(accident | cellphone) Compare P(accident|cellphone) and P(accident|occupant) We need to know the prevalence of cell phone use It is likely that much more people talk to another occupant in the car while driving than talking on the cell phone 10 Jessica Utts, What Educated Citizens Should Know about Statistics and Probability,The American Statistician, Vol. 57, No. 2 (May, 2003), pp. 74-79
- 11. Ecological Fallacy Illiteracy rate in each US state and the proportion of immigrants per state Negative correlation of −0.53 ▪ The greater the proportion of immigrants in a state, the lower its average illiteracy. When individuals are considered, the correlation was +0.12 — immigrants were on average more illiterate than native citizens. 11 Robinson, W.S. (1950). "Ecological Correlations and the Behavior of Individuals". American Sociological Review (American Sociological Review, Vol. 15, No. 3) 15 (3): 351–357.
- 12. Data Collection Data Preprocessing DataAnalysis DataVisualization Data Preservation
- 13. Found data or observational data Are observational data enough? Are such data available? Generate Data Designs the data generation process ▪ E.g., via surveys, experiments, crowdsourcing 13
- 14. 14http://www.intel.com/content/www/us/en/communications/internet-minute-infographic.html
- 15. Two general types of traces: 15 Accretion - a build-up of physical traces Erosion - the wearing away of material Webb, Eugene J. et al. Unobtrusive Measures: nonreactive research in the social sciences. Chicago: Rand McNally, 1966
- 16. Bulk downloads Wikipedia, IMDB, Million Song Database, etc. API access NYTimes,Twitter, Facebook, Foursquare, etc. Web scraping Tools e.g., http://scrapy.org/ What data is ok to scrap? ▪ Public, non-sensitive, anonymized, fully referenced information, Check terms of conditions! 16
- 17. Takes time to accumulate Conservative estimate Only what happened counts! Intentions, motivations or internal states don’t count. Inferentially weak Cannot answer “what-if” questions 17
- 18. Surveys Simulations Model behavior of users/agents on a micro-level Simulate what happens under different conditions Empirical validation Experiments Keep all variables constant and only manipulate one variable (e.g., emotions) 18
- 19. Simulations Study of macro-phenomena Difficult to validate empirically Surveys and/or Experiments We only get data from those who are accessible and willing to respond or participate Responders provide answers that are in line with self- image and researcher’s expectations Hawthorne effect, etc. 19
- 20. Data Collection Data Preprocessing DataAnalysis DataVisualization Data Preservation
- 21. 21 Data cleaning Fill in missing values Smooth noisy data Identify or remove outliers Resolve inconsistencies Data integration Integration of multiple databases, or files
- 22. 22 Data transformation Normalization: scaled to fall within a small, specified range Standardization: how many standard deviations from the mean lies each data point Discretization: divide the range of a continuous attribute into intervals some algorithms require discrete attributes. Data reduction Dimensionality reduction (remove unimportant attributes via feature selection, group features into factors e.g. PCA, SVD) Aggregation and clustering Sampling
- 23. Data Collection Data Preprocessing Data Mining DataAnalysis Statistical Inference DataVisualization Machine Learning Data Preservation
- 24. Problem: Given high dimensional space (e.g., fb-user which are described via various attributes such as locations they visited) Find pairs of data points (𝒙, y) that are within some distance threshold 𝒅(𝒙, y) ≤ 𝒔 We first need to decide what „distance“ means 24
- 25. Distance Measures Jaccard similarity between 2 sets of items I1, I2 sim(I1, I2) = |𝐼1 ∩ 𝐼2| |𝐼1 ∪ 𝐼2| dist(I1, I2) = 1- sim(I1, I2) Euclidian distance, Hamming distance, Cosine Similarity, etc. 25
- 26. Goal: Given a set of items group the items into some number of clusters, so that Members of a cluster are similar to each other Members of different clusters are dissimilar 26Anand Rajaraman, Jeffrey Ullman, Jure Leskovec, Mining of Massive Datasets, Cambridge University Press
- 27. Not-Hierarchical / Point assignment: Maintain a set of clusters Point belong to “nearest” cluster Hierarchical: Agglomerative (bottom up): ▪ Initially, each point is a cluster ▪ Repeatedly combine the two “nearest” clusters into one Divisive (top down): ▪ Start with one cluster and recursively split it 27Anand Rajaraman, Jeffrey Ullman, Jure Leskovec, Mining of Massive Datasets, Cambridge University Press
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- 31. 31
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- 33. Try different k, looking at the change in the average distance to centroid as k increases Average falls rapidly until right k, then changes little 33 Average Diameter k best k
- 34. Aim: Find hidden concepts/groups in a matrix Method: SingularValue Decomposition (SVD) 34 Lescovec et al., Mining of Massive Datasets, p. 418
- 35. Rank = 2 Rank denotes the information content of the matrix. For instance, a rank-1 matrix can be written as a product of one column and one vector 35
- 36. 36
- 37. 37 Lescovec et al., Mining of Massive Datasets, p. 418 Relates users and concepts Relates movies to concepts Strength of concepts
- 38. Data Collection Data Preprocessing Data Mining DataAnalysis Statistical Inference DataVisualization Machine Learning Data Preservation
- 39. Estimate population parameter from sample statistics Sampling Distribution of statistic: Draw a finite set of samples of size n from the population Computing the statistic on the sample Repeat this process The mean of the sampling distribution is the expected value of the statistic in the true population SD of the sampling distribution is the standard error 39
- 40. 40
- 41. Some descriptive statistics such as mean or median are unbiased estimators of central tendency Expected value of the statistic is the true population parameter Expected value of dispersion in a sample is an underestimate of the true population value 41
- 42. True population size is N Sample size n < N (e.g., n=100) Correction factor : 𝑛 𝑛−1 For n=100 the correction factor is ~ 1.01 For n=100.000 our correction factor is ~1.00001 Estimate PopulationVar: ( 𝑛 𝑛−1 ) ∗ (𝑥 𝑖−𝜇𝑛 𝑖=1 ) 𝑛 42
- 43. Specify the range of values that have a high probability of containing the true population parameter Confidence level α: the probability that confidence interval contains true population parameter 43
- 44. CI = sample statistic + MOE MOE = SE * Critical value MOE = 𝜎 𝑛 ∗ 𝑧 𝛼/2 CriticalValue: how far away from the mean must a point lie in order to be considered as “extreme” or “unexpected”? 44 n … sample size σ … standard deviation z α/2 … confidence coefficient
- 45. 45
- 46. Area under the curve is 0.475 What’s the z- score? 46
- 47. Select 1000 fb-user randomly Average number of bar visits per year X = 78 Standard Deviation: (𝑥 𝑖−𝜇𝑛 𝑖=1 ) 2 𝑛 = 30 Confidence level is 95% divide 0.95 by 2 to get 0.475 Check out the z table z = 1.98 MOE = 𝜎 𝑛 ∗ 𝑧 𝛼/2 = 30 1000 ∗ 1.98= 1.88 78 +/- 1.88 CI: [76.12 ; 79.88] 47
- 48. Exact CI can only be computed when the sampling distribution and SD of sampling distribution (i.e., SE) are known Otherwise we have to estimate the Standard Error (SE) Bootstrap 48
- 49. Sampling with replacement Population is unknown But we observe one sample from the population of size n=4: {2, 3, 8, 8} We use this sample to generate a large number of bootstrap samples of size n: ▪ 8, 8, 8, 3 ▪ 3, 3, 8, 2 ▪ … Compute statistic (e.g. ,mean) for each bootstrap sample Estimate SE from the bootstrap distribution 49
- 50. 50 Population Sample Bootstrap Sample Bootstrap Sample Bootstrap Sample Bootstrap Sample Calculate statistic for each bootstrap sample Statistic +/- MOE MOE for 95% CI = 2 * SE Bootstrap Distribution Standard Error (SE): SD of bootstrap distribution
- 51. Randomly selected sample of fb-user Have they ever checked in at a nightclub? Democrats: 100/1000 yes Republican: 90/1000 yes Do the nightlife preferences differ significantly across political parties? Give 95% CI for difference in proportions 51
- 52. dems = rep( c(0,1), c(1000-100, 100) ) repubs = rep( c(0,1), c(1000-90, 90) ) mean(dems) #0.1 mean(repubs) #0.09 del.p = mean(dems) - mean(repubs) #0.01 (point estimate) reps = replicate( 1000, { ds = sample( dems, 1000, replace=TRUE ) rs = sample( repubs, 1000, replace=TRUE ) mean( ds ) - mean( rs ) } ) SE = sd( reps ) # 0.0131 c( del.p - 2*SE, del.p + 2*SE ) #-0.0162 0.0362 (interval estimate) 52
- 53. H1: political party affects the nightlife-preferences H0: political party does not affects the nightlife- preferences Proportion of users who visited nightclubs not matter which party they belong to: 190/2000 = 0.095 If political affinities have no effect, we would expect the following frequencies: 53 Democrats Republicans yes 100 90 190 no 900 910 1810 Democrats Republicans yes 95 95 190 no 905 905 1810
- 54. χ2= 𝑜−𝑒 2 𝑒 = 0.5815 DF = (number of rows – 1) x (number of columns – 1) = 1 Critical value of χ2 at 5% significance and 1 DF is 3.84 Our χ2 does not exceed the critical value We cannot reject H0 54 Democrats Republicans yes 100 90 190 no 900 910 1810
- 55. If α=0.05 then 95% of all values fall in this interval Two-tail test: 2.5% of values in the upper tail and 2.5% of the lower tail are considered as so extreme that we reject H0 if we observe them 55
- 56. Test if democrats on fb, on average, have more than 60 bar visits per year H1: µ > 60 H0: µ <= 60 Random sample of 20 democratic fb-user: {65 73 51 67 48 80 69 53 59 62 71 67 64 78 65 490 80 60 51 70} Sample mean 𝜇=64.1 Assume we know SD in population = 10 𝑧 = 𝜇− 𝜇 𝑆𝐸 𝑆𝐸 = 𝑆𝐷 𝑛 𝑧 = 64.1−60 10/ 20 = 1.8336 56
- 57. Would we expect that? How extreme is this observation? If H0 is true (mean<=60) in which area around the mean do 95% of all points lie Pick alpha level α=0.05 that’s the maximum probability where you reject the null hypothesis if the null hypothesis is true Right-tail test: find our critical value for 0.45 using the z-distribution If the z-score of our observed data exceed this value we have to reject H0 57 1.8336 > 1.645 reject the null hypothesis
- 58. Large Effects, Small Samples: In small samples it is easy to overestimate an effect which might have happened by chance Small Effects, Large Samples: The smaller the effect you want to measure the larger the sample size you need to prove it significant! Example: Assume a coin is biased: 10% head and 90% tail Tossing the coin 10 times should be enough to convince people that the coin is biased. Example: Assume a coin is biased: 51% head and 49% tail Minimum sample size increases with decreasing effect size which one wants to demonstrate 58
- 59. The more we analyze, the more we find by chance! If you calculate correlation between 10 variables (i.e., 44 different correlation coefficients) you should expect that at least 2 correlations are significant with p < 0.05 by chance (one in every 20) Corrections or adjustments for the total number of comparison are needed! 59
- 60. Many tests such as z-test, t-test, ANOVA make the normality assumption. If true population is very skewed (e.g. power law) the sampling distribution of the statistic will not be normal Nonparametric methods like sign-test use e.g. median rather than the mean Hypothesis about the median of the true population (e.g. H1: median < 100, H0: median = 100) Count number of measurements that favor the null hypothesis If H0 is true half of the measurement should fall on each side. 60
- 61. Data Collection Data Preprocessing Data Mining DataAnalysis Statistical Inference DataVisualization Machine Learning Data Preservation
- 62. Aim Find a function that describes the relation between X (e.g. bar visits) andY (e.g. new friends) Given X predictY Problem Infinite number of ways X andY could be related Idea Reduce space of possible function and start with the simplest one (linear relation) Y= 𝑏0 + 𝑏1 𝑋 62
- 63. Y = 2 + 0.5 X 63 6 4 2 0 Y X 0 2 4 6 8
- 64. Use Gradient Descent to minimize Cost function C 𝑏0, 𝑏1 C 𝑏0, 𝑏1 = 1 2𝑁 (𝑌𝑖−𝑌𝑖)2𝑁 𝑖=1 C 𝑏0, 𝑏1 = 1 2𝑁 (𝑌𝑖 − 𝑏0 − 𝑏1 𝑋)2𝑁 𝑖=1 Start with some guess for 𝑏0, 𝑏1 Keep changing 𝑏0, 𝑏1 to reduce C 𝑏0, 𝑏1 until we hopefully end up at a minimum 64
- 65. 𝑏0 ≔ 𝑏0 − 𝛼 𝜕 𝜕𝑏 𝑗 C 𝑏0, 𝑏1 𝑏1 ≔ 𝑏1 − 𝛼 𝜕 𝜕𝑏 𝑗 C 𝑏0, 𝑏1 Simultaneous updates of b0 and b1 65 Derivative of cost function informs us about the slope of the cost function Learning rate
- 66. 66 C(b) b
- 67. Residuals: deviation between the observed and the predicted values Residual sum of squares: 67 Is this a good measure? No it depends on the number of observations N What if we multiply it with 1/N?
- 68. 𝑦𝑖… observed value 𝑦 … value predicted by the model 𝑦 … mean of observed data 68 Total variability in the outcome that needs to be explained Unexplained variability! Residuals: difference between the observed value and the estimated value Proportion of the total variability unexplained by the model
- 69. Independent variable is binary (e.g., went to nightclub or not) We can group users by number of new friends year (20-25, 25-30, 30-35, etc.) and compute the proportion of people with high “nightclub-probability” 69
- 70. Logistic Regression: Maximum Likelihood Estimator Estimate unknown coefficients by maximizing the log likelihood function Coefficient is interpreted as the rate of change in the "log odds" as X changes 70 ln 𝑃(𝑌 = 1) 1 − 𝑃(𝑌 = 1) = 𝑏0 + 𝑏1X + ϵ
- 71. Simple Example: You have a coin that you know is biased towards heads and you want to know what the probability of heads (p) is. We want to estimate the unknown parameter p! 71
- 72. You flip the coin 10 times and the coin comes up head 7 times. What’s your best guess for p? 72
- 73. 3737 )1( !3!7 !10 )1( 7 10 )heads7( ppppP Find the value for p that makes our data most likely! The probability of observing 7 times head when tossing a coin 10 times is given by this binomial distribution: 73
- 74. )1log(3log7 !3!7 !10 loglog ppLikelihood Set the derivative equal to 0 and solve for p. Derivative with respect to p. pp Likelihood dp d 1 37 0log 10 7 107377 3)1(70 )1( 3)1(7 0 1 37 p ppp pp pp pp pp *derivative of a constant is 0 *derivative 7f(x)=7f '(x) *derivative of log x is 1/x 3737 )1( !3!7 !10 )1( 7 10 ppppLikelihood 74 web.stanford.edu/~kcobb/hrp261/lecture4.ppt
- 75. 267.)3(.)7(.120)3(.)7(. 7 10 LikelihoodtheofValue 3737 Likelihood of observing 7 times head when tossing a biased coin with p(head) = 0.7 and p(tail)=0.3 10 times is: 75
- 76. Linear Regression (R-squared) Logistic Regression (pseudo R-squared) 76
- 77. you can “prove” anything with graphics Data Collection Data Preprocessing DataAnalysis DataVisualization Data Preservation
- 78. 78
- 79. 79 http://www.motherjones.com/kevin-drum/2012/01/lying-charts-global-warming-edition
- 80. 80 http://www.motherjones.com/kevin-drum/2012/01/lying-charts-global-warming-edition
- 81. Be careful when drawing conclusions from graphs Size of effect shown in graphic != Size of effect in sample data != Size of the effect in the true population Scale Disorting (e.g., bar charts not starting with zero) Snapshot … 81
- 82. Data Collection Data Preprocessing DataAnalysis DataVisualization Data Preservation
- 83. GESIS Data Archives & Data Centers Preserve research data and make them accessible for reuse. Competencies and infrastructure ▪ e.g. https://datorium.gesis.org/xmlui/ CESSDA: umbrella organisation for the European national data archives (http://www.cessda.net/) Re3data browse data archives by topic: http://www.re3data.org/ 83 DPC Digital Preservation Handbook: http://www.dpconline.org/advice/preservationhandbook
- 84. Legal and regulatory framework including open access and licenses Incentives to share data Credentials? Citation principles under development (see e.g. http://www.datacite.org/). Long term preservation strategies software and hardware changes, documentation, metadata and retrieval/access Data preservation starts at an individual level Reasons for data loss often on an individual level, e.g. broken hardware, researchers leaving a group. 84
- 85. http://claudiawagner.info/teaching/WebSciSS2014/
- 86. Vasant Dhar. Data Science and Prediction. In: Communications of the ACM, December 2013,Vol. 56, No. 12, pp. 64-73 Anand Rajaraman, Jeffrey Ullman, Jure Leskovec, Mining of Massive Datasets, Cambridge University Press (free download) Jeffrey Stanton, Introduction to Data Science (free download) Steffen Staab, Data Science Course University Koblenz-Landau, https://www.uni-koblenz-landau.de/campus- koblenz/fb4/west/teaching/ss14/data-science/data-science1 Serious Stats,Thom Baguley 86

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