Interacting with Data

1. Interacting with Data Materials from a Course in Princeton University -- Hu Yan

2. Outline • Introduction to this course • Introduction to Classification • The Nearest Neighbor Algorithm • Decision Tree Algorithm • Conclusion and future talks

3. What is this course about? • This course is about data! • how to get the most out of data and convert data into knowledge, information or predictions. • Examples of the datasets • credit cards: every purchase you make is tracked, used to detect fraud, marketing purposes, make predictions • security cameras: used for tracking (enforce fine), or finding criminals via facial recognition software. • articles: articles are indexed in multiple databases, organize articles by topics or even track the evolution of topics over time. • There are all kinds of data • Text, images, transaction records, etc.

4. Tasks • make predictions or classifications • classify customers whether or not switch companies • cluster or organize data • cluster articles by topic • different from classification: don’t know the classes ahead of time • find “simple” descriptions of complex objects • find a simple description of faces • identify what is typical and what is an outlier • identify purchases that are typical or unusual for a given customer

5. Perspective • Related fields • Pattern recognition (from 60s) primarily concerns with images • Machine learning (from 80s) was a natural outgrowth of Artificial Intelligence (AI) • Data mining (from 90s) in order to deal with the vast amounts of data to discover “interesting patterns” • This course is largely a mixture of statistics, machine learning, and data mining • Look at interacting with data: • Classification, clustering, regression, and dimensionality reduction

6. Outline • Introduction to this course • Introduction to Classification • The Nearest Neighbor Algorithm • Decision Tree Algorithm • Conclusion and future talks

7. Introduction to Classification • Classifying objects from a data set based on a certain characteristic. • Binary classification: positive or negative. • Classification learning algorithm • Input: labeled data sets • Output: classifier (predict the label of input unclassified examples)

8. Example • classification criterion: any integer greater than 196 or less than 47 will be labeled negative, and positive otherwise.

9. Example • a decimal integer is positive if the second and sixth most significant bits in its binary representation are set; it’s negative otherwise.

10. Outline • Introduction to this course • Introduction to Classification • The Nearest Neighbor Algorithm • Decision Tree Algorithm • Conclusion and future talks

11. The Nearest Neighbor Algorithm • Training • There are m training examples. • Each training example is of the form (xi, yi), where xi \in Rn and yi \in {v1, …, vs}. • Store all the training examples. • Testing. • Given a test point x, predict yi where xi is the closest training example to x.

12. The Nearest Neighbor Algorithm • is a kind of Instance-based learning methods. • referred as to “lazy” learning methods. • Simply store the training examples, delay processing until a new instance must be classified • Some methods construct a general, explicit description of the target function when training examples are provided • advantage: instead of estimating the target function once for the entire space, estimate it locally and differently for each new instance. • disadvantage: the cost of classifying new instances can be high.

13. k-Nearest Neighbor Algorithm

14. k-Nearest Neighbor Algorithm • Two-dimensional space • Positive, negative • 1-nearest neighbor: xq + • 5-nearest neighbor: xq -

15. k-Nearest Neighbor Algorithm • Never forms an explicit general hypothesis f^ regarding the target function f • Simply computes the classification of each new query instance as needed • What’s the implicit general function?

16. Distance-weighted k-Nearest Neighbor Algorithm • Obvious refinement • Weight the contribution of each of the k neighbors according to their distance to the query point.

17. Curse of dimensionality • Imagine instances described by 20 attributes but only 2 are relevant to target function • Curse of dimensionality nearest neighbor is easily mislead when high-dimensional • One approach • Stretch jth axis by weight zj where z1, …, zn chosen to minimize prediction error • Use cross-validation to automatically choose weights z1, …, zn • Note setting zj to zero eliminates this dimension altogether

18. Outline • Introduction to this course • Introduction to Classification • The Nearest Neighbor Algorithm • Decision Tree Algorithm • Decision tree representation • ID3 learning algorithm • Entropy, Information gain • Overfitting • Conclusion and future talks

19. Decision tree for PlayTennis

20. Decision tree representation • Instances are represented by attribute-value pairs • Each internal node tests an attribute • Each branch corresponds to attribute value • Each leaf node assigns a classification • In general, decision tree represent a disjunction of conjunctions of constraints on the attribute values of attributes tests.

21. Building a Decision tree • ID3 (1986), C4.5 (1993) • A top-down, greedy search through the space of possible decision trees. • Main loop: • A the best decision attribute for next node; • Assign A as decision attribute for node; • For each value of A create new branch of node; • Sort training examples to leaf nodes; • If training examples perfectly classified Then STOP Else iterate over new leaf nodes;

22. Entropy • S is a sample of training examples • p+ is the proportion of positive examples in S • p - is the proportion of negative examples in S • Entropy measures the impurity of S Entropy ([9+,5-]) = -(9/14)log2(9/14) - (5/14)log2(5/14) = 0.940

23. Entropy function • Entropy(S) = expected number of bits needed to encode class (+ or -) of randomly drawn member of S (under the optimal shortest-length code)

24. Information Gain

25. Information Gain • S is a collection of training example days described by attributes including Wind, which have the values Weak and Strong. • S contains 14 examples, [9+, 5-] • 6 of the positive and 2 of the negative examples have Wind = Weak, and the remainder have Wind = Strong.

26. Training Examples

27. Which Attribute Is the Best Classifier • Information gain is the measure used by ID3 to select the best attribute at each step in growing the tree. • Example: information gain of two attributes: Humidity, and Wind, is computed to determine witch is better for classifying the training examples.

28. An Illustrative Example Gain(S,Outlook) = 0.245 Gain(S,Humidity) = 0.151 Gain(S,Wind) = 0.048 Gain(S,Temp) = 0.029 Which attributes should be tested here?

29. Selecting the Next Attribute Ssunny = {D1,D2,D8,D9,D11} Gain (Ssunny, Humidity) =0 .970 Gain (Ssunny, Temp) = 0.570 Gain (Ssunny, Wind)= 0.019 4,5,6,10,14 1,2,8,9,11 3,7,12,13 1,2,8 9,11

30. Hypothesis Space Search by ID3 ID3 search through the space of possible decision trees from simple to increasingly complex, guided by the information gain Gain(S,A)

31. Hypothesis Space Search by ID3 • ID3 searches a complete hypothesis space, it searches incompletely through the space. • Outputs a single hypothesis; • No back tracking, converging to Local optimal solution (maybe not global optimal); • Using statistical properties, robust to noisy data; • Inductive bias: Preference for short trees and for those with high information gain attributes near the root

32. Gain(s) = -2/5 log22/5 – 3/5 log23/5 = 0.971 Gain(S,humid) = 0.405 Gain(S,wind) = Gain(S,Temp) =0.805 humid [2+,3-] [2+,3-] normal high wind 2,4,5 1,3 weak strong [2+,1-] temp N 1,2,4 3,5 hot cool [1+,2-] temp humid [1+,1-] 2, 5 4 [1+,1-] wind Y cool normal high hot 1,2 weak 4 5 3 strong 5 N Y Y N 2 N Y

33. Overfitting in Decision Tree Learning Consider error of hypothesis h over • training data errortrain(h) • entire distribution D of data errorD(h) Hypothesis h \in H overfits training data if there is an alternative hypothesis h’ \in H such that errortrain(h) < errortrain(h’) AND errorD(h) >errorD(h’)

34. Overfitting in Decision Tree Learning

35. Avoiding Overfitting • How can we avoid overfitting? • stop growing before it reaches the point where it perfect classifies the training dada • grow full tree then post-prune (widely used) • How to select best tree during the pruning? • Split data into training and validation set • build decision tree over training data • measure performance over separate validation data set • Two ways of pruning: • reduced-error pruning • rule post pruning

36. Reduced Error Pruning 1. Split data into training and validation set 2. Build the tree over training data 3. For each of the decision node • Evaluate impact on validation set of pruning each decision node • remove the one that improves validation set accuracy • removing the subtree rooted at that node, making it a leaf node • assigning it the most common classification of the training examples affiliated with that node

37. Effect of Reduced-Error Pruning

38. Rule Post Pruning • Convert tree to equivalent set of rules (if-then expression) • Prune (generalize) each rule by removing any preconditions that improves its estimated accuracy • Sort the pruned rules by their estimated accuracy (can be used in classifying subsequent instances) IF (Outlook= Sunny) and (Humidity = High) THEN PlayTennis = No IF (Outlook = Sunny) and (Humidity = Normal) THEN PlayTennis = Yes ….

39. Conclusion • Interacting with data • how to get the most out of data and convert data into knowledge, information or predictions • Classification, clustering, regression, and dimensionality reduction • Classification • categorize objects into particular classes based on their attributes • The Nearest Neighbor Algorithm • Decision Tree Algorithm

40. Contents • Classification • K-nearest-neighbor algorithm, Decision trees • Computational learning theory • Boosting, Support vector machines • Clustering • K-means clustering, Agglomerative clustering • Graphic Models (a marriage of probability theory and graph theory) • Naive Bayes classification, EM (Expectation-Maximization) algorithm • Regression (predict a real value quantity based on observed data) • Linear regression, Logistic regression • Dimensionality Reduction (reduce the representation of data) • PCA (Principal Components Analysis), Factor analysis • Advanced Topics and Applications

41. Thank you !