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Decision Tree Learning

Decision Tree Learning. 主講人：虞台文 大同大學資工所 智慧型多媒體研究室. Content. Introduction CLS ID3 C4.5 References. Decision Tree Learning. Introduction. Examples. Generalize. Instantiated for another case. Inductive Learning. Prediction. Model.

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Decision Tree Learning

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  1. Decision Tree Learning 主講人：虞台文 大同大學資工所 智慧型多媒體研究室

  2. Content • Introduction • CLS • ID3 • C4.5 • References

  3. Decision Tree Learning Introduction

  4. Examples Generalize Instantiated for another case Inductive Learning Prediction Model The general conclusion should apply to unseen examples.

  5. Decision Tree • A decision tree is a tree in which • each branch node represents a choice between a number of alternatives • each leaf node represents a classification or decision

  6. Example I

  7. Example II

  8. Decision Rules

  9. Decision Tree Learning • We wish to be able to induce a decision tree from a set of data about instances together with the decisions or classifications for those instances. • Learning Algorithms: • CLS (Concept Learning System) • ID3  C4  C4.5 C5

  10. Appropriate Problems forDecision Tree Learning • Instances are represented by attribute-value pairs. • The target function has discrete output values. • Disjunctive descriptions may be required. • The training data may contain errors. • The training data may contain missing attribute values.

  11. Decision Tree Learning CLS

  12. CLS Algorithm • T the whole training set. Create a T node. • If all examples in T are positive, create a ‘P’ node with T as its parent and stop. • If all examples in T are negative, create a ‘N’ node with T as its parent and stop. • Select an attribute X with values v1, v2, …, vN and partition T into subsets T1, T2, …, TN according their values on X. Create N nodes Ti(i = 1,..., N) with T as their parent and X = vi as the label of the branch from T to Ti. • For each Tido: TTi and goto step 2.

  13. (tall, blond, blue) w (short, black, brown) e (short, silver, blue) w (tall, silver, black) e (short, black, blue) w (short, black, brown) e (tall, blond, brown) w (tall, black, brown) e (tall, silver, blue) w (tall, black, black) e (short, blond, blue) w (short, blond, black) e Example

  14. (tall, blond, blue) w (short, black, brown) e (short, silver, blue) w (tall, silver, black) e (short, black, blue) w (short, black, brown) e tall short (tall, blond, brown) w (tall, black, brown) e (tall, silver, blue) w (tall, black, black) e (short, blond, blue) w (short, blond, black) e (tall, blond, blue) w (tall, silver, black) e (short, silver, blue) w (short, black, brown) e (tall, blond, brown) w (tall, black, brown) e (short, black, blue) w (short, black, brown) e blond black black silver (tall, silver, blue) w (tall, black, black) e (short, blond, blue) w (short, blond, black) e (short, black, blue) w (tall, blond, blue) w (tall, black, brown) e (short, silver, blue) w (short, black, brown) e (tall, blond, brown) w blond (tall, black, black) e silver (short, black, brown) e brown (short, blond, blue) w (short, blond, black) e (short, black, brown) e (tall, silver, black) e (short, black, brown) e blue (tall, silver, blue) w black blue blue black (short, blond, blue) w (short, black, blue) w (tall, silver, black) e (tall, silver, blue) w (short, blond, black) e Example

  15. (tall, blond, blue) w (short, black, brown) e (short, silver, blue) w (tall, silver, black) e (short, black, blue) w (short, black, brown) e (tall, blond, brown) w (tall, black, brown) e (tall, silver, blue) w (tall, black, black) e (short, blond, blue) w (short, blond, black) e blue brown black (tall, blond, blue) w (short, black, brown) e (tall, silver, black) e (short, black, brown) e (short, silver, blue) w (tall, black, black) e (tall, black, brown) e (short, black, blue) w (short, blond, black) e (tall, blond, brown) w (tall, silver, blue) w (short, blond, blue) w blond black (tall, blond, brown) w (short, black, brown) e (short, black, brown) e (tall, black, brown) e Example

  16. Decision Tree Learning ID3

  17. (tall, blond, blue) w (short, black, brown) e (short, silver, blue) w (tall, silver, black) e (short, black, blue) w (short, black, brown) e (tall, blond, brown) w (tall, black, brown) e (tall, silver, blue) w (tall, black, black) e (short, blond, blue) w (short, blond, black) e Entropy (Binary Classification) S= C1 : Class 1 C2: Class 2

  18. Entropy (Binary Classification)

  19. Entropy (Binary Classification)

  20. + +  + +   + + + + +   Entropy (Binary Classification) # + = 9 # – = 6

  21. + + + + + +  + + + + + + + + Entropy (Binary Classification) # + = 14 # – = 1

  22. S v1 v2 vn S1 S2 Sn Information Gain

  23. (tall, blond, blue) w (short, black, brown) e (short, silver, blue) w (tall, silver, black) e (short, black, blue) w (short, black, brown) e tall short (tall, blond, brown) w (tall, black, brown) e (tall, silver, blue) w (tall, black, black) e (short, blond, blue) w (short, blond, black) e (tall, blond, blue) w (tall, silver, black) e (short, silver, blue) w (short, black, brown) e (tall, blond, brown) w (tall, black, brown) e (short, black, blue) w (short, black, brown) e (tall, silver, blue) w (tall, black, black) e (short, blond, blue) w (short, blond, black) e Information Gain

  24. (tall, blond, blue) w (short, black, brown) e (short, silver, blue) w (tall, silver, black) e (short, black, blue) w (short, black, brown) e (tall, blond, brown) w (tall, black, brown) e (tall, silver, blue) w (tall, black, black) e (short, blond, blue) w (short, blond, black) e blond silver black (tall, blond, blue) w (short, silver, blue) w (short, black, blue) w (tall, silver, blue) w (tall, blond, brown) w (short, black, brown) e (tall, silver, black) e (short, blond, blue) w (short, black, brown) e (tall, black, brown) e (short, blond, black) e (tall, black, black) e Information Gain

  25. (tall, blond, blue) w (short, black, brown) e (short, silver, blue) w (tall, silver, black) e (short, black, blue) w (short, black, brown) e blue brown black (tall, blond, brown) w (tall, black, brown) e (tall, silver, blue) w (tall, black, black) e (short, blond, blue) w (short, blond, black) e (tall, blond, blue) w (short, black, brown) e (tall, silver, black) e (short, black, brown) e (short, silver, blue) w (tall, black, black) e (tall, black, brown) e (short, black, blue) w (short, blond, black) e (tall, blond, brown) w (tall, silver, blue) w (short, blond, blue) w Information Gain

  26. (tall, blond, blue) w (short, black, brown) e (short, silver, blue) w (tall, silver, black) e (short, black, blue) w (short, black, brown) e (tall, blond, brown) w (tall, black, brown) e (tall, silver, blue) w (tall, black, black) e (short, blond, blue) w (short, blond, black) e Information Gain

  27. ID3 • Iterative Dichotomizer (version) 3 • developed by Quinlan • Select decision sequence of the tree based on information gain.

  28. ID3 (modify of CLS) • T the whole training set. Create a T node. • If all examples in T are positive, create a ‘P’ node with T as its parent and stop. • If all examples in T are negative, create a ‘N’ node with T as its parent and stop. • Select an attribute X with values v1, v2, …, vN and partition T into subsets T1, T2, …, TN according their values on X. Create N nodes Ti(i = 1,..., N) with T as their parent and X = vi as the label of the branch from T to Ti. • For each Tido: TTi and goto step 2.

  29. ID3 (modify of CLS) By maximizing the information gain. • T the whole training set. Create a T node. • If all examples in T are positive, create a ‘P’ node with T as its parent and stop. • If all examples in T are negative, create a ‘N’ node with T as its parent and stop. • Select an attribute X with values v1, v2, …, vN and partition T into subsets T1, T2, …, TN according their values on X. Create N nodes Ti(i = 1,..., N) with T as their parent and X = vi as the label of the branch from T to Ti. • For each Tido: TTi and goto step 2.

  30. (tall, blond, blue) w (short, black, brown) e (short, silver, blue) w (tall, silver, black) e (short, black, blue) w (short, black, brown) e (tall, blond, brown) w (tall, black, brown) e (tall, silver, blue) w (tall, black, black) e (short, blond, blue) w (short, blond, black) e blue brown black (tall, blond, blue) w (short, black, brown) e (tall, silver, black) e (short, black, brown) e (short, silver, blue) w (tall, black, black) e (tall, black, brown) e (short, black, blue) w (short, blond, black) e (tall, blond, brown) w (tall, silver, blue) w (short, blond, blue) w blond black (tall, blond, brown) w (short, black, brown) e (short, black, brown) e (tall, black, brown) e Example

  31. + + + + – + + + + + + + – + + + – + + + + + – + + – + + + + – – – + – + – + – + + – + + – + – + – – + + – + – + + + – + – + + + – – + – – + + + + – – – + + + – – – + + – + + – – – + – + – + + – + – + – – + + – + + + + – – + + – + + – – + – + + + – – – – Windowing

  32. Windowing • ID3 can deal with very large data sets by performing induction on subsets or windows onto the data. • Select a random subset of the whole set of training instances. • Use the induction algorithm to form a rule to explain the current window. • Scan through all of the training instances looking for exceptions to the rule. • Add the exceptions to the window • Repeat steps 2 to 4 until there are no exceptions left.

  33. Inductive Biases • Shorter trees are preferred. • Attributes with higher information gain are selected first in tree construction. • Greedy Search • Preference bias (relative to restriction bias as in the VS approach) • Why prefer short hypotheses? • Occam's razor Generalization

  34. Hypothesis Space Search • Complete hypothesis space • because of disjunctive representation • Incomplete search • No backtracking • Non-incremental • but can be modified to be incremental • Ensemble statistical information for node selection • less sensitive to noise than the VS approach in this sense

  35. Overfitting to the Training Data • The training error is statistically smaller than the test error for a given hypothesis. • Solutions: • Early stopping • Validation sets • Statistical criterion for continuation (of the tree) • Post-pruning • Minimal description length cost-function = error + complexity

  36. Overfitting to the Training Data

  37. Pruning Techniques • Reduced error pruning (of nodes) • Used by ID3 • Rule post-pruning • Used by C4.5

  38. Reduced Error Pruning • Use a separated validation set • Tree accuracy: • percentage of correct classifications on validation set • Method: Do until further pruning is harmful • Evaluate the impact on validation set of pruning each possible node. • Greedily remove the one that most improves the validation set accuracy.

  39. Reduced Error Pruning

  40. Decision Tree Learning C4.5

  41. C4.5:An Extension of ID3 • Some additional features of C4.5 are: • Incorporation of numerical (continuous) attributes. • Nominal (discrete) values of a single attribute may be grouped together, to support more complex tests. • Post-pruning after induction of trees, e.g. based on test sets, in order to increase accuracy. • C4.5 can deal with incomplete information (missing attribute values).

  42. Rule Post-Pruning • Fully induce the decision tree from the training set (allowing overfitting) • Convert the learned tree to rules • one rule for each path from the root node to a leaf node • Prune each rule by removing any preconditions that result in improving its estimated accuracy • Sort the pruned rules by their estimated accuracy, and consider them in this sequence when classifying subsequent instances

  43. Converting to Rules . . .

  44. Temerature<54 Temerature54-85 Temerature>85 Continuous Valued Attributes Example:

  45. Attributes with Many Values • Information Gain – biases to attribute with many values • e.g., date • One approach – use GainRatio instead

  46. Associate Attributes of Cost • The availability of attributes may vary significantly in costs. • Example: Medical disease classification • Temperature • BiopsyResult • Pulse • BloodTestResult High High

  47. Associate Attributes of Cost • Tan and Schlimmer (1990) • Nunez (1988) w [0, 1] determines the importance of cost.

  48. S = Unknown Attribute Values Attribute A={x, y, z} • Assign most common value of A to the unknown one. • Assign most common value of A with the same target value to the unknown one. • Assign probability to each possible value. Possible Approaches:

  49. Decision Tree Learning References

  50. References • “Building Decision Trees with the ID3 Algorithm”, by: Andrew Colin, Dr. Dobbs Journal, June 1996 • “Incremental Induction of Decision Trees”, by Paul E. Utgoff, Kluwer Academic Publishers, 1989 • “Machine Learning”, by Tom Mitchell, McGraw-Hill, 1997 pp. 52-81 • “C4.5 Programs for Machine Learning”, by J. Ross Quinlan, Morgan Kaufmann, 1993 • “Algorithm Alley Column: C4.5”, by Lynn Monson, Dr. Dobbs Journal, Jan 1997

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