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**Learning Rules from Data**

Olcay Taner Yıldız, Ethem Alpaydın Department of Computer Engineering Boğaziçi University

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**Rule Induction? Derive meaningful rules from data**

Mainly used in classification problems Attribute types (Continuous, Discrete) Name Income Owns a house? Marital status Default Ali 25,000 $ Yes Married No Veli 18,000 $ No Married Yes

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**Rules Disjunction: conjunctions are binded via OR's**

Conjunction: propositions are binded via AND's Proposition: relation on an attribute Attribute is Continuous (defines a subinterval) Attribute is Discrete (= one of the values of the attribute)

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**How to generate rules? Rule Induction Techniques Via Trees**

C4.5Rules Directly from Data Ripper

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**C4.5Rules (Quinlan, 93) Create decision tree using C4.5**

Convert the decision tree to a ruleset by writing each path from root to the leaves as a rule

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**C4.5Rules q1 x1 > q1 x2 > q2 y = 0 y = 1 yes no q2 x2 : savings**

x1 : yearly-income q1 x1 > q1 x2 > q2 y = 0 y = 1 yes no OK DEFAULT q2 Rules: IF (x1 > q1) AND (x2 > q2) THEN Y = OK IF (x1 < q1) OR ((x1 > q1) AND (x2 < q2)) THEN Y = DEFAULT

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**RIPPER (Cohen, 95) Learn rule for each class Two Steps**

Objective class is positive, other classes are negative Two Steps Initialization Learn rules one by one Immediately prune learned rule Optimization Since search is greeedy, pass k times over the rules to optimize

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**RIPPER (Initialization)**

Split (pos, neg) into growset and pruneset Rule := grow conjunction with growset Add propositions one by one IF (x1 > q1) AND (x2 > q2) AND (x2 < q3) THEN Y = OK Rule := prune conjunction with pruneset Remove propositions IF (x1 > q1) AND (x2 < q3) THEN Y = OK If MDL < Best MDL + 64 Add conjunction Else Break

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**Ripper (Optimization)**

Repeat K times For each rule IF (x1 > q1) AND (x2 < q3) THEN Y = OK Generate revisionrule by adding propositions IF (x1 > q1) AND (x2 < q3) AND (x1 > q3) THEN Y = OK Generate replacementrule by regrowing IF (x1 > q4) THEN Y = OK Compare current rule with revisionrule and replacementrule Take the best according to MDL

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**Minimum Description Length**

Description Length of a Ruleset Description Length of Rules S = ||k|| + k log2 (n / k) + (n – k) log2 (k / (n – k)) Description Length of Exceptions S = log2 (|D| + 1) + fp (-log2 (e / 2C)) + (C – fp) (-log2 (1 - e / 2C)) + fn (-log2 (fn / 2U)) + (U – fn) (-log2 (1 - fn / 2U))

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Ripper* Finding best condition is done by trying all possible split points (time-consuming) Shortcut: Linear Discriminant Analysis Split point is calculated analytically To be more robust Instances further than 3 are removed If number of examples < 20, shortcut not used

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**Experiments 29 datasets from UCI repository are used**

10 fold cross-validation Comparison done using one-sided t test Comparison of three algorithms C4.5Rules, Ripper, Ripper* Comparison based on Error Rate Complexity of the rulesets Learning Time

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Error Rate (I) Ripper and its variant have better performance than C4.5Rules Ripper* has similar performance compared to Ripper C4.5Rules has advantage when the number of rules are small (Exhaustive Search)

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Error Rate (II) C4.5Rules Ripper Ripper* Total - 4 7 12 2 10 1 5 9

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**Ruleset Complexity (I)**

Ripper and Ripper* produce significantly small number of rules compared to C4.5Rules C4.5Rules starts with an unpruned tree, which is a large amount of rule to start

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**Ruleset Complexity (II)**

C4.5Rules Ripper Ripper* Total - 1 26 10 27 2 3 11

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Learning Time (I) Ripper* better than Ripper, which is better than C4.5Rules C4.5Rules O(N3) Ripper O(Nlog2N) Ripper* O(NlogN)

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Learning Time (II) C4.5Rules Ripper Ripper* Total - 2 23 25 13 27

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Conclusion Comparison of two rule induction algorithms C4.5Rules and Ripper Proposed a shortcut in learning conditions using LDA (Ripper*) Ripper is better than C4.5Rules Ripper* improves learning time of Ripper without decreasing its performance

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