CS 478 - Learning Rules PowerPoint Presentation, PPT - DocSlides

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Slide1

CS 478 - Learning Rules

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Learning Sets of Rules

Slide2

CS 478 - Learning Rules

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Learning Rules

If (Color = Red) and (Shape = round) then Class is A

If (Color = Blue) and (Size = large) then Class is B

If (Shape = square) then Class is A

Natural and intuitive hypotheses

Comprehensibility - Easy to understand?

Slide3

CS 478 - Learning Rules

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Learning Rules

If (Color = Red) and (Shape = round) then Class is A

If (Color = Blue) and (Size = large) then Class is B

If (Shape = square) then Class is A

Natural and intuitive hypotheses

Comprehensibility - Easy to understand?

Ordered (Prioritized) rules - default at the bottom, common but not so easy to comprehend

Unordered rules

Theoretically easier to understand, except must

Force consistency, or

Create a separate unordered list for each output class and use a tie-break scheme when multiple lists are matched

Slide4

CS 478 - Learning Rules

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Sequential Covering Algorithms

There are a number of rule learning algorithms based on different variations of sequential covering

CN2, AQx, etc.

Find a “good” rule for the current training set

Delete covered instances (or those covered correctly) from the training set

Go back to 1 until the training set is empty or until no more “good” rules can be found

Slide5

CS 478 - Learning Rules

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Finding “Good” Rules

The large majority of instances covered by the rule infer the same output class

Rule covers as many instances as possible (general vs specific rules)

Rule covers enough instances (statistically significant)

Example rules and approaches?

How to find good rules efficiently? - General to specific search is common

Continuous features - some type of ranges/discretization

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CS 478 - Learning Rules

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Common Rule “Goodness” Approaches

Relative frequency: nc/nm-estimate of accuracy (better when n is small): where p is the prior probability of a random instance having the output class of the proposed rule, penalizes rules with small n, Laplacian common: (nc+1)/(n+|C|) (i.e. m = 1/pc)Entropy - Favors rules which cover a large number of examples from a single class, and few from othersEntropy can be better than relative frequencyImproves consequent rule induction. R1:(.7,.1,.1,.1) R2 (.7,0.3,0) - entropy selects R2 which makes for better subsequent specializations during later rule growthEmpirically, rules of low entropy have higher significance than relative frequency, but Laplacian often better than entropy

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CS 478 - Learning Rules

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CS 478 - Learning Rules

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CS 478 - Learning Rules

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Slide10

CS 478 - Learning Rules

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Learning First Order Rules

Inductive Logic Programming

Propositional vs. first order rules

1st order allows variables in rules

If Color of object1 =

x

and Color of object 2 =

x

then Class is A

More expressive

FOIL - Uses a sequential covering approach from general to specific which allows the addition of literals with variables

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CS 478 - Learning Rules

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RIPPER

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Insert Rules at Top or Bottom

Typically would like focused exception rules higher and more general rules lower in the listTypical (CN2): Delete all instances covered by a rule during learningPutting new rule on the bottom (i.e. early learned rules stay on top) makes sense since this rule is rated good only after removing all instances covered by previous rules, (i.e. instances which can get by the earlier rules).Still should get exceptions up top and general rules lower in the list because exceptions will achieve a higher score and thus be added first (assuming statistical significance) than a general rule which has to cover more cases. Even though E keeps getting diminished there should still be enough data to support reasonable general rules later (in fact the general rules should get increasing scores after true exceptions are removed).Highest scoring rules: Somewhat specific, high accuracy, sufficient coverageMedium scoring rules: General and specific with reasonable accuracy and coverageLow scoring rules: Specific with low coverage, and general with low accuracy

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Rule Order - Continued

If delete only correct instances covered by a rulePutting new rule on the the top (i.e. first learned rule stays on bottom) could make sense because we could learn exception rules for those instances not covered by general rules at the bottomThis only works if the rule placed at the bottom is truly more general than the later rules (i.e. many novel instances will slide past the more exceptional rules and get covered by the general rules at the bottom)Sort after: (Mitchell) Proceed with care because rules were learned based on specific subsets of the training setOther variations possible, but many could be problematic because there are an exponential number of possible orderingsAlso can do unordered lists with tie-breaking mechanisms

CS 478 - Learning Rules

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