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Rule Induction

Rule Induction. Rule Induction Algorithms. Hypothesis Space: Sets of rules (any boolean function) Many ways to search this large space Decision trees -> Rules is one ( simultaneous covering ) Following example: greedy sequential covering algorithm (similar to CN2). Some FOL Terminology.

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Rule Induction

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  1. Rule Induction

  2. Rule Induction Algorithms • Hypothesis Space: Sets of rules (any boolean function) • Many ways to search this large space • Decision trees -> Rules is one (simultaneous covering) • Following example: greedy sequential covering algorithm (similar to CN2)

  3. Some FOL Terminology • Constants: (Mary, 23, Joe) • Variables: (e.g., x, can refer to any constant) • Predicates: (have a truth value; e.g. Female as in Female(Mary)) • Functions: (apply to terms and evaluate to a constant value, e.g. Age(Mary)) • Terms: any constant, variable, or function applied to a term (e.g. Mary, x, Age(x)) • Literals: any predicate applied to terms, e.g. Female(x) or Greater_than(Age(Mary), 20)

  4. Some FOL Terminology (cont.) • Clause: Disjunction of literals with universally quantified variables, e.g. Greater_than(Age(x), 23) v Female(Mary)

  5. Example • Learning Granddaughter(x,y) • Training Data: Target Predicates: Input Predicates: Granddaughter(Victor, Sharon) Father(Sharon, Bob) Father(Tom, Bob) Female(Sharon) Father(Bob, Victor) …all other possible predicates defined over the constants are false (e.g.  Granddaughter(Tom, Bob)…so 15 negative examples of Granddaughter(x, y) as well)

  6. Example: Learning a Rule • Learning one rule: Granddaughter(x, y)  Classifies all examples as positive (makes 15 mistakes) Granddaughter(x, y)  Father(y, z) Makes fewer mistakes Granddaughter(x, y)  Father(y, z) ^ Father(z, x) Makes only one mistake Granddaughter(x, y)  Father(y, z) ^ Father(z, x) ^ Female(y) Makes zero mistakes – output rule; because rule set now covers all positive examples, we are done.

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