Rule Induction

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Rule Induction

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Rule Induction Algorithms

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

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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)

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Some FOL Terminology (cont.)

• Clause Disjunction of literals with universally
  quantified variables, e.g. Greater_than(Age(x),
  23) v Female(Mary)

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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)

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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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