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Ch. 19 – Knowledge in Learning Supplemental slides for CSE 327 Prof. Jeff Heflin

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Current Best Hypothesis Search function CURRENT-BEST-LEARNING(examples) returns a hypothesis H any hypothesis consistent with the first example in examples for each remaining example in examples do if e is false positive for H then H choose a specialization of H consistent with examples else if e is false negative for H then H choose a generalization of H consistent with examples if no consistent specialization/generalization can be found then fail return H Note: here choose is a special operator that allows you to backtrack to a previous choice and select another option when the search fails. An actual implementation would probably use depth-first search instead. From Figure 19.2, p. 681

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Example Learning Problem ExampleDescriptionsClassifications X1X1 Color(X 1,Red) Size(X 1,Large) Shape(X 1,Circle) Q(X 1 ) X2X2 Color(X 2,Blue) Size(X 2,Small) Shape(X 2,Square) Q(X 2 ) X3X3 Color(X 3,Red) Size(X 3, Small) Shape(X 3,Square) Q(X 3 ) X4X4 Color(X 4,Green) Size(X 4,Large) Shape(X 4,Triangle) Q(X 4 ) X5X5 Color(X 5,Red) Size(X 5,Small) Shape(X 5,Circle) Q(X 5 ) Only consider candidate definitions that are positive conjunctive sentences Training Set

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Version Space Learning function VERSION-SPACE-LEARNING(examples) returns a version space local variables: V, the version space (the set of all hypotheses) V the set of all hypotheses for each example e in examples do if V is not empty then V VERSION-SPACE-UPDATE(V,e) return V function VERSION-SPACE-UPDATE(V,e) returns an updated version space V {h V: h is consistent with e} return V From Figure 19.3, p. 683

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Version Space Update Details function VERSION-SPACE-UPDATE(G,S,e) returns an updated G-set and S-set (version space) for each g in G if e is a false positive for g G G – g G G {h : h is the most general specialization of g that is consistent with e and h is more general than some member of S} else if e is a false negative for g G G – g for each s in S if e is a false positive for s S S – s else if e is a false negative for s S S – s S S {h : h is the most specific generalization of s that is consistent with e and h is more specific than some member of G} return G,S

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Example Learning Problem Only consider candidate definitions that are positive conjunctive sentences Training Set Descriptions Classifications Size(X 1,Large) Shape(X 1,Circle) Color(X 1,Red) Q(X 1 ) Size(X 2,Large) Shape(X 2,Square) Color(X 2,Blue) Q(X 2 ) Size(X 3,Small) Shape(X 3,Circle) Color(X 3,Red) Q(X 3 ) Size(X 4,Small) Shape(X 4,Circle) Color(X 4,Blue) Q(X 4 ) Size(X 5,Large) Shape(X 5,Square) Color(X 5,Red) Q(X 5 )

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