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

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

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

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

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

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 )