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 (current best hypothesis search) Training Set Example Descriptions Classifications X1 Color(X1,Red)  Size(X1,Large)  Shape(X1,Circle) Q(X1) X2 Color(X2,Blue)  Size(X2,Large)  Shape(X2,Square) Q(X2) X3 Color(X3,Red)  Size(X3,Small)  Shape(X3,Square) Q(X3) X4 Color(X4,Green)  Size(X4,Large)  Shape(X4,Triangle) Q(X4) X5 Color(X5,Red)  Size(X5,Small)  Shape(X5,Circle) Q(X5) Only consider candidate definitions that are positive conjunctive sentences

Current-Best Hypothesis Search 1 hypothesis True example: status X1: ok FP = false positive 2 True FN = false negative X2: FP 3 Color(x,Red) Shape(x,Circle) X3: FP X3: ? 4 Color(x,Red)  Size(x,Large) 6 Color(x,Red)  Shape(x,Circle) X4: ok X4: ok 5 Color(x,Red)  Size(x,Large) 7 Color(x,Red)  Shape(x,Circle) X5: FN X5: ok

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

Ordering on Hypothesis Space P(x) Q(x) R(x) P(x)  Q(x) P(x)  R(x) Q(x)  R(x) P(x)  Q(x)  R(x)

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 (version space learning) Training Set Descriptions Classifications Size(X1,Large)  Shape(X1,Circle)  Color(X1,Red) Q(X1) Size(X2,Large)  Shape(X2,Square)  Color(X2,Blue) Q(X2) Size(X3,Small)  Shape(X3,Circle)  Color(X3,Red) Q(X3) Size(X4,Small)  Shape(X4,Circle)  Color(X4,Blue) Q(X4) Size(X5,Large)  Shape(X5,Square)  Color(X5,Red) Q(X5) Only consider candidate definitions that are positive conjunctive sentences