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Attribute-valued Problem

Attribute-valued Problem. Table of cars: Predict the attribute ‘ affordable ’ ! Rule discovered: Attribute learning is appropriate. size=small & luxury=low  affordable. Relational Problem (1) [L. De Raedt, 2000]. Positive Examples Negative Examples.

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Attribute-valued Problem

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  1. Attribute-valued Problem • Table of cars: • Predict the attribute ‘ affordable ’ ! • Rule discovered: • Attribute learning is appropriate. size=small & luxury=low  affordable

  2. Relational Problem (1)[L. De Raedt, 2000] • Positive Examples • Negative Examples

  3. Relational Problem (2)[L. De Raedt, 2000] • How to represent in AVL? • Assume fixed number of objects • Problem 1: exchange objects 1 & 2 • exponential number of different representations for the same entity

  4. Relational Problem (3)[L. De Raedt, 2000] • Problem 2: Positional relations •  explosion of false atributes • Problem 3: Variable number of objects • explosion of empty fields • explosion of entire table • We need a more powerful representation!

  5. Relational Problem (4) • Prolog representation positive(example1). Example description in background knowledge: contains(example,object1). contains(example,object2). circle(object1). triangle(object2, down). left_of(object1,object2). Common background knowledge: left_of(X,Y):- left_of(X,Z), left_of(Z,Y).left_of(X,Y):- left_of(Z,Y), inside(Z,X).(…) Possible rule:positive(X) :- contains(X,O), triangle(O,down).

  6. Deduction (in Logic Programming) Apriori (background) knowledge about integers Theory (hypothesis) about addition suc(X,Y)  X is Y-1. add(0,X,X). add(X,Y,Z)  suc(A,X) & suc(B,Z) & add(A,Y,B). add(1,1,2), add(3,5,8), add(4,1,5), ... add(1,3,5), add(8,7,6), add(1,1,1), ... Positive examples of addition Negative examples of addition

  7. Induction(in Inductive Logic Programming) Apriori (background) knowledge about integers Positive and negative examples of addition suc(X,Y)  X is Y-1. add(1,1,2), add(3,5,8), add(4,1,5), ... add(1,3,5), add(8,7,6), add(1,1,1), ... add(0,X,X). add(X,Y,Z)  suc(A,X) & suc(B,Z) & add(A,Y,B). Theory (hypothesis) about addition

  8. Basic ILP Technique (1) • Search through a clause implication lattice • From general to specific (top-down) • From specific to general (bottom-up) add(X,Y,Z) add(X,Y,Z)  suc(A,X) add(X,Y,Z)  suc(B,Z) add(X,Y,Z)  suc(A,X), suc(B,X) ... etc. add(X,Y,Z)  suc(A,X) & suc(B,Z) & add(A,Y,B)

  9. Basic ILP Technique (2) • Clauses usually constructed one-by-one • e.g. specialize until covers no negatives,then begin a new clause for the rest of positives • Implication is undecidable • instead use syntactic. subsumtion (NP - hard) • measure generality of clause with background knowledge • Efficiency: use strong bias! • syntactical: • indicate input/output vars; maximum clause length • semantical: e.g. preference heuristics

  10. Mutagenecity Prediction[Srinivasan, 1995] • Predict mutagenecity (carcinogenecity) of chemicals with general system Progol [Muggleton] • Examples: compounds Active Inactive • Result: structural alert

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