Speeding Up Relational Data Mining by Learning to Estimate Candidate Hypothesis Scores Frank DiMaio and Jude Shavlik UW-Madison Computer Sciences ICDM Foundations and New Directions of Data Mining Workshop 19 November 2003

Rule-Based Learning Goal: Induce a rule (or rules) that explains ALL positive examples and NO negative examples positive examplesnegative examples

Inductive Logic Programming (ILP) Encode background knowledge in first-order logic as facts… containsBlock(ex1,block1A). containsBlock(ex1,block1B). is_red(block1A). is_square(block1A). is_blue(block1B). is_round(block1B). on_top_of(block1B,block1A). above(A,B) :- onTopOf(A,B) above(A,B) :- onTopOf(A,Z), above(Z,B). and logical relations …

Inductive Logic Programming (ILP) Covering algorithm applied to explain all data Choose some positive exampleGenerate best rule that covers this exampleRemove all examples covered by this ruleRepeat until every positive example is covered

Inductive Logic Programming (ILP) Saturate an example by writing everything true about it The saturation of an example is the bottom clause (  ) A C B positive(ex2) :- contains_block(ex2,block2A), contains_block(ex2,block2B), contains_block(ex2,block2C), isRed(block2A), isRound(block2A), isBlue(block2B), isRound(block2B), isBlue(block2C), isSquare(block2C), onTopOf(block2B,block2A), onTopOf(block2C,block2B), above(block2B,block2A), above(block2C,block2B), above(block2C,block2A). ex2

Inductive Logic Programming (ILP) Candidate clauses are generated by  choosing literals from   converting ground terms to variables Search through the space of candidate clauses using standard AI search algo Bottom clause ensures search finite Selected literals from  containsBlock(ex2,block2B) isRed(block2A) onTopOf(block2B,block2A) Candidate Clause positive(A) :- containsBlock(A,B), onTopOf(B,C), isRed(C).

ILP Time Complexity Time complexity of ILP systems depends on  Size of bottom clause |  |  Maximum clause length c  Number of examples | E |  Search algorithm Π O(|  | c | E |) for exhaustive search O(|  || E |) for greedy search Assumes constant-time clause evaluation!

Ideas in Speeding Up ILP Search algorithm improvements  Better heuristic functions, search strategy  Srinivasan’s (2000) random uniform sampling (consider O(1) candidate clauses) Faster clause evaluations  Evaluation time of a clause (on 1 example) exponential in number of variables  Clause reordering & optimizing (Blockeel et al 2002, Santos Costa et al 2003) Evaluation of a candidate still O(|E|)

A Faster Clause Evaluation Our idea: predict clause’s evaluation in O(1) time (i.e., independent of number of examples) Use multilayer feed-forward neural network to approximately score candidate clauses NN inputs specify bottom clause literals selected There is a unique input for every candidate clause in the search space

Neural Network Topology Selected literals from  containsBlock(ex2,block2B) isRed(block2A) onTopOf(block2B,block2A) 1 containsBlock(ex2,block2B) 1 onTopOf(block2B,block2A) 1 isRed(block2A) 0 isRound(block2A) predicted output Σ Candidate Clause positive(A) :- containsBlock(A,B), onTopOf(B,C), isRed(C).

Speeding Up ILP Trained neural network provides a tool for approximate evaluation in O(1) time Given enough examples (large |E|), approximate evaluation is free versus evaluation on data During ILP’s search over hypothesis space …  Approximately evaluate every candidate explored  Only evaluate a clause on data if it is “promising”  Adaptive Sampling – use real evaluations to improve approximation during search

When to Evaluate Approximated Clauses? Treat neural network-predicted score as a Gaussian distribution of true score Only evaluate clauses when there is sufficient likelihood it is the best seen so far, e.g. Best = 22 Pred = 18.9 Pred = 11.1 current hypothesis potential moves P(Best) = 0.03 don’t evaluate P(Best) = 0.24 evaluate ← clause scores → current best

Results Trained learning only on benchmark datasets  Carcinogenesis  Mutagenesis  Protein Metabolism  Nuclear Smuggling Clauses generated by random sampling Clause evaluation metric compression = posCovered – negCovered – length + 1 totalPositives 10-fold c.v. learning curves

Results

Future Work Test in an ILP system  Potential for speedup in datasets with many examples  Will inaccuracy hurt search? Space of Clauses Predicted Score The trained network defines a function over the space of candidate clauses We can use this function …  Extract concepts  Escape local maxima in heuristic search

Acknowledgements Funding provided by  NLM grant 1T15 LM  NLM grant 1R01 LM  DARPA EELD grant F