Hybrid Learning of Ontology Classes

Transcription

1 Hybrid Learning of Ontology Classes Jens Lehmann July 18, 2007 Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

2 Outline 1 Introduction to Description Logics, OWL, and the Learning Problem 2 Solving the Learning Problem with Genetic Programming (GP) 3 Genetic Refinement Operators 4 Preliminary Evaluation 5 Conclusions & Future Work Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

3 Outline 1 Introduction to Description Logics, OWL, and the Learning Problem 2 Solving the Learning Problem with Genetic Programming (GP) 3 Genetic Refinement Operators 4 Preliminary Evaluation 5 Conclusions & Future Work Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

4 Introduction to Description Logics Description Logics (DL) is the name of a family of languages for knowledge representation fragment of first order predicate logic less expressive power than predicate logic, but decidable inference problems intuitive variable free syntax basis of the ontology language OWL (W3C recommendation) OWL ontology convertable to DL knowledge base and vice versa Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

5 The Learning Problem in DLs Woman Man Mother Person Person Female Person Female Woman haschild. Man Woman Male Female ALC Description Logic knowledge base TBox - terminological knowledge Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

6 The Learning Problem in DLs Woman Person Female Man Person Female Mother Woman haschild. Person Man Woman Male(JOHN) Male Female Male(MARC) Male(STEPHEN) haschild(stephen,marc) Male(JASON) haschild(marc,anna) Female(MICHELLE) haschild(john,maria) Female(ANNA) haschild(anna,jason) Female(MARIA) ALC Description Logic knowledge base ABox - assertional knowledge Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

7 The Learning Problem in DLs Woman Person Female Man Person Female Mother Woman haschild. Person Man Woman Male(JOHN) Male Female Male(MARC) Male(STEPHEN) haschild(stephen,marc) Male(JASON) haschild(marc,anna) Female(MICHELLE) haschild(john,maria) Female(ANNA) haschild(anna,jason) Female(MARIA) positive examples:{stephen, MARC, JOHN} negative examples:{jason, ANNA, MARIA, MICHELLE} Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

8 The Learning Problem in DLs Woman Person Female Man Person Female Mother Woman haschild. Person Man Woman Male(JOHN) Male Female Male(MARC) Male(STEPHEN) haschild(stephen,marc) Male(JASON) haschild(marc,anna) Female(MICHELLE) haschild(john,maria) Female(ANNA) haschild(anna,jason) Female(MARIA) positive examples:{stephen, MARC, JOHN} negative examples:{jason, ANNA, MARIA, MICHELLE} possible solution: Target Male haschild. Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

9 Outline 1 Introduction to Description Logics, OWL, and the Learning Problem 2 Solving the Learning Problem with Genetic Programming (GP) 3 Genetic Refinement Operators 4 Preliminary Evaluation 5 Conclusions & Future Work Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

10 Genetic Programming (GP) Algorithm (Genetic Programming) create population while the termination criterion is not met: select a subset of the population based on their fitness produce offspring using genetic operators on selected individuals create a new population from the old one and the offspring genetic operators: crossover, mutation, editing selection: rank selection, FPS, tournament selection tree representation common in GP Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

11 Applying Standard GP representing ALC concepts: terminal set T = N C {, } function set F = {,, } { r r N R } { r r N R } Male haschild Female Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

12 Applying Standard GP representing ALC concepts: terminal set T = N C {, } function set F = {,, } { r r N R } { r r N R } Male haschild Female possible fitness function: f K (C) = E + \ pos K (C) + neg K (C) E + + E a C (0 < a < 1) pos K (C)... set of covered positive examples neg K (C)... set of covered negative examples a... concept length penalty Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

13 Advantages&Disadvantages of the Standard GP Approach Tree encoding and fitness measurement are sufficient to apply GP! Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

14 Advantages&Disadvantages of the Standard GP Approach Tree encoding and fitness measurement are sufficient to apply GP! Advantages: very flexible learning method (can handle other description languages) parallelisable algorithms GP is robust to noise Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

15 Advantages&Disadvantages of the Standard GP Approach Tree encoding and fitness measurement are sufficient to apply GP! Advantages: very flexible learning method (can handle other description languages) parallelisable algorithms GP is robust to noise Disadvantages: crossover operator too destructive: small syntactic changes - drastic semantic changes does not use all of the available background knowledge: no exploitation of the subsumption hierarchy of concepts Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

16 Outline 1 Introduction to Description Logics, OWL, and the Learning Problem 2 Solving the Learning Problem with Genetic Programming (GP) 3 Genetic Refinement Operators 4 Preliminary Evaluation 5 Conclusions & Future Work Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

17 Refinement Operators idea: combine refinement operators and GP definition of refinement operators: consider quasi-ordered space (ALC, ) ALC downward (upward) refinement operator ρ is a mapping from S to 2 S such that for any C S: example: C ρ(c) implies C C (C C ) Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

18 Refinement Operators idea: combine refinement operators and GP definition of refinement operators: consider quasi-ordered space (ALC, ) ALC downward (upward) refinement operator ρ is a mapping from S to 2 S such that for any C S: example: Person C ρ(c) implies C C (C C ) Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

19 Refinement Operators idea: combine refinement operators and GP definition of refinement operators: consider quasi-ordered space (ALC, ) ALC downward (upward) refinement operator ρ is a mapping from S to 2 S such that for any C S: C ρ(c) implies C C (C C ) example: Person Person takespartin.conference Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

20 Refinement Operators idea: combine refinement operators and GP definition of refinement operators: consider quasi-ordered space (ALC, ) ALC downward (upward) refinement operator ρ is a mapping from S to 2 S such that for any C S: C ρ(c) implies C C (C C ) example: Person Person takespartin.conference refinement operators... Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

21 Refinement Operators idea: combine refinement operators and GP definition of refinement operators: consider quasi-ordered space (ALC, ) ALC downward (upward) refinement operator ρ is a mapping from S to 2 S such that for any C S: C ρ(c) implies C C (C C ) example: Person Person takespartin.conference refinement operators can make use of the generality order of concepts w.r.t. K... are less destructive w.r.t. the semantics of a concept... can use the (precomputed) subsumption hierarchy Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

22 Genetic Refinement Operators What distinguishes refinement and genetic operators? refinement operators map one concept to many concepts refinement operators are either downward or upward operators Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

23 Genetic Refinement Operators What distinguishes refinement and genetic operators? refinement operators map one concept to many concepts refinement operators are either downward or upward operators solution: Genetic Refinement Operators rand(φ (C)) φ K (C) = rand(φ (C)) with probability with probability neg K (C) E 1+ neg K (C) E pos K (C) E + 1 pos K (C) E + 1+ neg K (C) E pos K (C) E + Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

24 Genetic Refinement Operators What distinguishes refinement and genetic operators? refinement operators map one concept to many concepts refinement operators are either downward or upward operators solution: Genetic Refinement Operators rand(φ (C)) φ K (C) = rand(φ (C)) with probability with probability neg K (C) E 1+ neg K (C) E pos K (C) E + 1 pos K (C) E + 1+ neg K (C) E pos K (C) E + we created a complete and proper operator based on a full property analysis [Lehmann et. al, ILP 2007] Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

25 Outline 1 Introduction to Description Logics, OWL, and the Learning Problem 2 Solving the Learning Problem with Genetic Programming (GP) 3 Genetic Refinement Operators 4 Preliminary Evaluation 5 Conclusions & Future Work Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

26 Evaluation - Uncle Problem learn definition of uncle from FORTE family data set (337 assertions, 86 examples) problem is challenging - relatively complex solution and no search space restrictions possible solution: Uncle Male ( sibling. parent. married. sibling. parent. ) Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

27 Evaluation - Uncle Problem learn definition of uncle from FORTE family data set (337 assertions, 86 examples) problem is challenging - relatively complex solution and no search space restrictions compare against state of the art DL learning system YinYang compare improvement over standard GP possible solution: Uncle Male ( sibling. parent. married. sibling. parent. ) Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

28 Evaluation - Accuracy classification accuracy in % refinement mixed standard GP population size YinYang: 73.5% Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

29 Evaluation - Concept Length syntactic length of solution refinement mixed standard GP population size YinYang: 12.2 Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

30 Outline 1 Introduction to Description Logics, OWL, and the Learning Problem 2 Solving the Learning Problem with Genetic Programming (GP) 3 Genetic Refinement Operators 4 Preliminary Evaluation 5 Conclusions & Future Work Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

31 Contributions to the State of the Art first time to apply evolutionary techniques to learning problem in DLs first framework for combining refinement operators and GP directly creation of a concrete operator based on a full property analysis implemented in a system called DL-Learner and shown to be feasible in a preliminary evaluation Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

32 Future Work more evaluation examples, e.g. asses performance on noisy or inconsistent data create (more) benchmarks to assess scalability and enable easier comparison between different algorithms tests on real world data, e.g. DBpedia embed learning algorithm in ontology editor e.g. OntoWiki extend algorithm to other description languages (cardinality restrictions, datatype integer) Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20

33 The End Thank you for your attention. contact: Jens Lehmann (Uni Leipzig) Hybrid Ontology Class Learning July 18, / 20