Rule Learning from Knowledge Graphs Guided by Embedding Models Vinh - PowerPoint PPT Presentation

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Learning from Knowledge Graphs Guided by Embedding Models Vinh Thinh Ho 1 , Daria Stepanova 1 , Mohamed Gad-Elrab 1 , Evgeny Kharlamov 2 , Gerhard Weikum 1 1 Max Planck Institute for Informatics, Saarbr¨ ucken, Germany 2 University of Oxford, Oxford, United Kingdom ISWC 2018 1 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Learning from KGs 1 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Learning from KGs Confidence, e.g., WARMER [Goethals and den Bussche, 2002] CWA: whatever is missing is false | | + | | = 2 | | conf ( r ) = 4 r : livesIn ( X , Y ) ← isMarriedTo ( Z , X ) , livesIn ( Z , Y ) 1 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Learning from KGs Confidence, e.g., WARMER [Goethals and den Bussche, 2002] CWA: whatever is missing is false | | + | | = 2 | | conf ( r ) = 4 r : livesIn ( X , Y ) ← isMarriedTo ( Z , X ) , livesIn ( Z , Y ) 1 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Learning from KGs PCA confidence AMIE [Gal´ arraga et al. , 2015] PCA: Since Alice has a living place already, all others are incorrect. isMarriedTo Brad hasBrother Ann isMarriedTo John Kate livesIn livesIn livesIn livesIn Berlin Researcher Chicago livesIn IsA IsA livesIn isMarriedTo isMarriedTo Bob Alice Dave Clara livesIn | | + | | = 2 | | conf PCA ( r ) = 3 Amsterdam r : livesIn ( X , Y ) ← isMarriedTo ( Z , X ) , livesIn ( Z , Y ) 1 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Learning from KGs Exception-enriched rules: [ISWC 2016, ILP 2016] isMarriedTo hasBrother Brad isMarriedTo Ann John Kate livesIn livesIn livesIn livesIn Researcher Berlin Chicago livesIn IsA IsA livesIn isMarriedTo isMarriedTo Bob Alice Dave Clara livesIn | | conf ( r ) = conf PCA ( r ) = | | + | | = 1 Amsterdam r : livesIn ( X , Y ) ← isMarriedTo ( Z , X ) , livesIn ( Z , Y ) , not isA ( X , researcher ) 1 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Absurd Rules due to Data Incompleteness Problem: rules learned from highly incomplete KGs might be absurd.. worksAt Brad ITech worksAt John OpenSys livesIn officeIn livesIn officeIn ItCompany Berlin Chicago officeIn IsA IsA officeIn worksAt worksAt Bob ITService SoftComp Clara conf ( r ) = conf PCA ( r ) = 1 livesIn ( X , Y ) ← worksAt ( X , Z ) , officeIn ( Z , Y ) , not isA ( Z , itCompany ) 2 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Ideal KG µ ( r , G i ) : measure quality of the rule r on G i KG Ideal KG  i  3 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Ideal KG µ ( r , G i ) : measure quality of the rule r on G i , but G i is unknown KG Ideal KG  i  3 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Probabilistic Reconstruction of Ideal KG µ ( r , G i p ) : measure quality of r on G i p  i p probabilistic KG reconstruction of  i  3 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Hybrid Rule Measure µ ( r , G i p ) = ( 1 − λ ) × µ 1 ( r , G ) + λ × µ 2 ( r , G i p )  i p probabilistic KG reconstruction of  i  3 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Hybrid Rule Measure µ ( r , G i p ) = ( 1 − λ ) × µ 1 ( r , G ) + λ × µ 2 ( r , G i p ) • λ ∈ [ 0 .. 1 ] : λ ∈ [ 0 .. 1 ] : weighting factor λ ∈ [ 0 .. 1 ] : µ 1 : • µ 1 : µ 1 : descriptive quality of rule r over the available KG G • confidence • PCA confidence µ 2 : predictive quality of r relying on G i • µ 2 : µ 2 : p (probabilistic reconstruction of the ideal KG G i ) 3 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion KG Embeddings • Popular approach to KG completion, which proved to be effective • Relies on translation of entities and relations into vector spaces livesIn Mat SFO Bob is a Bob and Mat have Berlin Bob developer in Text successfully colleagueOf ITService, CA completed a project livesIn livesIn initiated by the SFO Jane department of Berlin Bob Patti Jane ITService Patti colleagueOf colleagueOf colleagueOf Mat SFO is a cultural score(<Bob livesIn SFO>) = 0.8 and commercial Mat working as livesIn center of CA a developer in score(<Bob livesIn Berlin>) = 0.4 ITService, CA ... SFO TransE [Bordes et al. , 2013], SSP [Xiao et al. , 2017], TEKE [Wang and Li, 2016] 4 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Our Approach 5 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Construction • Clause exploration from general to specific • all first-order clauses: [Shapiro, 1991] livesIn ( X , Y ) ← add atom unify variable to unify constant variables livesIn(X, Y) ← livesIn(U, V) livesIn(bob, Y) ← livesIn(X, X) ← 6 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Construction • Clause exploration from general to specific • closed rules: AMIE [Gal´ arraga et al. , 2015] livesIn ( X , Y ) ← marriedTo ( X , Z ) , livesIn ( Z , Y ) livesIn ( X , Y ) ← add dangling atom add instantiated atom livesIn(X, Y) ← marriedTo(X, Z) livesIn(X, Y) ← isA(X, researcher) add closing atom livesIn(X, Y) ← marriedTo(X, Z), livesIn(Z, Y) 6 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Construction • Clause exploration from general to specific • closed rules: AMIE [Gal´ arraga et al. , 2015] livesIn ( X , Y ) ← marriedTo ( X , Z ) , livesIn ( Z , Y ) livesIn ( X , Y ) ← add dangling atom add instantiated atom livesIn(X, Y) ← marriedTo(X, Z) livesIn(X, Y) ← isA(X, researcher) add closing atom livesIn(X, Y) ← marriedTo(X, Z), livesIn(Z, Y) 6 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Construction • Clause exploration from general to specific • closed rules: AMIE [Gal´ arraga et al. , 2015] livesIn ( X , Y ) ← marriedTo ( X , Z ) , livesIn ( Z , Y ) livesIn ( X , Y ) ← add dangling atom add instantiated atom livesIn(X, Y) ← marriedTo(X, Z) livesIn(X, Y) ← isA(X, researcher) add closing atom livesIn(X, Y) ← marriedTo(X, Z), livesIn(Z, Y) 6 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Construction • Clause exploration from general to specific • This work: closed and safe rules with negation livesIn ( X , Y ) ← marriedTo ( X , Z ) , livesIn ( Z , Y ) , not isA ( X , researcher ) livesIn ( X , Y ) ← add dangling atom add instantiated atom livesIn(X, Y) ← marriedTo(X, Z) livesIn(X, Y) ← isA(X, researcher) add closing atom livesIn(X, Y) ← marriedTo(X, Z), livesIn(Z, Y) add negated atom add negated instantiated atom livesIn(X, Y) ← marriedTo(X, Z), livesIn(Z, Y), livesIn(X, Y) ← marriedTo(X, Z), livesIn(Z, Y), not isA(X, researcher) not moved(X, Y) 6 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Construction • Clause exploration from general to specific • This work: closed and safe rules with negation livesIn ( X , Y ) ← marriedTo ( X , Z ) , livesIn ( Z , Y ) , not isA ( X , researcher ) livesIn ( X , Y ) ← add dangling atom add instantiated atom livesIn(X, Y) ← marriedTo(X, Z) livesIn(X, Y) ← isA(X, researcher) add closing atom livesIn(X, Y) ← marriedTo(X, Z), livesIn(Z, Y) add negated atom add negated instantiated atom livesIn(X, Y) ← marriedTo(X, Z), livesIn(Z, Y), livesIn(X, Y) ← marriedTo(X, Z), livesIn(Z, Y), not isA(X, researcher) not moved(X, Y) 6 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Rule Prunning livesIn ( X , Y ) ← ... ... livesIn(X, Y) ← worksAt(X, Z) livesIn(X, Y) ← marriedTo(X, Z) livesIn(Z, Y) ... livesIn(X, Y) ← worksAt(X, Z), officeIn(Z, Y) livesIn(X, Y) ← marriedTo(X, Z), livesIn(Z, Y) not researcher(X) Prune rule search space relying on • novel hybrid embedding-based rule measure 7 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Embedding-based Rule Quality • Estimate average quality of predictions made by a given rule r 1 µ 2 ( r , G i G i p ) = � p ( fact ) | predictions ( r , G ) | fact ∈ predictions ( r , G ) • Rely on truthfulness of predictions made by r based on the probabilistic reconstruction G i p of G i 8 / 13

Motivation Our Approach Rule Construction Rule Prunning Evaluation Conclusion Embedding-based Rule Quality • Estimate average quality of predictions made by a given rule r 1 µ 2 ( r , G i G i p ) = � p ( fact ) | predictions ( r , G ) | fact ∈ predictions ( r , G ) • Rely on truthfulness of predictions made by r based on the probabilistic reconstruction G i p of G i Example: livesIn ( X , Y ) ← marriedTo ( X , Z ) , livesIn ( Z , Y ) • Rule predictions: livesIn ( mat , monterey ) , livesIn ( dave , chicago ) G i p ( < mat livesIn monterey > )+ G i p ( < dave livesIn chicago > ) µ 2 ( r , G i p )= 2 8 / 13