Machine Learning Methods for Analysing and Linking RDF Data

Machine Learning Methodsfor Analysing and Linking RDF Data

Jens Lehmann

September 16, 2014

Jens Lehmann (AKSW, Uni Leipzig) Analysing and Linking RDF Data September 16, 2014 1 / 35

Structured Machine Learning

How to analysestructured data?

Structured Machine Learning

How to analysestructured data?

Detecting Prime Patterns: Series Finder

Construct "Modus operandi" of criminals - identified 9 new crimepatterns in Cambridge MA, USA

Wang, Tong, et al. "Detecting Patterns of Crime with Series Finder." AAAI 2013.

Discovery of Laws of Physics

Background data generated using experimentsMathematical functions on input variables form hypothesis space

Schmidt, Lipson. "Distilling free-form natural laws from experimental data." Science 2009.

Protein Interaction

Rules learned via Inductive Logic Programming (ProGolem)understandable by experts and competitive with statistical learnersPossibly better drug design and reduction of side effects

Santos et al. "Automated identification of protein-ligand interaction features using InductiveLogic Programming: a hexose binding case study." BMC Bioinformatics 2012.

Background Knowledge

RDF and the Linked Data Principles

RDF Triple:

Example:http://cs.ox.ac.uk/John︸︷︷︸

Subject

http://cs.ox.ac.uk/studies︸︷︷︸Predicate

http://cs.ox.ac.uk/CS︸︷︷︸Object

The term Linked Data refers to a set of best practices for publishing andinterlinking structured data on the Web.

Linked Data principles (simplified version):1 Use RDF and URLs as identifiers2 Include links to other datasets

RDF Triple:

Subject

RDF Triple:

Subject

RDF Triple:

Subject

OWL Ontologies

Web Ontology Language (OWL) builds on RDF and DescriptionLogics

ObjectsSpecific resources (constants)Examples: MARIA, LEIPZIG

ClassesSets of objects (unary predicates)Examples: Student, Car, Country

PropertiesConnections between objects (binary predicates)Examples: hasChild, partOf

Can be combined to complex concepts (OWL Class Expressions), e.g.:Child u ∃hasParent.Professor

OWL Ontologies

Web Ontology Language (OWL) builds on RDF and DescriptionLogicsObjects

Specific resources (constants)Examples: MARIA, LEIPZIG

OWL Ontologies

Web Ontology Language (OWL) builds on RDF and DescriptionLogicsObjects

Specific resources (constants)Examples: MARIA, LEIPZIG

Learning OWL Class Expressions - Definition

Given:Background Knowledge (OWL ontologies and RDF datasets)Positive and negative examples (objects in datasets)

Goal:Find OWL class expression describing positive but not negativeexamples

Application Example: Therapy Response Prediction

≈ 0.5-1% of population affected by Rheumatoid ArthritisAnti-TNF not effective for several million persons for unknown reasons

Learning OWL Class Expressions - Approaches

Least common subsumersCohen et al. "Computing least common subsumers in descriptionlogics." AAAI 1992

Terminological decision treesFanizzi et al. "Induction of concepts in web ontologies throughterminological decision trees." ECML PKDD 2010

Rule-basedFanizzi et al. "DL-FOIL concept learning in description logics." ILP2008

Genetic ProgrammingLehmann, Jens. "Hybrid learning of ontology classes." MLDM 2007

Refinement operatorsLehmann et al. "Concept learning in description logics using refinementoperators." ML 2010Iannone et al. "An algorithm based on counterfactuals for conceptlearning in the semantic web." AI 2007

Refinement Operators - Definitions

Given a DL L, consider the quasi-ordered space 〈C(L),vT 〉 overconcepts of Lρ : C(L)→ 2C(L) is a downward L refinement operator if for anyC ∈ C(L):

D ∈ ρ(C) implies D vT C

Notation: Write C ρ D instead of D ∈ ρ(C)Example refinement chain:

> ρ Person ρ Man ρ Man u ∃hasChild.>

Learning using Refinement Operators

Cartoo weak

Person0,73

Person u ∃attends.>0,78

Person u ∃attends.Talk

0,97. . .

Start with mostgeneral concept(top down)Heuristic evaluatesusing pos/negexamples

Operator specialisesContinue untilterminationcriterion met

Cartoo weak

Person0,73

0,97. . .

Start with mostgeneral concept(top down)Heuristic evaluatesusing pos/negexamplesOperator specialises

Continue untilterminationcriterion met

Cartoo weak

Person0,73

0,97. . .

Start with mostgeneral concept(top down)Heuristic evaluatesusing pos/negexamplesOperator specialises

Continue untilterminationcriterion met

Cartoo weak

Person0,73

0,97. . .

Start with mostgeneral concept(top down)Heuristic evaluatesusing pos/negexamplesOperator specialisesContinue untilterminationcriterion met

=Learning Algorithm

Properties of Refinement Operators

An L downward refinement operator ρ is calledFinite iff ρ(C) is finite for any concept C ∈ C(L)

Redundant iff there exist two different ρ refinement chains from aconcept C to a concept D.Proper iff for C ,D ∈ C(L), C ρ D implies C 6≡T DComplete iff for C ,D ∈ C(L) with D @T C there is a concept E withE ≡T D and a refinement chain C ρ · · · ρ EWeakly complete iff for any concept C with C @T > we can reach aconcept E with E ≡T C from > by ρ.

C1 . . . . . . Cn

E . . .

C ≡ E

D ≡ E

An L downward refinement operator ρ is calledFinite iff ρ(C) is finite for any concept C ∈ C(L)Redundant iff there exist two different ρ refinement chains from aconcept C to a concept D.

Proper iff for C ,D ∈ C(L), C ρ D implies C 6≡T DComplete iff for C ,D ∈ C(L) with D @T C there is a concept E withE ≡T D and a refinement chain C ρ · · · ρ EWeakly complete iff for any concept C with C @T > we can reach aconcept E with E ≡T C from > by ρ.

C1 . . . . . . Cn

E . . .

C ≡ E

D ≡ E

An L downward refinement operator ρ is calledFinite iff ρ(C) is finite for any concept C ∈ C(L)Redundant iff there exist two different ρ refinement chains from aconcept C to a concept D.Proper iff for C ,D ∈ C(L), C ρ D implies C 6≡T D

Complete iff for C ,D ∈ C(L) with D @T C there is a concept E withE ≡T D and a refinement chain C ρ · · · ρ EWeakly complete iff for any concept C with C @T > we can reach aconcept E with E ≡T C from > by ρ.

C1 . . . . . . Cn

E . . .

C ≡ E

D ≡ E

An L downward refinement operator ρ is calledFinite iff ρ(C) is finite for any concept C ∈ C(L)Redundant iff there exist two different ρ refinement chains from aconcept C to a concept D.Proper iff for C ,D ∈ C(L), C ρ D implies C 6≡T DComplete iff for C ,D ∈ C(L) with D @T C there is a concept E withE ≡T D and a refinement chain C ρ · · · ρ EWeakly complete iff for any concept C with C @T > we can reach aconcept E with E ≡T C from > by ρ.

C1 . . . . . . Cn

E . . .

C ≡ E

D ≡ EJens Lehmann (AKSW, Uni Leipzig) Analysing and Linking RDF Data September 16, 2014 14 / 35

Properties indicate how suitable a refinement operator is for solvingthe learning problem:

Incomplete operators may miss solutionsRedundant operators may lead to duplicate concepts in the search treeImproper operators may produce equivalent concepts (which cover thesame examples)For infinite operators it may not be possible to compute all refinementsof a given concept

Key question: Which properties can be combined?

Theorem: Properties of L Refinement Operators

Theorem

Maximum sets of combinable properties of L refinement operators forL ∈ {ALC,ALCN ,SHOIN ,SROIQ} are:

1 {weakly complete, complete, finite}2 {weakly complete, complete, proper}3 {weakly complete, non-redundant, finite}4 {weakly complete, non-redundant, proper}5 {non-redundant, finite, proper}

Foundations of Refinement Operators for Description Logics; Lehmann, Hitzler, ILP confer-ence, 2008

Concept Learning in Description Logics Using Refinement Operators, Lehmann, Hitzler, Ma-chine Learning journal, 2010

Definition of ρ

ρ(C) =

{{⊥} ∪ ρ>(C) if C = >ρ>(C) otherwise

ρB (C) =

∅ if C = ⊥{C1 t · · · t Cn | Ci ∈ MB (1 ≤ i ≤ n)} if C = >{A′ | A′ ∈ sh↓(A)} if C = A (A ∈ NC )∪{A u D | D ∈ ρB (>)}

{¬A′ | A′ ∈ sh↑(A)} if C = ¬A (A ∈ NC )∪{¬A u D | D ∈ ρB (>)}

{∃r.E | A = ar(r), E ∈ ρA(D)} if C = ∃r.D∪ {∃r.D u E | E ∈ ρB (>)}∪ {∃s.D | s ∈ sh↓(r)}

{∀r.E | A = ar(r), E ∈ ρA(D)} if C = ∀r.D∪ {∀r.D u E | E ∈ ρB (>)}∪ {∀r.⊥ |

D = A ∈ NC and sh↓(A) = ∅}∪ {∀s.D | s ∈ sh↓(r)}

{C1 u · · · u Ci−1 u D u Ci+1 u · · · u Cn | if C = C1 u · · · u CnD ∈ ρB (Ci ), 1 ≤ i ≤ n} (n ≥ 2)

{C1 t · · · t Ci−1 t D t Ci+1 t · · · t Cn | if C = C1 t · · · t CnD ∈ ρB (Ci ), 1 ≤ i ≤ n} (n ≥ 2)

∪ {(C1 t · · · t Cn) u D |D ∈ ρB (>)}

Base Operator (Excerpt)

Definition of ρ

ρ(C) =

{{⊥} ∪ ρ>(C) if C = >ρ>(C) otherwise

ρB (C) =

∅ if C = ⊥{C1 t · · · t Cn | Ci ∈ MB (1 ≤ i ≤ n)} if C = >{A′ | A′ ∈ sh↓(A)} if C = A (A ∈ NC )∪{A u D | D ∈ ρB (>)}

{¬A′ | A′ ∈ sh↑(A)} if C = ¬A (A ∈ NC )∪{¬A u D | D ∈ ρB (>)}

{∃r.E | A = ar(r), E ∈ ρA(D)} if C = ∃r.D∪ {∃r.D u E | E ∈ ρB (>)}∪ {∃s.D | s ∈ sh↓(r)}

{∀r.E | A = ar(r), E ∈ ρA(D)} if C = ∀r.D∪ {∀r.D u E | E ∈ ρB (>)}∪ {∀r.⊥ |

D = A ∈ NC and sh↓(A) = ∅}∪ {∀s.D | s ∈ sh↓(r)}

{C1 u · · · u Ci−1 u D u Ci+1 u · · · u Cn | if C = C1 u · · · u CnD ∈ ρB (Ci ), 1 ≤ i ≤ n} (n ≥ 2)

{C1 t · · · t Ci−1 t D t Ci+1 t · · · t Cn | if C = C1 t · · · t CnD ∈ ρB (Ci ), 1 ≤ i ≤ n} (n ≥ 2)

∪ {(C1 t · · · t Cn) u D |D ∈ ρB (>)}

Base Operator (Excerpt)

Definition of ρ

{∃r .E | A = ar(r),E ∈ ρA(D)} if C = ∃r .D∪ {∃r .D u E | E ∈ ρB(>)}

∪ {∃s.D | s ∈ sh↓(r)}

Examples:

∃takesPartIn.SocialEvent

∃takesPartIn.Meeting

Student u ∃takesPartIn.SocialEvent

∃leads.SocialEvent

Definition of ρ

∪ {∃s.D | s ∈ sh↓(r)}

Examples:

Definition of ρ

∪ {∃s.D | s ∈ sh↓(r)}

Examples:

Properties of ρ

ρ↓ is completeρ↓ is infinite, e.g. there are infinitely many refinement steps of theform:

> ρ↓ C1 t C2 t C3 t . . .

ρcl↓ is properρ↓ is redundant: ∀r1.A1 t ∀r2.A1 ρ↓ ∀r1.(A1 u A2) t ∀r2.A1

∀r1.A1 t ∀r2.(A1 u A2) ρ↓ ∀r1.(A1 u A2) t ∀r2.(A1 u A2)

“DL-Learner: Learning Concepts in Description Logics”,Jens Lehmann, Journal of Machine Learning Research (JMLR), 2009

>0,47 [0]0,45 [1]

Cartoo weak