Ways to Incorporate Ontology and Bayesian Network

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Ways to Incorporate Ontology and Bayesian Network. Presented By: Asma Sanam Larik. Three Approaches. Following ways have been applied to incorporate them: 1) Ontology Mapping Enhancement using BN 2) Extending Ontology queries by BN reasoning - PowerPoint PPT Presentation

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Incorporation of Uncertainty in Ontology

Ways to Incorporate Ontology and Bayesian NetworkPresented By:Asma Sanam Larik1Three ApproachesFollowing ways have been applied to incorporate them: 1) Ontology Mapping Enhancement using BN 2) Extending Ontology queries by BN reasoning 3) Semi automated construction of BN from domain ontology2Purpose of the Mapping ApproachMapping Approach Designers of Ontology apply different views of the same domain during ontology development. This yields heterogeneity at ontology level which is the main obstacle to semantic interoperability. Ontology mapping is the approach trying to solve this problem 3Research in Ontology Mapping1. OMEN (Ontology Mapping ENhancer 2004) OMEN: A Probabilistic Ontology Mapping Tool by Prasenjit Mitra, Anuj Jaiswal, Pennsylvania State University and Stanford University2. BayesOWL (2005) A Bayesian Network Approach to Ontology mapping by Zhongli Ding, Yun Peng, UMBC3. OntoBayes (2006) OntoBayes:An Ontology driven Uncertainty Model by Yi Yang and Jacques Calmet, University of Karlsruhe, Germany

4Purpose of Extending Ontology reasoning ApproachExtending Ontology Queries: Existing ontology query languages cannot provide answers to queries involving probabilities like the following ones:What is the likelihood of default of a company given that it is limited and has branches outside Europe?What is the likelihood of a particular project type given that it is led by male managers working for a ltd company? Thus BN are applied for this sort of probabilistic reasoning

Proposed by Bellandi Andrea, Turini Franco April 2009, University of Pisa, Italy

5Purpose of automatic BN construction approachAutomatic BN Construction: The creation of BN requires identifying variables of interest, their influence on each other and construction of CPT. Based on existing domain ontologies these methods propose methodology for Ontology based generation of Bayesian Networks

6Research on Automated BN ConstructionStefan Fenz (University of Vienna, Austria) 2008

Ann Devitt and K. Mutosikova 2006 (Network Management Research Centre, Ireland)

Hai-tao Zhang , B-Yoeng Kang (Soeul National University, Korea ) 2007

7Ontology Mapping with BN8BayesOWL Approach Probabilistic Ontology is an Annotated Ontology that contains set of prior and Conditional Distributions

This approach takes a simple Ontology file and a Probability file and maps both of them to generate a Bayesian Network

Purpose of doing so is to use Bayesian Inference for OWL reasoning9Purpose/ Direction of ApproachIn domain modeling I know that A is a subclass of B now one may wish to express the probability that an instance of B belongs to an instance of A Also if A and B are not logically related one may still wish to express how much A is overlapped with BIn Ontology Reasoning one may wish to know degree of similarity of A to B even if A and B are not subsumed by each other

10Its purpose is in Concept Mapping between two ontologies where it is often the case that concept defined by one ontology has partial matching with concept in other Ontology 11How to Incorporate PO?Probabilistic Information Markups

Structural translation

Constructing CPT for L-Nodes

Constructing CPT for Concept Nodes12Structural Translation

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14CPT for L-Nodes

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CPT for Concept NodesExample taken from Zhongli Dings ThesisNext a constraint on B is applied R1(B)=(0.61,0.39) 1717ABCDQ(X)TTTT0.0048TTTF0.0432TTFT0.0272TTFF0.0048TFTT0.0864TFTF0.1056TFFT0.0896TFFF0.0384FTTT0.0126FTTF0.1134FTFT0.1989FTFF0.0351FFTT0.0378FFTF0.0462FFFT0.1092FFFF0.0468Initial Knowledge Base

BQ(B)T0.44F0.56Marginal on BBR(B)T0.61F0.39Constraint on BBR(B)/Q(B)T1.386F0.6964New JPD ABCDQ(X)TTTT0.006653TTTF0.059875TTFT0.037699TTFF0.006653TFTT0.060169TFTF0.07354TFFT0.062397TFFF0.026742FTTT0.017464FTTF0.157172FTFT0.275675FTFF0.048649FFTT0.026324FFTF0.032174FFFT0.076047FFFF0.032592From new JPD the constraint is satisfied. Next another constraint on C is applied

R2(C)= (0.83,0.17) shown in next slide1818Initial Knowledge Base

CQ(C)T0.433F0.567Marginal on CCR(C)T0.83F0.17Constraint on CCR(C)/Q(C)T1.9168F0.2998New JPD ABCDQ(X)TTTT0.006653TTTF0.059875TTFT0.037699TTFF0.006653TFTT0.060169TFTF0.07354TFFT0.062397TFFF0.026742FTTT0.017464FTTF0.157172FTFT0.275675FTFF0.048649FFTT0.026324FFTF0.032174FFFT0.076047FFFF0.03259219ABCDQ(X)TTTT0.0127525TTTF0.1147684TTFT0.0113022TTFF0.0019946TFTT0.1153319TFTF0.1409615TFFT0.0187066TFFF0.0080173FTTT0.033475FTTF0.3012673FTFT0.0826474FTFF0.014585FFTT0.0504578FFTF0.0616711FFFT0.0227989FFFF0.009771119ReasoningThe BayesOWL framework can support common ontology reasoning tasks as probabilistic reasoning in the translated BNConcept OverlappingConcept Subsumption

20Automated BN Construction21Ontology-based generation of Bayesian NetworksBy Stefan Fenz and Min Tjoa University of Vienna

S.Fenz Ontology and Bayesian-based information security risk management PhD. Thesis, Vienna University of Technology, Oct 2008

22MotivationCreation of BN requires at least three challenging tasks:Determination of relevant influence factorsDetermination of relationships between identified influence factorsCalculation of CPTsOntologies are a potential solution to address stated challenges 23Example Security Ontology

1) Security Attribute: Confidentiality Integrity Availability2) Threat Source: Accidental Deliberate3) Threat origin: Human Natural4) Vulnerability: Physical Technical Administrative5) Control Type: Preventive Corrective Recovery 6) Severity Level High, Medium, Low 24Methodology Proposed Concepts Nodes in BNRelations LinksAxioms Node statesInstances Findings

25Concept NodesFollowing factors have been identified:1) Predecessor Threats (PT1Ti , , PTnTi ) influence the considered threat Ti which influences it successor threats (ST1Ti , , STnTi)

26Continue.. 2) Each threat (Ti) requires one or more vulnerabilities (V1,.,Vn) to become effective

27Axiomsnode scales and weightsThree point Likert scale (High, Medium)For CPT construction Severity rating Svi is defined for each vulnerability therefore a numerical weight Wppvi for each vulnerability is identified by dividing severity of vulnerability by the sum of all vulnerabilities relevant to the threat

28Continue..3) Controls can be used to mitigate identified vulnerabilities, mitigation depends on the effectiveness of a potential control combination (CCEvi) which again depends on the actual effectiveness of control implementation (CE1,., CEn)

29Continue..4) a) Incase of deliberate threat sources, the vulnerability exploitation probability PPVi is determined by the effectiveness of a potential attacker (AEVi) which is again determined by the motivation (AMVi) and the capabilities of the attacker (ACVi)

b) Incase of accidental threat sources (PPVi) is determined by a prior probability (APTi) of corresponding threat Ti

30

31Relations Links

32LimitationsFunctions for calculating CPT are not provided by Ontology and have to be modeled externally

Human Intervention is necessary if the ontology provides a knowledge model that does not exactly fit the domain of interest33Clinical CPGs34Extending Ontology Query with BN Inference35StrategyExtracting the BN directly from the ontology:Definition of the ontology compiling process for extracting the Bayesian network structure directly from the schema of the knowledge base. Learning the initial probability distributions.

Providing a Bayesian query language for answering queries involving probabilities

Using inference over the BN for answering queries involving probabilities:Definition of the language operational semantics, based on the well-known Bayesian network reasoning schemas

36An example of Ontology Compiling Process3737Extracting a Bayesian network from an Ontology An Example (1)An Ontology O is a pair whereT = {T1,..,Ti,..,Tn} is a set of hierarchies called domain conceptsR Ti x Tj is a set of arcs binding elements of T such that the resulting graph is acyclic.

COMPANYPATENTRESEARCHPROJECTMANCOMPTETITORVENDORPERSONSUPPLIERJOINTVENTUREWOMANhasCeoleadsT1T3T2LIFEINSURANCEFINANCIALCREDITCARDSERVICESSECTORT4hasSectorR1=R2=R3=T1= COMPANY = {Company,Vendor, Jointv, Compet, Suplier}T2= PERSON = {Person, Man, Woman}

T3= PROJECT = {Project, Research,PAtent}

T4= SECTOR = {Sector,Services,Financial,CreditCard,LifeIns}R1 : COMPANY PERSONR2 : PERSON PROJECTR3 : COMPANY SECTORis-a relationObject property38COMPANYCOMPETITORVENDORSUPPLIERJOINTVENTUREMANPERSONWOMANPATENTRESEARCHPROJECTP(COMPANY)P(JOINTVENTURE|COMPANY)P(VENDOR|COMPANY)P(COMPETITOR|VENDOR)P(SUPPLIER|VENDOR)P(PERSON)P(MAN|PERSON)P(WOMAN|PERSON)P(PROJECT)P(RESEARCH|PROJECT)P(PATENT|PROJECT)LIFEINSURANCEFINANCIALCREDIT CARDSERVICESSECTORP(SECTOR)P(SERVICES|SECTOR)P(FINANCIAL|SECTOR)P(CREDITCARD|FINANCIAL)P(LIFEINSURANCE|FINANCIAL)P(Company=c)P(Person=p |hasCeo Company=c)P(Project=pr |leads Person=p)P(Sector=s |hasSector Company=c)R1R2R3High Level NodeHigh Level RelationLow Level NodeLow Level RelationExtracting a Bayesian network from an Ontology An Example (2)T1T2T3T439Ontology Compiling Process4040Ontology Compiling ProcessIt is composed of two phases:Phase one: compiling TBox ontology in a 2lBN structural partPhase two: compiling ABox ontology in a 2lBN probabilistic part

Company Customer Partenrship Jointventure

0.56 0.86 0.36 0.29

0.44 0.14 0.64 0.71

1 1 1 1Man

Woman

Person hasCeoLLRTHLRTHLN_COMPANYLLNHLN_PERSONHLR_Ceo412lBN structural partThe compiling process of a TBox component maps:Each ontology class to a booelan random variable (LLN)Each concept domain to a multi-valued random variable (HLN)Each object property to a Bayesian arc (HLR)

2lBN probabilistic partThe initial probability distribution is computed on the basis of the distribution of the instances, that is the ABox component.Two kind of probability exists:Low Level Relation Probability Table (LLRT)A Prior probability P(A) represents the probability that an arbitrary ontology instance belongs to the class A.A Conditional Probability P(A|B) represents the probability that an arbitrary ontology instance belonging to the class B, belongs also to the class A. High Level Relation Probability Table (HLRT)A Conditional Probability P(A|RB) represents the probability that it does exist a relation R (i.e., an object property or a path of object properties) between arbitrary ontology instances of A and arbitrary ontology instances of B

42Low Level Relations probability distribution - example

Starting from this table, we can compute the probability distribution by applying the Bayes formula in the following form:

43High Level Relations probability distribution - example

Number of triples satisfyingthe TBox schema

Number of instances belonging to the sub-space of Companycorresponding to Company with a CEO 44Inference over Bayesian network4545Inference over Bayesian network (1)Top-Down. Causal Reasoning

P(D | A) =Bottom-Up. Diagnostic Reasoning P(A | D) =Top-Down/Bottom-Up. Explaining Away Reasoning P(A | B, D) =ACBDP(D|A,B)P(C|B)P(B)P(A)P(D,B | A) + P(D,B | A)P(D | A) * P(A)P(D)P(D, B | A) * P(A)P(B,D)P(D | B,A) * P(B | A) * P(A)P(B,D)=Inference over Bayesian networks is, in general, NP-hard.46Inference over Bayesian network (2)

Polytree is a class of Bayesian Networks that can efficiently be solved in time linear in the number of nodes.

Polytree property: Exists a unique path between each possible couple of nodes.Fixed a node D, is always possible to partition all the other nodes into two disjoint sets: set over D, which is the set of nodes that are connected to D only by the fathers of D.set under D, which is the set of nodes that are connected to D only by the immediate descendents of D.47Bayesian query structureThe general structure of a probabilistic query is P(QUERY |path EVIDENCE) where:QUERY is a node of the polytree EVIDENCE can be both one node over and one node under w.r.t query, one node over w.r.t. query, one node under w.r.t. queryEVIDENCE can refer:is-a ontology relations (classical bayesian conditioning, that is path is empty)object properties (bayesian conditioning is annotated with the path binding query to evidence)

QUERY node (D)EVIDENCE over QUERY(A, B, C, E)EVIDENCE under QUERY(F, G, H, I)48Which is the probability that a Patent project is led by person which is CEO of a company operating in the financial sector ? P(PROJECT=patent |(leads.hasCeo.hasSector) SECTOR=financial)COMPANYCOMPETITORVENDORSUPPLIERJOINTVENTUREMANPERSONWOMANPATENTRESEARCHPROJECTSERVICESFINANCIALSECTORP(COMPANY)P(JOINTVENTURE|COMPANY)P(VENDOR|COMPANY)P(COMPETITOR|VENDOR)P(SUPPLIER|VENDOR)P(PERSON)P(MAN|PERSON)P(WOMAN|PERSON)P(PROJECT)P(RESEARCH|PROJECT)P(PATENT|PROJECT)P(SECTOR)P(FINANCIAL|SECTOR)P(SERVICES|SECTOR)P(Company=c)hasCeoTop Down InferenceP(PATENT |(leads.hasCeo.hasSector) FINANCIAL) =

P(PATENT |(leads) Person) * P(Person |(hasCeo.hasSector) S1)

EVIDENCE FINANCIAL is over QUERY PATENTTop Down InferenceP(Person |(hasCeo.hasSector) FINANCIAL) =

P(Person |(hasCeo) Company) * P(Company |(hasSector) FINANCIAL)

EVIDENCE FINANCIAL is over QUERY PersonFINANCIALPATENTPERSONPERSONCOMPANYleadshasSectorEVIDENCE FINANCIAL is under QUERY CompanyP(Company |(hasSector) FINANCIAL) = P(FINANCIAL |(hasSector) Company) * P(Company) * 1

Normalisation factorP(FINANCIAL)Bottom-Up Inference (Bayes Formula)4949

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