Ways to Incorporate Ontology and Bayesian Network

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 3) Semi automated construction

of BN from domain ontology

Purpose of the Mapping Approach

Mapping 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

Research in Ontology Mapping

1. OMEN (Ontology Mapping ENhancer 2004) OMEN: A Probabilistic Ontology Mapping

Tool by Prasenjit Mitra, Anuj Jaiswal,

Pennsylvania State University and Stanford University

2. 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

Purpose of Extending Ontology reasoning Approach

Extending 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

Purpose of automatic BN construction approach

Automatic 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

Research on Automated BN Construction

Stefan 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

Ontology Mapping with BN

BayesOWL 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 reasoning

Purpose/ Direction of Approach In 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 B

In 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

Its 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

How to Incorporate PO?

Probabilistic Information Markups

Structural translation

Constructing CPT for L-Nodes

Constructing CPT for Concept Nodes

Structural Translation

CPT for L-Nodes

CPT for Concept NodesExample taken from Zhongli Ding’s Thesis

Next a constraint on B is applied R1(B)=(0.61,0.39) 17

A B C D Q(X)

T T T T 0.0048

T T T F 0.0432

T T F T 0.0272

T T F F 0.0048

T F T T 0.0864

T F T F 0.1056

T F F T 0.0896

T F F F 0.0384

F T T T 0.0126

F T T F 0.1134

F T F T 0.1989

F T F F 0.0351

F F T T 0.0378

F F T F 0.0462

F F F T 0.1092

F F F F 0.0468

Initial Knowledge Base( )iQ X

B Q(B)

T 0.44

F 0.56

Marginal on B

B R(B)

T 0.61

F 0.39

Constraint on B

B R(B)/Q(B)

T 1.386

F 0.6964

New JPD

A B C D Q(X)

T T T T 0.006653T T T F 0.059875T T F T 0.037699T T F F 0.006653T F T T 0.060169T F T F 0.07354T F F T 0.062397T F F F 0.026742F T T T 0.017464F T T F 0.157172F T F T 0.275675F T F F 0.048649F F T T 0.026324F F T F 0.032174F F F T 0.076047F F F F 0.032592

From new JPD the constraint is satisfied. Next another constraint on C is applied

R2(C)= (0.83,0.17) shown in next slide

18

Initial Knowledge Base( )iQ X

C Q(C)

T 0.433

F 0.567

Marginal on C

C R(C)

T 0.83

F 0.17

Constraint on C

C R(C)/Q(C)

T 1.9168

F 0.2998

New JPD

A B C D Q(X)


19

A B C D Q(X)


Reasoning

The BayesOWL framework can support common ontology reasoning tasks as probabilistic reasoning in the translated BN

Concept Overlapping Concept Subsumption

Automated BN Construction

Ontology-based generation of Bayesian Networks

By 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

Motivation

Creation of BN requires at least three challenging tasks: Determination of relevant influence

factors Determination of relationships between

identified influence factors Calculation of CPT’s

Ontologies are a potential solution to address stated challenges

Example 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

Methodology Proposed

Concepts Nodes in BN Relations Links Axioms Node states Instances Findings

Concept Nodes Following factors have been

identified:1) Predecessor Threats (PT1Ti , ……, PTnTi )

influence the considered threat Ti which influences it successor threats (ST1Ti , ……, STnTi)

Continue..

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

Axiomsnode scales and weights

Three 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

Continue..

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)

Continue..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

Relations Links

Limitations

Functions 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 interest

Clinical CPG’s

Extending Ontology Query with BN Inference

Strategy

Extracting 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:

o Definition of the language operational semantics, based on the well-known Bayesian network reasoning schemas

An example of Ontology Compiling Process

Extracting a Bayesian network from an Ontology – An Example (1) An Ontology O is a pair <T, R > where

- T = {T1,..,Ti,..,Tn} is a set of hierarchies called domain concepts

- R Ti x Tj is a set of arcs binding elements of T such that the resulting graph is acyclic.

COMPANY

PATENT

RESEARCH

PROJECT

MAN

COMPTETITOR

VENDOR

PERSON

SUPPLIERJOINTVENTURE

WOMAN

hasCeo

leads

T1

T3

T2

LIFEINSURANCE

FINANCIAL

CREDITCARD

SERVICES

SECTORT4hasSectorR1=

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 PERSON

R2 : PERSON PROJECT

R3 : COMPANY SECTOR

is-a relation

Object property

COMPANY

COMPETITOR

VENDOR

SUPPLIERJOINTVENTURE

MAN

PERSON

WOMAN

PATENTRESEARCH

PROJECT

P(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)

LIFEINSURANCE

FINANCIAL

CREDIT CARD

SERVICES

SECTORP(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)R1

R2

R3

High Level NodeHigh Level RelationLow Level Node

Low Level Relation

Extracting a Bayesian network from an Ontology – An Example (2)

T1

T2

T3

T4

Ontology Compiling Process

Ontology Compiling Process

It is composed of two phases:

- Phase one: compiling TBox ontology in a 2lBN structural part

- Phase 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 1

Man

Woman

Person

hasCeo

LLRT

HLRT

HLN_COMPANY

LLN

HLN_PERSON

HLR_Ceo

2lBN structural part

The 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 part The 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

Low Level Relations probability distribution - example

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

High Level Relations probability distribution - example

Number of triples satisfyingthe TBox schema

<Company, hasCeo, Person>

Number of instances belonging to the sub-space of Company

corresponding to “Company with a CEO”

Inference over Bayesian network

Inference 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) =

AA

CC

BB

DD

P(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.

Inference 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.

Bayesian query structure

The 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. query

• EVIDENCE 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)

Which 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)

COMPANY

COMPETITOR

VENDOR

SUPPLIER

JOINTVENTURE

MAN

PERSONPERSON

WOMAN

PATENTPATENTRESEARCH

PROJECT

SERVICESFINANCIAL

SECTOR

P(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)

hasCeo

Top Down Inference

P(PATENT |(leads.hasCeo.hasSector) FINANCIAL) =

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

EVIDENCE FINANCIAL is over QUERY PATENT

Top Down Inference

P(Person |(hasCeo.hasSector) FINANCIAL) =

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

EVIDENCE FINANCIAL is over QUERY Person

FINANCIAL

PATENT

PERSONPERSON

COMPANY

leads

hasSector

EVIDENCE FINANCIAL is under QUERY Company

P(Company |(hasSector) FINANCIAL) =

P(FINANCIAL |(hasSector) Company) * P(Company) * 1

Normalisation factorP(FINANCIAL)

Bottom-Up Inference (Bayes Formula)

Documents

Ways to Incorporate Ontology and Bayesian Network