Representing Probabilistic Relations in RDF

Talk at UMBC

2005-03-07

Yoshio Fukushige

W3C Fellow / Matsushita Electric Industrial Co., Ltd.(Panasonic)

fuku@w3.org / fukushige.yoshio@jp.panasonic.com

http://www.w3.org/2005/03/07-yoshio-UMBC/

Overview of this talk

Today's talk consists of:

Short introduction of myself
A description of my work on representing probabilistic relations in RDF
- Aim
- Overall framework
- Description of the vocabulary through an example
- Current situation and issues
Comparison with BayesOWL

Self Introduction

Name	Yoshio Fukushige 福重貴雄
Affiliate	Network Systems Development Center, Matsushita Electric Industrial Co., Ltd. fukushige.yoshio@jp.panasonic.com
Affiliate	W3C fellow, based at Keio Univ. fuku@w3.org
Research domain	Semantic Web (cf. RDF Data Access Working Group), Text classification/clustering, Application of Bayesian Network

Representing Probabilistic Relations in RDF

The aim of my ongoing work is to provide

a vocabulary for representing probabilistic relations in RDF
an algorithm for transform a set of probabilistic relations in a RDF graph to a Bayesian Network
a query language and protocol for querying the BN

and to provide them as a strawman for standard / best practice in processing uncertain information in RDF.

Overall Framework

Represent probabilistic relations in a RDF graph
Transform it into a Bayesian Network(BN) and store in a BN reasoner
Transform the observation graph (when provided) and feed it to the reasoner
Transform the query and feed it to the reasoner
Get the reasoning result, transform and answer back

(Provide as a Web Service?)

An Example for Discussion

Bayesian Network for the Metastatic Cancer problem

MetastaticCancer
TRUE	FALSE
0.20	0.80

		SerumCalcium
		TRUE	FALSE
Metastatic Cancer	TRUE	0.80	0.20
Metastatic Cancer	FALSE	0.20	0.80

		BrainTumor
		TRUE	FALSE
Metastatic Cancer	TRUE	0.20	0.80
Metastatic Cancer	FALSE	0.05	0.95

		BrainTumor	Coma
		BrainTumor	TRUE	FALSE
Serum Calcium	TRUE	TRUE	0.80	0.20
	TRUE	FALSE	0.80	0.20
	FALSE	TRUE	0.80	0.20
	FALSE	FALSE	0.05	0.95

		HeadAche
		TRUE	FALSE
Brain Tumor	TRUE	0.80	0.20
Brain Tumor	FALSE	0.60	0.40

Vocabulary for Representing Probabilistic Relations

A node in BN is represented as a node of type prob:ProbabilisticStatements.

Underlined nodes means an instance of that (label) class.
Default prefix is prob: (URL: to be determined)

Events as N-ary relations

The targets of description are probabilistic relations between events. An event is represented as a prob:Clause node. (prob:Event, prob:State or prob:Proposition are better namings?) A prob:Clause node has a predicate node and role nodes (all are instances).

e.g. Clause node with * represents a High Serum Calcium event

Representing P(SerumCalcium | MetastaticCancer)

RDF graph for P(SerumCalcium|MetastaticCancer)

		SerumCalcium
		TRUE	FALSE
Metastatic Cancer	TRUE	0.80	0.20
Metastatic Cancer	FALSE	0.20	0.80

PSs stands for prob:ProbabilisticRelations
PS stands for prob:ProbabilisticRelation
P stands for prob:Probability

Click here to see a representation in N3 format

Probabilistic Observation

e.g. Mary has a headache with probability of 70%.

CL stands for prob:Clause

Resultant Beliefs

e.g. Mary has a metastatic cancer with probability of 9.7%.

Current Status and Issues

I have examined the vocabulary needed for representing probabilistic relations in RDF, and now am writing code for transformation to BN. Query language and protocol are yet to be examined.

Remaining issues are among others,

How to get the RDF description from imperfect / partial descriptions?
How to deal with cyclic description?
How to incorporate ontological knowledge / restrictions?

Comparison with BayesOWL

	My approach	BayeseOWL
main target	Causal relationship (RDF)	Ontological relationship (OWL)
basic proposition	prob:Clause	Variable (?)
conditions are attached to	prob:ProbabilisticStatements (distribution)	CondProb (case in distribution)
probability	prob:Probability	literal

How can these approaches help each other?

Some Questions on BayesOWL

How to represent CPT's in OWL: need for marginalize out the contributions of control nodes in BN?
re: (D-)IPFP, is it globally maximal? Influence of initial value? Relation with EM?
re:Reasoning, how about calculating I-divergence between evidence and posterior by assuming each class?
re:Concept Mapping, how to learn mappings based on data and constraints?

Appendix

Why not use a predicate for a prob:Close?

In order not to make it a ground statement (= which is said to be real). The graph below says that Mary really has high serum calcium

Why the predicate node is an instance node, not a class node?

Suppose Hans may have dropped an ax. Clause 1 claims that it is a golden ax, and clause 2 claims that it is a silver ax. Both agree that he may have dropped something.

RDF graph for two claims on what Hans dropped