Contextual Weak Independence in Bayesian Networks

by   Michael S. K. M. Wong, et al.

It is well-known that the notion of (strong) conditional independence (CI) is too restrictive to capture independencies that only hold in certain contexts. This kind of contextual independency, called context-strong independence (CSI), can be used to facilitate the acquisition, representation, and inference of probabilistic knowledge. In this paper, we suggest the use of contextual weak independence (CWI) in Bayesian networks. It should be emphasized that the notion of CWI is a more general form of contextual independence than CSI. Furthermore, if the contextual strong independence holds for all contexts, then the notion of CSI becomes strong CI. On the other hand, if the weak contextual independence holds for all contexts, then the notion of CWI becomes weak independence (WI) nwhich is a more general noncontextual independency than strong CI. More importantly, complete axiomatizations are studied for both the class of WI and the class of CI and WI together. Finally, the interesting property of WI being a necessary and sufficient condition for ensuring consistency in granular probabilistic networks is shown.



There are no comments yet.


page 1

page 2

page 3

page 7

page 10


Context-Specific Independence in Bayesian Networks

Bayesian networks provide a language for qualitatively representing the ...

Conditional Independence in Max-linear Bayesian Networks

Motivated by extreme value theory, max-linear Bayesian networks have bee...

Argument Calculus and Networks

A major reason behind the success of probability calculus is that it pos...

Context-Specific Likelihood Weighting

Sampling is a popular method for approximate inference when exact infere...

Local Exchangeability

Exchangeability---in which the distribution of an infinite sequence is i...

Advances in Probabilistic Reasoning

This paper discuses multiple Bayesian networks representation paradigms ...

Reading Dependencies from Polytree-Like Bayesian Networks

We present a graphical criterion for reading dependencies from the minim...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.