Context-Specific Independence in Bayesian Networks

TL;DR

This paper introduces a formal concept of context-specific independence in Bayesian networks, proposes a method to identify it, and explores tree-structured CPTs to enhance inference efficiency.

Contribution

It formalizes context-specific independence, develops a d-separation based technique for detection, and leverages tree-structured CPTs for improved inference algorithms.

Findings

Tree-structured CPTs effectively capture context-specific independencies.

Structural decomposition improves clustering algorithm performance.

Alternative inference algorithms based on cutset conditioning are proposed.

Abstract

Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms. It is well-known, however, that there are certain independencies that we cannot capture qualitatively within the Bayesian network structure: independencies that hold only in certain contexts, i.e., given a specific assignment of values to certain variables. In this paper, we propose a formal notion of context-specific independence (CSI), based on regularities in the conditional probability tables (CPTs) at a node. We present a technique, analogous to (and based on) d-separation, for determining when such independence holds in a given network. We then focus on a particular qualitative representation scheme - tree-structured CPTs - for capturing CSI. We suggest ways in which this representation can be used to support effective inference algorithms. In particular, we present a structural decomposition of the resulting network which can improve the performance of clustering algorithms, and an alternative algorithm based on cutset conditioning.