Context-Specific Independence in Bayesian Networks
This work addresses the limitation of Bayesian networks in capturing context-specific independencies, which is a problem for researchers and practitioners in probabilistic graphical models, but it appears incremental as it builds on existing concepts like d-separation and tree-structured representations.
The paper tackles the problem of representing context-specific independencies (CSIs) in Bayesian networks, which are conditional independencies that hold only for specific variable assignments, by proposing a formal notion of CSI based on regularities in conditional probability tables and a technique analogous to d-separation to determine when such independence holds. It focuses on tree-structured CPTs as a qualitative representation scheme for capturing CSI and suggests ways to support effective inference algorithms, including a structural decomposition for clustering algorithms and an alternative algorithm based on cutset conditioning.
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.