Introduction |
Recently there has been work to extend belief networks by allowing more structured representations of the conditional probability of a variable given its parents [8]. This has been in terms of either causal independencies [16][34], parametric forms such as sigmoidal Bayesian networks [21][27], or by exploiting contextual independencies inherent in stating the conditional probabilities in terms of rules [23] or trees [29][5]. In this paper we show how an algorithm that exploits conditional independence for efficient inference in belief networks can be extended to also exploit contextual independence. [25] provides an earlier, less efficient, version in terms of rules. [32] give an abstract mathematical analysis of how contextual independence can be exploited in inference.
Section * introduces belief networks and an algorithm, variable elimination (VE) [33] or Bucket Elimination for belief assessment [11], for computing posterior probabilities in belief that is based on nonlinear dynamic programming [2]. Section * presents a representation for conditional probabilities that lets us state contextual independence in terms of confactors. Section * shows how the VE algorithm can be extended to exploit the contextual independence in confactors. Section * shows how we can improve efficiency by reducing the amount of splitting. Section * gives some empirical results on standard and random networks. The details of the experiments are given in Appendix *. Section * gives comparisons to other proposals for exploiting contextual independencies. Section * presents conclusions and future work.
Introduction |