Alexander V. Kozlov (PhD student)
(Professor Daphne Koller)
We consider the problem of reasoning in domains involving both continuous and discrete variables, and involving significant amounts of uncertainty. Such domains are modeled using hybrid Bayesian networks. Unfortunately, the inference task for such networks has been largely unresolved. The inference algorithms for such networks have either been highly inefficient or have been very limited in their applicability. In this work, we provide a new algorithm which is both efficient and fully general. It is based on automatic discretization of the continuous variables, by minimizing the information loss induced by the discretization. Rather than discretizing each variable separately, we use a nonuniform partition of continuous domains across all variables. We show that this can lead to an exponential factor savings in the size of the discretized network. We show how this representation can be utilized in standard Bayesian network inference algorithms.
We also consider a dynamic version of this algorithm which automatically adjusts the discretization to the evidence and to the requirements of the task at hand. We construct an iterative anytime algorithm that gradually improves the accuracy of the answer on a query and the quality of discretization given evidence. We provide empirical results showing that the algorithm rapidly converges to a very good discretization of the continuous variables, one which is tailored to the situation at hand.