Approximate Inference in Probabilistic Graphical Models with Determinism

In the proposed thesis, we study a special class of belief networks which contain both probabilistic and deterministic information. Deterministic information occurs as zero probabilities in the belief network. A majority of the work in the belief network community (see for example papers in conferences like UAI, AAAI, IJCAI and NIPS) addresses probabilistic inference tasks under the assumption that the underlying joint distribution represented by the belief network is strictly positive i.e. devoid of any determinism. The positivity assumption is problematic because (a) modeling many real-world problems such as genetic linkage analysis (Fishelson & Geiger 2003) requires that the inference method reason with both probabilistic and deterministic information and (b) inference is harder in presence of determinism or extreme probabilities (Dagum & Luby 1993). The purpose of the proposed thesis is to study both the representational and algorithmic issues involved in modeling deterministic information along with the usual probabilistic information in a belief network.