Min-based Possibilistic Networks Research Articles

Possibilistic Networks: Computational Analysis of MAP and MPE Inference

Possibilistic graphical models are powerful modeling and reasoning tools for uncertain information based on possibility theory. In this paper, we provide an analysis of computational complexity of MAP and MPE queries for possibilistic networks. MAP queries stand for maximum a posteriori explanation while MPE ones stand for most plausible explanation. We show that the decision problems of answering MAP and MPE queries in both min-based and product-based possibilistic networks is NP-complete. Definitely, such results represent an advantage of possibilistic graphical models over probabilistic ones since MAP queries are NPPP -complete in Bayesian networks. Our proofs for querying min-based possibilistic networks make use of reductions from the 3SAT problem to querying possibilistic networks decision problem. Moreover, the provided reductions may be useful for the implementation of MAP and MPE inference engines based on the satisfiability problem solvers. As for product-based networks, the provided proofs are incremental and make use of reductions from SAT and its weighted variant WMAXSAT.

An Approximate Algorithm for Min-Based Possibilistic Networks

Min-based or qualitative possibilistic networks are important tools to efficiently and compactly represent and analyze uncertain information. Inference is a crucial task in min-based networks, which consists of propagating information through the network structure to answer queries. Exact inference computes posteriori possibility distributions, given some observed evidence, in a time proportional to the number of nodes of the network when it is simply connected without loops. On multiply connected networks with loops, exact inference is known as a hard problem. This paper proposes an approximate algorithm for inference in min-based possibilistic networks. More precisely, we adapt the well-known approximate algorithm Loopy Belief Propagation LBP on qualitative possibilistic networks. We provide different experimental results that analyze the convergence of possibilistic LBP.