Inference in Credal Networks with Branch-and-Bound Algorithms

A credal network associates sets of probability distributions with directed acyclic graphs. Under strong independence assumptions, inference with credal networks is equivalent to a signomial program under linear constraints, a problem that is NP-hard even for categorical variables and polytree models. We describe an approach for inference with polytrees that is based on branch-and-bound optimization/search algorithms. We use bounds generated by Tessem’s A/R algorithm, and consider various branch-and-bound schemes.