Keywords: probabilistic dependency graphs, PDGs, probabilistic inference, clique trees, tree decomposition, exponential cones, convex programming, inconsistency
TL;DR: we give the first inference algorithm for probabilistic dependency graphs, prove that it is correct and runs in polynomial time, implement it, and evaluate its performance.
Abstract: Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this inconsistency. We present the first tractable inference algorithm for PDGs with discrete variables, making the asymptotic complexity of PDG inference similar that of the graphical models they generalize. The key components are: (1) the observation that PDG inference can be reduced to convex optimization with exponential cone constraints, (2) a construction that allows us to express these problems compactly for PDGs of boundeed treewidth, for which we needed to further develop the theory of PDGs, and (3) an appeal to interior point methods that can solve such problems in polynomial time. We verify the correctness and time complexity of our approach, and provide an implementation of it. We then evaluate our implementation, and demonstrate that it outperforms baseline approaches. Our code is available at http://github.com/orichardson/pdg-infer-uai.
Supplementary Material: pdf
Other Supplementary Material: zip