A novel inference algorithm on graphical model

Abstract

We present a framework for approximate inference that, given a factor graph and a subset of its variables, produces an approximate marginal distribution over these variables with bounds. The factors of the factor graph are abstracted as as piecewise polynomial functions with lower and upper bounds, and a variant of the variable elimination algorithm solves the inference problem over this abstraction. The resulting distributions bound quantifies the error between it and the true distribution. We also give a set of heuristics for improving the bounds by further refining the binary space partition trees.