Weighted Positive Binary Decision Diagrams for Exact Probabilistic Inference

TL;DR

This paper introduces Weighted Positive Binary Decision Diagrams, a novel approach that leverages variable constraints to optimize probabilistic inference in Bayesian networks, reducing computational costs.

Contribution

It presents a new language and method that incorporate background constraints into decision diagrams, improving efficiency over existing weighted model counting techniques.

Findings

Reduces inference cost using the new decision diagram structure.

Optimizes Shannon decomposition with background constraints.

Demonstrates improved efficiency in probabilistic inference.

Abstract

Recent work on weighted model counting has been very successfully applied to the problem of probabilistic inference in Bayesian networks. The probability distribution is encoded into a Boolean normal form and compiled to a target language, in order to represent local structure expressed among conditional probabilities more efficiently. We show that further improvements are possible, by exploiting the knowledge that is lost during the encoding phase and incorporating it into a compiler inspired by Satisfiability Modulo Theories. Constraints among variables are used as a background theory, which allows us to optimize the Shannon decomposition. We propose a new language, called Weighted Positive Binary Decision Diagrams, that reduces the cost of probabilistic inference by using this decomposition variant to induce an arithmetic circuit of reduced size.