A Differential Approach to Inference in Bayesian Networks

TL;DR

This paper introduces a novel differential approach for inference in Bayesian networks by compiling them into multivariate polynomials and using partial derivatives to efficiently answer various probabilistic queries.

Contribution

It proposes a new framework that simplifies and unifies inference, parameter estimation, and sensitivity analysis in Bayesian networks through polynomial derivatives.

Findings

Constant-time computation of many probabilistic queries

Complexity results for polynomial compilation and derivatives

Unique simplicity and comprehensiveness of the framework

Abstract

We present a new approach for inference in Bayesian networks, which is mainly based on partial differentiation. According to this approach, one compiles a Bayesian network into a multivariate polynomial and then computes the partial derivatives of this polynomial with respect to each variable. We show that once such derivatives are made available, one can compute in constant-time answers to a large class of probabilistic queries, which are central to classical inference, parameter estimation, model validation and sensitivity analysis. We present a number of complexity results relating to the compilation of such polynomials and to the computation of their partial derivatives. We argue that the combined simplicity, comprehensiveness and computational complexity of the presented framework is unique among existing frameworks for inference in Bayesian networks.