Node Splitting: A Scheme for Generating Upper Bounds in Bayesian Networks

TL;DR

This paper introduces a new formulation of the mini-bucket algorithm for approximate inference in Bayesian networks, enabling more efficient search, new heuristics, and improved approximation capabilities by leveraging exact inference techniques.

Contribution

It reformulates mini-bucket as exact inference on an approximate model, leading to theoretical insights, new heuristics, and enhanced approximation methods.

Findings

Reduced search space in branch-and-bound algorithms using mini-bucket bounds

Development of new mini-bucket heuristics inspired by the formulation

Enhanced mini-bucket approximations leveraging recent advances in exact inference

Abstract

We formulate in this paper the mini-bucket algorithm for approximate inference in terms of exact inference on an approximate model produced by splitting nodes in a Bayesian network. The new formulation leads to a number of theoretical and practical implications. First, we show that branchand- bound search algorithms that use minibucket bounds may operate in a drastically reduced search space. Second, we show that the proposed formulation inspires new minibucket heuristics and allows us to analyze existing heuristics from a new perspective. Finally, we show that this new formulation allows mini-bucket approximations to benefit from recent advances in exact inference, allowing one to significantly increase the reach of these approximations.