Finding Non-overlapping Clusters for Generalized Inference Over Graphical Models

TL;DR

This paper introduces a novel block-graph framework that enhances approximate inference in graphical models by clustering nodes into non-overlapping groups, leading to more accurate marginal estimates.

Contribution

The authors propose a simple, efficient block-graph construction method that improves the accuracy of approximate inference algorithms on graphical models.

Findings

Improved inference accuracy demonstrated through extensive simulations.

The block-graph approach enhances estimates across various inference algorithms.

Longer cycles in graphs contribute to better approximation quality.

Abstract

Graphical models use graphs to compactly capture stochastic dependencies amongst a collection of random variables. Inference over graphical models corresponds to finding marginal probability distributions given joint probability distributions. In general, this is computationally intractable, which has led to a quest for finding efficient approximate inference algorithms. We propose a framework for generalized inference over graphical models that can be used as a wrapper for improving the estimates of approximate inference algorithms. Instead of applying an inference algorithm to the original graph, we apply the inference algorithm to a block-graph, defined as a graph in which the nodes are non-overlapping clusters of nodes from the original graph. This results in marginal estimates of a cluster of nodes, which we further marginalize to get the marginal estimates of each node. Our proposed block-graph construction algorithm is simple, efficient, and motivated by the observation that approximate inference is more accurate on graphs with longer cycles. We present extensive numerical simulations that illustrate our block-graph framework with a variety of inference algorithms (e.g., those in the libDAI software package). These simulations show the improvements provided by our framework.