Loopy Belief Propagation for Approximate Inference: An Empirical Study

TL;DR

This paper empirically evaluates loopy belief propagation's effectiveness as an approximate inference method across various Bayesian networks, highlighting its strengths and limitations in different contexts.

Contribution

It provides a comparative analysis of loopy belief propagation's accuracy and convergence behavior in multiple Bayesian network architectures, including real-world examples.

Findings

Loopy belief propagation often converges and approximates true marginals well.

In some networks, like QMR, it oscillates and fails to approximate correctly.

Simple methods to prevent oscillations can sometimes lead to incorrect results.

Abstract

Recently, researchers have demonstrated that loopy belief propagation - the use of Pearls polytree algorithm IN a Bayesian network WITH loops OF error- correcting codes.The most dramatic instance OF this IS the near Shannon - limit performance OF Turbo Codes codes whose decoding algorithm IS equivalent TO loopy belief propagation IN a chain - structured Bayesian network. IN this paper we ask : IS there something special about the error - correcting code context, OR does loopy propagation WORK AS an approximate inference schemeIN a more general setting? We compare the marginals computed using loopy propagation TO the exact ones IN four Bayesian network architectures, including two real - world networks : ALARM AND QMR.We find that the loopy beliefs often converge AND WHEN they do, they give a good approximation TO the correct marginals.However,ON the QMR network, the loopy beliefs oscillated AND had no obvious relationship TO the correct posteriors. We present SOME initial investigations INTO the cause OF these oscillations, AND show that SOME simple methods OF preventing them lead TO the wrong results.