Mean Field Theory for Sigmoid Belief Networks

TL;DR

This paper introduces a mean field theory approach for sigmoid belief networks, offering a computationally feasible approximation of their probability distributions and a lower bound on evidence likelihood, demonstrated on digit classification.

Contribution

It develops a novel mean field framework for sigmoid belief networks, bridging statistical mechanics and probabilistic modeling, with practical application to pattern recognition.

Findings

Provides a tractable approximation to true distributions

Yields a lower bound on evidence likelihood

Successfully applied to handwritten digit classification

Abstract

We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence. We demonstrate the utility of this framework on a benchmark problem in statistical pattern recognition---the classification of handwritten digits.