Effective Mean-Field Inference Method for Nonnegative Boltzmann Machines

TL;DR

This paper introduces an efficient mean-field inference approach for Nonnegative Boltzmann Machines, leveraging the Thouless--Anderson--Palmer equation and diagonal consistency to improve probabilistic modeling of nonnegative data.

Contribution

It proposes a novel inference method combining the Thouless--Anderson--Palmer equation with diagonal consistency for NNBMs, enhancing inference accuracy.

Findings

Improved inference accuracy for NNBMs.

Effective handling of multi-modal nonnegative data.

Potential applications in biological neural networks and matrix factorization.

Abstract

Nonnegative Boltzmann machines (NNBMs) are recurrent probabilistic neural network models that can describe multi-modal nonnegative data. NNBMs form rectified Gaussian distributions that appear in biological neural network models, positive matrix factorization, nonnegative matrix factorization, and so on. In this paper, an effective inference method for NNBMs is proposed that uses the mean-field method, referred to as the Thouless--Anderson--Palmer equation, and the diagonal consistency method, which was recently proposed.