# Mean-Field Inference in Gaussian Restricted Boltzmann Machine

arXiv: https://arxiv.org/abs/1512.00927 · HTML: https://mlsanity.com/paper/1512.00927/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2015.

## Built on by (most cited first, 3 of 3)

- [Gaussian-Bernoulli RBMs Without Tears](https://mlsanity.com/paper/2210.10318/) (2022)
- [Fundamental operating regimes, hyper-parameter fine-tuning and glassiness: towards an interpretable replica-theory for trained restricted Boltzmann machines](https://mlsanity.com/paper/2406.09924/) (2024)
- [Dataset-Free Weight-Initialization on Restricted Boltzmann Machine](https://mlsanity.com/paper/2409.07708/) (2024)

## Abstract (arXiv)

A Gaussian restricted Boltzmann machine (GRBM) is a Boltzmann machine defined on a bipartite graph and is an extension of usual restricted Boltzmann machines. A GRBM consists of two different layers: a visible layer composed of continuous visible variables and a hidden layer composed of discrete hidden variables. In this paper, we derive two different inference algorithms for GRBMs based on the naive mean-field approximation (NMFA). One is an inference algorithm for whole variables in a GRBM, and the other is an inference algorithm for partial variables in a GBRBM. We compare the two methods analytically and numerically and show that the latter method is better.