# Population-Contrastive-Divergence: Does Consistency help with RBM training?

arXiv: https://arxiv.org/abs/1510.01624 · HTML: https://mlsanity.com/paper/1510.01624/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2015.

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

- [Equilibrium and non-Equilibrium regimes in the learning of Restricted Boltzmann Machines](https://mlsanity.com/paper/2105.13889/) (2021)
- [Fast training and sampling of Restricted Boltzmann Machines](https://mlsanity.com/paper/2405.15376/) (2024)
- [Equilibrium Training of Energy-Based Models with Parallel Trajectory Tempering](https://mlsanity.com/paper/2607.27077/) (2026)

## Abstract (arXiv)

Estimating the log-likelihood gradient with respect to the parameters of a Restricted Boltzmann Machine (RBM) typically requires sampling using Markov Chain Monte Carlo (MCMC) techniques. To save computation time, the Markov chains are only run for a small number of steps, which leads to a biased estimate. This bias can cause RBM training algorithms such as Contrastive Divergence (CD) learning to deteriorate. We adopt the idea behind Population Monte Carlo (PMC) methods to devise a new RBM training algorithm termed Population-Contrastive-Divergence (pop-CD). Compared to CD, it leads to a consistent estimate and may have a significantly lower bias. Its computational overhead is negligible compared to CD. However, the variance of the gradient estimate increases. We experimentally show that pop-CD can significantly outperform CD. In many cases, we observed a smaller bias and achieved higher log-likelihood values. However, when the RBM distribution has many hidden neurons, the consistent estimate of pop-CD may still have a considerable bias and the variance of the gradient estimate requires a smaller learning rate. Thus, despite its superior theoretical properties, it is not advisable to use pop-CD in its current form on large problems.