# Boltzmann Machine Learning with a Parallel, Persistent Markov chain Monte Carlo method for Estimating Evolutionary Fields and Couplings from a Protein Multiple Sequence Alignment

arXiv: https://arxiv.org/abs/2604.18022 · HTML: https://mlsanity.com/paper/2604.18022/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 34 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 2 of 2)

- [Fast and accurate multivariate Gaussian modeling of protein families: Predicting residue contacts and protein-interaction partners](https://mlsanity.com/paper/1404.1240/) (2014)
- [Boltzmann machine learning and regularization methods for inferring evolutionary fields and couplings from a multiple sequence alignment](https://mlsanity.com/paper/1909.05006/) (2019)

## Abstract (arXiv)

The inverse Potts problem for estimating evolutionary single-site fields and pairwise couplings in homologous protein sequences from their single-site and pairwise amino acid frequencies observed in their multiple sequence alignment would be still one of useful methods in the studies of protein structure and evolution. Since the reproducibility of fields and couplings are the most important, the Boltzmann machine method is employed here, although it is computationally intensive. In order to reduce computational time required for the Boltzmann machine, parallel, persistent Markov chain Monte Carlo method is employed to estimate the single-site and pairwise marginal distributions in each learning step. Also, stochastic gradient descent methods are used to reduce computational time for each learning. Another problem is how to adjust the values of hyperparameters; there are two regularization parameters for evolutionary fields and couplings. The precision of contact residue pair prediction is often used to adjust the hyperparameters. However, it is not sensitive to these regularization parameters. Here, they are adjusted for the fields and couplings to satisfy a specific condition that is appropriate for protein conformations. This method has been applied to eight protein families.