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.

翻译：从同源蛋白质序列的多重序列比对中观察到的单点和成对氨基酸频率来估计进化单点场和成对耦合的逆波茨模型问题，仍然是蛋白质结构与进化研究中有效的方法之一。由于场和耦合的可重复性最为重要，本文采用玻尔兹曼机方法，尽管其计算量较大。为减少玻尔兹曼机所需的计算时间，在每个学习步骤中采用并行、持久的马尔可夫链蒙特卡洛方法来估计单点和成对边际分布。同时，使用随机梯度下降方法减少每次学习的计算时间。另一个问题是如何调整超参数值：进化场和耦合各有一个正则化参数。接触残基对预测的精度常被用于调整超参数，然而该指标对这些正则化参数并不敏感。本文针对场和耦合进行调整，使其满足适合蛋白质构象的特定条件。该方法已应用于八个蛋白质家族。