Du Bochuan, Tian Pu
School of Life Sciences, Jilin University, Changchun 130012, China.
School of Artificial Intelligence, Jilin University, Changchun 130012, China.
Math Biosci Eng. 2023 Nov 27;20(12):21147-21162. doi: 10.3934/mbe.2023935.
Factorization reduces computational complexity, and is therefore an important tool in statistical machine learning of high dimensional systems. Conventional molecular modeling, including molecular dynamics and Monte Carlo simulations of molecular systems, is a large research field based on approximate factorization of molecular interactions. Recently, the local distribution theory was proposed to factorize joint distribution of a given molecular system into trainable local distributions. Belief propagation algorithms are a family of exact factorization algorithms for (junction) trees, and are extended to approximate loopy belief propagation algorithms for graphs with loops. Despite the fact that factorization of probability distribution is the common foundation, computational research in molecular systems and machine learning studies utilizing belief propagation algorithms have been carried out independently with respective track of algorithm development. The connection and differences among these factorization algorithms are briefly presented in this perspective, with the hope to intrigue further development of factorization algorithms for physical modeling of complex molecular systems.
因式分解降低了计算复杂度，因此是高维系统统计机器学习中的一个重要工具。传统的分子建模，包括分子系统的分子动力学和蒙特卡罗模拟，是一个基于分子相互作用近似因式分解的大型研究领域。最近，提出了局部分布理论，将给定分子系统的联合分布分解为可训练的局部分布。置信传播算法是一类用于（连接）树的精确因式分解算法，并扩展为用于有环图的近似循环置信传播算法。尽管概率分布的因式分解是共同基础，但分子系统的计算研究和利用置信传播算法的机器学习研究是各自独立进行的，有着各自的算法发展轨迹。从这个角度简要介绍了这些因式分解算法之间的联系和差异，希望能激发用于复杂分子系统物理建模的因式分解算法的进一步发展。
