相关潜变量的可扩展边缘化及其在粒子相互作用核学习中的应用

Mengyang Gu, Xubo Liu, X. Fang, Sui Tang
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引用次数: 6

摘要

潜在变量或有害参数的边缘化是贝叶斯推理和不确定性量化的一个基本方面。在这项工作中,我们专注于建模相关数据(如时空或功能观测)中潜在变量的可扩展边缘化。我们首先引入高斯过程(GPs)来建模相关数据,并强调计算挑战,其中计算复杂性随着观测数量的增加而快速增加。然后,我们回顾了状态空间模型和具有时间输入mat协方差的GPs之间的联系。引入卡尔曼滤波和Rauch-Tung-Striebel平滑作为一种可扩展的边缘化技术,用于计算gp的可能性并在没有近似的情况下进行预测。我们介绍了将可扩展边缘化思想扩展到多变量相关输出和时空观测的共区域化线性模型的最新研究成果。在本文的最后,我们介绍了一种新的边缘化技术来估计相互作用核和预测粒子轨迹。计算的进步在于对潜变量的协方差逆矩阵进行稀疏表示,然后应用共轭梯度来提高大数据集的预测精度。在这项工作中取得的计算进步概述了分子动力学模拟,细胞迁移和基于代理的模型的广泛应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Scalable Marginalization of Correlated Latent Variables with Applications to Learning Particle Interaction Kernels
Marginalization of latent variables or nuisance parameters is a fundamental aspect of Bayesian inference and uncertainty quantification. In this work, we focus on scalable marginalization of latent variables in modeling correlated data, such as spatio-temporal or functional observations. We first introduce Gaussian processes (GPs) for modeling correlated data and highlight the computational challenge, where the computational complexity increases cubically fast along with the number of observations. We then review the connection between the state space model and GPs with Matérn covariance for temporal inputs. The Kalman filter and Rauch-Tung-Striebel smoother were introduced as a scalable marginalization technique for computing the likelihood and making predictions of GPs without approximation. We introduce recent efforts on extending the scalable marginalization idea to the linear model of coregionalization for multivariate correlated output and spatio-temporal observations. In the final part of this work, we introduce a novel marginalization technique to estimate interaction kernels and forecast particle trajectories. The computational progress lies in the sparse representation of the inverse covariance matrix of the latent variables, then applying conjugate gradient for improving predictive accuracy with large data sets. The computational advances achieved in this work outline a wide range of applications in molecular dynamic simulation, cellular migration, and agent-based models.
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