贝叶斯推理与并行回火研究综述

Overview of Research on Bayesian Inference and Parallel Tempering

贝叶斯推理是统计学中的主要问题之一,旨在根据观测数据更新概率分布模型的先验知识。对于真实情况下常遇到的无法观测或难以直接计算的后验概率,贝叶斯推理可以对其进行近似,它是一种以贝叶斯定理为基础的重要方法。在许多机器学习问题中都涉及对包含各类特征数据的真实分布进行模拟和近似的过程,如分类模型、主题建模和数据挖掘等,因此贝叶斯推理在当今机器学习领域里具有重要而独特的研究价值。随着大数据时代的开始,研究者经由实际信息采集到海量的实验数据,导致需要模拟和计算的目标分布也非常复杂,如何在复杂数据下对目标分布进行结果精确和时间高效的近似推理,成为了当今贝叶斯推理问题的重难点。针对这一复杂分布模型下的推理问题,文中对近年来解决贝叶斯推理问题的两大主要方法——变分推理和采样方法,进行系统性地介绍和综述。首先,给出变分推理的问题定义与理论知识,详细介绍以坐标上升为基础的变分推理算法,并给出这一方法的已有应用与未来展望。然后,对国内外现有的采样方法的研究成果进行综述,给出各类主要采样方法的具体算法流程,并总结和对比这些方法的特性与优缺点。最后,引入并行回火技术,对其基本理论和方法进行概述,探讨并行回火与采样方法的结合与应用,为未来贝叶斯推理问题的发展探讨了新的研究方向。

Bayesian inference is one of the main problems in statistics.It aims to update the prior knowledge of the probability distribution model based on the observation data.For the posterior probability that cannot be observed or is difficult to directly calculate,which is often encountered in real situations,Bayesian inference can obtain a good approximation.It is a kind of important method based on Bayesian theorem.Many machine learning problems involve the process of simulating and approximating the target distribution of various types of feature data,such as classification models,topic modeling,and data mining.Therefore,Bayesian inference has shown important and unique research value in the field of machine learning.With the beginning of the big data era,the experimental data collected by researchers through actual information is very large,resulting in the complex distribution of targets to be simulated and calculated.How to perform accurate and time-efficient approximation inferences on target distributions under complex data has become a major and difficult point in Bayesian inference problems today.Aiming at the infe-rence problem under this complex distribution model,this paper systematically introduces and summarizes the two main methods for solving Bayesian inference problems in recent years,which are variational inference and sampling methods.Firsly,this paper gives the problem definition and theoretical knowledge of variational inference,introduces in detail the variational inference algorithm based on coordinate ascent,and gives the existing applications and future prospects of this method.Next,it reviews the research results of existing sampling methods at home and abroad,gives the specific algorithm procedure of various main sampling methods,as well as summarizes and compares the characteristics,advantages and disadvantages of these methods.Finally,this paper introduces parallel tempering technique,outlines its basic theories and methods,discusses the combination and application of parallel tempering and sampling methods,and explores new research directions for the future development of Bayesian inference problems.