近似Bayes计算前沿研究进展及应用

Recent Progress of Approximate Bayesian Computation and Its Applications

在大数据和人工智能时代,建立能够有效处理复杂数据的模型和算法,以从数据中获取有用的信息和知识是应用数学、统计学和计算机科学面临的共同难题.为复杂数据建立生成模型并依据这些模型进行分析和推断是解决上述难题的一种有效手段.从一种宏观的视角来看,无论是应用数学中常用的微分方程和动力系统,或是统计学中表现为概率分布的统计模型,还是机器学习领域兴起的生成对抗网络和变分自编码器,都可以看作是一种广义的生成模型.随着所处理的数据规模越来越大,结构越来越复杂,在实际问题中所需要的生成模型也变得也越来越复杂,对这些生成模型的数学结构进行精确地解析刻画变得越来越困难.如何对没有精确解析形式(或其解析形式的精确计算非常困难)的生成模型进行有效的分析和推断,逐渐成为一个十分重要的问题.起源于Bayes统计推断,近似Bayes计算是一种可以免于计算似然函数的统计推断技术,近年来在复杂统计模型和生成模型的分析和推断中发挥了重要作用.该文从经典的近似Bayes计算方法出发,对近似Bayes计算方法的前沿研究进展进行了系统的综述,并对近似Bayes计算方法在复杂数据处理中的应用前景及其和前沿人工智能方法的深刻联系进行了分析和讨论.

In the era of big data and artificial intelligence,it is a common challenge for applied mathematics,statistics and computer science to extract valuable information and knowledge from complex data and models.Generative models are a class of powerful models which can potentially handle the above difficulty.From a macro point of view,the differential equations and dynamic systems in applied mathematics,the probability distribution in statistical models,and the typical generative models(generative adversarial networks and variational auto-encoders)in computer science could be considered as generalized generative models.Along with larger and larger-size data,the structure of data becomes more and more complicated simultaneously.Therefore,more powerful generative models are essential to process real problems.It is a challenge to describe mathematical structures of these generative models.It poses a natural question of how to analyze such generative models without analytic forms(or hard to obtain their analytic forms).Originated from the Bayesian inference,the approximate Bayesian computation,as a likelihood-free technique,plays an important role in processing complex statistical models and generative models.Based on the classic approximate Bayesian computation,the development and recent advance of approximate Bayesian computation were systematically reviewed.Finally,the application of the approximate Bayesian computation to complex data and the deep connection between the approximate Bayesian computation and cutting-edge artificial intelligence methods were discussed.