贝叶斯分层模型变分推理与概率编程方法综述

在贝叶斯模型中，往往无法解析计算后验概率，在实践中依赖于近似推理。变分推理（VI,Variational Inference）是重要的确定性近似推理方法，比马尔科夫链蒙特卡罗（MCMC,Markov Chain Monte Carlo）采样具有更高的计算效率，在大数据时代有着显著优势。文章通过贝叶斯分层模型，回顾了经典VI，分析了随机变分推理（SVI,Stochastic Variational Inference）及其在主题模型中的应用，综述了更稳健的VI，概述了概率编程系统的研究进展，并对VI的未来发展趋势做出了展望。

Overview of variational inference methods and probabilistic programming of Bayesian hierarchical models

In Bayesian model, it is often impossible to calculate the posterior analytically, and in practice, it relies on approximate inference. Variational Inference (VI) is an important deterministic approximate inference method, which has a higher computational efficiency than Markov Chain Monte Carlo (MCMC) sampling, and has a distinct advantage in the era of big data. This paper reviewed classical VI, analyzed Stochastic Variational Inference (SVI) and its application in subject model, reviewed more robust VI, summarized the research progress of probabilistic programming system, and prospected the future development trend of VI.