VAE-KRnet and its Applications to Variational Bayes

作     者：Xiaoliang Wan Shuangqing Wei 

作者机构：Department of MathematicsCenter for Computation and TechnologyLouisiana State UniversityBaton Rouge 70803USA Division of Electrical&Computer EngineeringLouisiana State UniversityBaton Rouge 70803USA 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2022年第31卷第4期

页      面：1049-1082页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：X.Wan has been supported by NSF grant DMS-1913163 S.Wei has been supported by NSF grant ECCS-1642991 

主　　题：Deep learning variational Bayes uncertainty quantification Bayesian inverse problems generative modeling 

摘      要：In this work,we have proposed a generative model,called VAE-KRnet,for density estimation or approximation,which combines the canonical variational autoencoder(VAE)with our recently developed flow-based generativemodel,called *** is used as a dimension reduction technique to capture the latent space,and KRnet is used to model the distribution of the latent *** a linear model between the data and the latent variable,we show that VAE-KRnet can be more effective and robust than the canonical ***-KRnet can be used as a density model to approximate either data distribution or an arbitrary probability density function(PDF)known up to a ***-KRnet is flexible in terms of *** the number of dimensions is relatively small,KRnet can effectively approximate the distribution in terms of the original random *** high-dimensional cases,we may use VAE-KRnet to incorporate dimension *** important application of VAE-KRnet is the variational Bayes for the approximation of the posterior *** variational Bayes approaches are usually based on the minimization of the Kullback-Leibler(KL)divergence between the model and the *** highdimensional distributions,it is very challenging to construct an accurate densitymodel due to the curse of dimensionality,where extra assumptions are often introduced for *** instance,the classical mean-field approach assumes mutual independence between dimensions,which often yields an underestimated variance due to *** alleviate this issue,we include into the loss the maximization of the mutual information between the latent random variable and the original random variable,which helps keep more information from the region of low density such that the estimation of variance is *** experiments have been presented to demonstrate the effectiveness of our model.