The core of the nonparametric/semiparametric Bayesian analysis is to relax the particular parametric assumptions on the distributions of interest to be unknown and random,and assign them a prior.Selecting a suitable p...The core of the nonparametric/semiparametric Bayesian analysis is to relax the particular parametric assumptions on the distributions of interest to be unknown and random,and assign them a prior.Selecting a suitable prior therefore is especially critical in the nonparametric Bayesian fitting.As the distribution of distribution,Dirichlet process(DP)is the most appreciated nonparametric prior due to its nice theoretical proprieties,modeling flexibility and computational feasibility.In this paper,we review and summarize some developments of DP during the past decades.Our focus is mainly concentrated upon its theoretical properties,various extensions,statistical modeling and applications to the latent variable models.展开更多
Residual allocation models (RAMs) arise in many subjects including Bayesian statistics, combinatorics, ecology, finance, information theory, machine learning, and population genetics. In this paper, we give a brief re...Residual allocation models (RAMs) arise in many subjects including Bayesian statistics, combinatorics, ecology, finance, information theory, machine learning, and population genetics. In this paper, we give a brief review of RAM and presents a few examples where the model arises. An extended discussion will focus a concrete model, the GEM distribution, and its ordered analogue, the Poisson-Dirichlet distribution. The paper concludes with a discussion of the GEM process.展开更多
This study proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates in relation to commodity prices for three commodity-exporting countries:Canada,Australia,and New Zealan...This study proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates in relation to commodity prices for three commodity-exporting countries:Canada,Australia,and New Zealand.We propose a new time-dependent infinite mixture of a normal linear regression model of the conditional distribution of the commodity price index.The mixing weights follow a set of Probit stick-breaking priors that are time-varying.We find that exchange rates have a positive predictive effect in general,but accounting for time variation does not improve forecasting performance.By contrast,the intercept in the regression and the lagged dependent variable show signs of parameter change over time in most cases,which is important in forecasting both the mean and the density of commodity prices one period ahead.The results also suggest that the variance is a large source of the time variation in the conditional distribution of commodity prices.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant No.11471161)the Technological Innovation Item in Jiangsu Province(No.BK2008156).
文摘The core of the nonparametric/semiparametric Bayesian analysis is to relax the particular parametric assumptions on the distributions of interest to be unknown and random,and assign them a prior.Selecting a suitable prior therefore is especially critical in the nonparametric Bayesian fitting.As the distribution of distribution,Dirichlet process(DP)is the most appreciated nonparametric prior due to its nice theoretical proprieties,modeling flexibility and computational feasibility.In this paper,we review and summarize some developments of DP during the past decades.Our focus is mainly concentrated upon its theoretical properties,various extensions,statistical modeling and applications to the latent variable models.
基金This work was supported by the Natural Science and Engineering Research Council of Canada.
文摘Residual allocation models (RAMs) arise in many subjects including Bayesian statistics, combinatorics, ecology, finance, information theory, machine learning, and population genetics. In this paper, we give a brief review of RAM and presents a few examples where the model arises. An extended discussion will focus a concrete model, the GEM distribution, and its ordered analogue, the Poisson-Dirichlet distribution. The paper concludes with a discussion of the GEM process.
基金The author acknowledges financial support from the National Natural Science Foundation of China(NSFC,No.71773069).
文摘This study proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates in relation to commodity prices for three commodity-exporting countries:Canada,Australia,and New Zealand.We propose a new time-dependent infinite mixture of a normal linear regression model of the conditional distribution of the commodity price index.The mixing weights follow a set of Probit stick-breaking priors that are time-varying.We find that exchange rates have a positive predictive effect in general,but accounting for time variation does not improve forecasting performance.By contrast,the intercept in the regression and the lagged dependent variable show signs of parameter change over time in most cases,which is important in forecasting both the mean and the density of commodity prices one period ahead.The results also suggest that the variance is a large source of the time variation in the conditional distribution of commodity prices.
文摘变分自编码(variational autoencoder,VAE)是一种基于连续隐向量的生成模型,通过变分近似构建目标函数,其中的生成模型及变分推理模型均采用神经网络结构.传统变分自编码模型中的变分识别模型假设多维隐变量之间是相互独立的,这种假设简化了推理过程,但是这使得变分下界过于松弛,同时限制了隐向量空间的表示能力.提出混合变分自编码(mixture of variational autoencoder,MVAE)模型,它通过多个变分自编码组件生成样本数据,丰富了变分识别模型结构,同时扩展了隐向量表示空间.该模型以连续型隐向量作为模型的隐层表示,其先验分布为高斯分布;以离散型隐向量作为各组件的指示向量,其先验分布为多项式分布.对于MVAE模型的变分优化目标,采用重参策略和折棍参数化策略处理目标函数,并用随机梯度下降方法求解模型参数.MVAE采用混合组件的方法可以增强隐变量空间的表示能力,提高近似推理精度,重参策略和折棍参数化策略可以有效求解对应的优化问题.最后在MNIST和OMNIGLOT数据集上设计了对比实验,验证了MVAE模型较高的推理精度及较强的隐变量空间表示能力.
