报告人：李成  新加坡国立大学

时间：2020.11.02  19:00-20:00

腾讯会议: 492 653 482

 报告摘要：

Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited attention in massive data applications, mainly due to the prohibitively slow posterior computations using Markov chain Monte Carlo (MCMC) algorithms. We address this problem using a divide-and-conquer Bayesian approach. We first create a large number of data subsamples with much smaller sizes. Then, we formulate the VCM as a linear mixed-effects model and develops a data augmentation algorithm for obtaining MCMC draws on all the subsets in parallel. Finally, we aggregate the MCMC-based estimates of subset posteriors into a single Aggregated Monte Carlo (AMC) posterior, which is used as a computationally efficient alternative to the true posterior distribution. Theoretically, we derive minimax optimal posterior convergence rates for the AMC posteriors of both the varying coefficients and the mean regression function. We provide quantification on the orders of subset sample sizes and the number of subsets. The empirical results show that the combination schemes that satisfy our theoretical assumptions, including the AMC posterior, have better estimation performance than their main competitors across diverse simulations and in a real data analysis.

 报告人简介：

李成，新加坡国立大学助理教授，杜克大学博后，美国西北大学博士，本科毕业于北京大学；主要研究方向为贝叶斯分析、函数型数据和模型选择等，学术论文在Econometric Theory、Biometrika和Journal of Machine Learning Research等学术期刊发表。

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 邀请人：马学俊