Journal article
Distributed Bayesian Varying Coefficient Modeling Using a Gaussian Process Prior
Journal of machine learning research, Vol.23(1), pp.3642-3700
01/01/2022
Abstract
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 appli-cations, 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 develop 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 conver-gence 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 theoret-ical assumptions, including the AMC posterior, have better estimation performance than their main competitors across diverse simulations and in a real data analysis.
Details
- Title: Subtitle
- Distributed Bayesian Varying Coefficient Modeling Using a Gaussian Process Prior
- Creators
- Rajarshi Guhaniyogi - Texas A&M Univ, Dept Stat, College Stn, TX 77843 USACheng Li - Natl Univ Singapore, Dept Stat & Data Sci, Singapore 117546, SingaporeTerrance D. Savitsky - Bureau of Labor StatisticsSanvesh Srivastava - Univ Iowa, Dept Stat & Actuarial Sci, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Journal of machine learning research, Vol.23(1), pp.3642-3700
- Publisher
- Microtome Publ
- ISSN
- 1532-4435
- eISSN
- 1533-7928
- Number of pages
- 59
- Grant note
- DMS-1854667/1854662 / National Science Foundation; National Science Foundation (NSF) R-155-000- 201-114; R-155-000-223-114 / Singapore Ministry of Education Academic Research Funds Tier 1 grants ONR-BAA N000141812741 / Office of Naval Research
- Language
- English
- Date published
- 01/01/2022
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984438959702771
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