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A variational Bayes approach to a semiparametric regression using Gaussian process priors

Authors
Ong, Victor M. H.Mensah, David K.Nott, David J.Jo, SeongilPark, BeomjoChoi, Taeryon
Issue Date
2017
Publisher
INST MATHEMATICAL STATISTICS
Keywords
Cosine series; Gaussian process; model selection; shape restricted regression; variational Bayes
Citation
ELECTRONIC JOURNAL OF STATISTICS, v.11, no.2, pp.4258 - 4296
Indexed
SCIE
SCOPUS
Journal Title
ELECTRONIC JOURNAL OF STATISTICS
Volume
11
Number
2
Start Page
4258
End Page
4296
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/86332
DOI
10.1214/17-EJS1324
ISSN
1935-7524
Abstract
This paper presents a variational Bayes approach to a semiparametric regression model that consists of parametric and nonparametric components. The assumed univariate nonparametric component is represented with a cosine series based on a spectral analysis of Gaussian process priors. Here, we develop fast variational methods for fitting the semiparametric regression model that reduce the computation time by an order of magnitude over Markov chain Monte Carlo methods. Further, we explore the possible use of the variational lower bound and variational information criteria for model choice of a parametric regression model against a semiparametric alternative. In addition, variational methods are developed for estimating univariate shape-restricted regression functions that are monotonic, monotonic convex or monotonic concave. Since these variational methods are approximate, we explore some of the trade-offs involved in using them in terms of speed, accuracy and automation of the implementation in comparison with Markov chain Monte Carlo methods and discuss their potential and limitations.
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