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June 2010 Bayesian density regression with logistic Gaussian process and subspace projection
Surya T. Tokdar, Yu M. Zhu, Jayanta K. Ghosh
Bayesian Anal. 5(2): 319-344 (June 2010). DOI: 10.1214/10-BA605

Abstract

We develop a novel Bayesian density regression model based on logistic Gaussian processes and subspace projection. Logistic Gaussian processes provide an attractive alternative to the popular stick-breaking processes for modeling a family of conditional densities that vary smoothly in the conditioning variable. Subspace projection offers dimension reduction of predictors through multiple linear combinations, offering an alternative to the zeroing out theme of variable selection. We illustrate that logistic Gaussian processes and subspace projection combine well to produce a computationally tractable and theoretically sound density regression procedure that offers good out of sample prediction, accurate estimation of subspace projection and satisfactory estimation of subspace dimensionality. We also demonstrate that subspace projection may lead to better prediction than variable selection when predictors are well chosen and possibly dependent on each other, each having a moderate influence on the response.

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Surya T. Tokdar. Yu M. Zhu. Jayanta K. Ghosh. "Bayesian density regression with logistic Gaussian process and subspace projection." Bayesian Anal. 5 (2) 319 - 344, June 2010. https://doi.org/10.1214/10-BA605

Information

Published: June 2010
First available in Project Euclid: 20 June 2012

zbMATH: 1330.62182
MathSciNet: MR2719655
Digital Object Identifier: 10.1214/10-BA605

Keywords: Bayesian inference , Dimension reduction , Gaussian process , Markov chain Monte Carlo , posterior consistency , Semiparametric model

Rights: Copyright © 2010 International Society for Bayesian Analysis

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Vol.5 • No. 2 • June 2010
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