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2016 Scalable Bayesian nonparametric regression via a Plackett-Luce model for conditional ranks
Tristan Gray-Davies, Chris C. Holmes, François Caron
Electron. J. Statist. 10(2): 1807-1828 (2016). DOI: 10.1214/15-EJS1032

Abstract

We present a novel Bayesian nonparametric regression model for covariates $X$ and continuous response variable $Y\in\mathbb{R}$. The model is parametrized in terms of marginal distributions for $Y$ and $X$ and a regression function which tunes the stochastic ordering of the conditional distributions $F(y|x)$. By adopting an approximate composite likelihood approach, we show that the resulting posterior inference can be decoupled for the separate components of the model. This procedure can scale to very large datasets and allows for the use of standard, existing, software from Bayesian nonparametric density estimation and Plackett-Luce ranking estimation to be applied. As an illustration, we show an application of our approach to a US Census dataset, with over 1,300,000 data points and more than 100 covariates.

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Tristan Gray-Davies. Chris C. Holmes. François Caron. "Scalable Bayesian nonparametric regression via a Plackett-Luce model for conditional ranks." Electron. J. Statist. 10 (2) 1807 - 1828, 2016. https://doi.org/10.1214/15-EJS1032

Information

Received: 1 December 2014; Published: 2016
First available in Project Euclid: 18 July 2016

zbMATH: 06624502
MathSciNet: MR3522661
Digital Object Identifier: 10.1214/15-EJS1032

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 2 • 2016
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