Scalable Bayesian nonparametric regression via a Plackett-Luce model for conditional ranks.

We present a novel Bayesian nonparametric regression model for covariates X and continuous response variable Y ∈ 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.

• Publication year

  2015

• Venue

  Electronic Journal of Statistics

• Publication date

  2015-06-24

• Fields of study

  Mathematics, Computer Science, Medicine

• Identifiers
  DOI 10.1214/15-EJS1032arXiv 1506.07412PMID 29623150PMCID PMC5881922
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Fundamentals of Nonparametric Bayesian Inference

  2017cited by this paper
• Improving prediction from dirichlet process mixtures via enrichment

  2014cited by this paper
• Bayesian nonparametric regression with varying residual density

  2013cited by this paper
• Composite Likelihood Methods

  2012cited by this paper
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  2011cited by this paper
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  2011cited by this paper
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  2011cited by this paper
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  2011cited by this paper
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  2011cited by this paper
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  2009cited by this paper
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  2009cited by this paper
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  2009cited by this paper
• On a Class of Bayesian Nonparametric Estimates : I . Density Estimates

  2008cited by this paper
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  2008cited by this paper
• Kernel stick-breaking processes.

  2008cited by this paper
• Applied Bayesian Non-and Semi-parametric Inference using DPpackage

  2007cited by this paper
• Generalized Polya Urn for Time-varying Dirichlet Process Mixtures

  2007influential reference
• Bayesian density regression

  2007influential reference
• Bayesian Inference for Linear Dynamic Models With Dirichlet Process Mixtures

  2007influential reference
• Nonlinear Models Using Dirichlet Process Mixtures

  2007cited by this paper
• Extending the rank likelihood for semiparametric copula estimation

  2006cited by this paper
• Order-Based Dependent Dirichlet Processes

  2006cited by this paper
• The Bernstein–von Mises theorem for the proportional hazard model

  2006influential reference
• A note on pseudolikelihood constructed from marginal densities

  2004cited by this paper
• Bayesian Methods for Nonlinear Classification and Regression

  2004cited by this paper
• An ANOVA Model for Dependent Random Measures

  2004cited by this paper
• Bayesian Semiparametric Regression for Median Residual Life

  2003influential reference
• Bayesian Semiparametric Median Regression Modeling

  2001cited by this paper
• Markov Chain Sampling Methods for Dirichlet Process Mixture Models

  2000cited by this paper
• Estimating mixture of dirichlet process models

  1998cited by this paper
• Bayesian curve fitting using multivariate normal mixtures

  1996cited by this paper
• Bayesian Density Estimation and Inference Using Mixtures

  1995cited by this paper
• A nonparametric Bayes method for isotonic regression

  1995cited by this paper
• Polya Trees and Random Distributions

  1992cited by this paper
• More Aspects of Polya Tree Distributions for Statistical Modelling

  1992influential reference
• On a Class of Bayesian Nonparametric Estimates: I. Density Estimates

  1984influential reference
• Individual Choice Behavior: A Theoretical Analysis

  1979cited by this paper
• The Analysis of Permutations

  1975cited by this paper
• Prior Distributions on Spaces of Probability Measures

  1974cited by this paper
• A Bayesian Analysis of Some Nonparametric Problems

  1973cited by this paper
• Individual Choice Behavior: A Theoretical Analysis.

  1960cited by this paper
• © Institute of Mathematical Statistics, 2004 Nonparametric Bayesian Data Analysis

  year unknowncited by this paper
• Regression Models and Life-Tables

  year unknowncited by this paper

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  2016cites this paper
• Bayesian Analysis of Rank Data with Covariates and Heterogeneous Rankers

  2016cites this paper
• Scalable Bayesian Kernel Models with Variable Selection

  2015cites this paper
• Bayesian Approximate Kernel Regression With Variable Selection

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