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

TL;DR

This paper introduces a scalable Bayesian nonparametric regression model that leverages a Plackett-Luce model for conditional ranks, enabling efficient analysis of large datasets with many covariates.

Contribution

It proposes a novel regression framework combining marginal distributions and stochastic ordering, scalable via an approximate composite likelihood approach.

Findings

Successfully applied to a US Census dataset with over 1.3 million data points.

Allows use of existing Bayesian nonparametric density estimation software.

Demonstrates scalability and effectiveness in large-scale regression analysis.

Abstract

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