Density Regression with Conditional Support Points

TL;DR

This paper introduces a novel data reduction method using conditional support points for density regression, enabling efficient modeling of complex conditional distributions in large datasets with multiple covariates.

Contribution

It develops a new approach combining conditional support points with penalized likelihood for scalable density regression, with theoretical convergence analysis and practical application.

Findings

Effective data reduction for density regression in large datasets

Theoretical convergence rates established for the estimator

Successful application to wind turbine power output data

Abstract

Density regression characterizes the conditional density of the response variable given the covariates, and provides much more information than the commonly used conditional mean or quantile regression. However, it is often computationally prohibitive in applications with massive data sets, especially when there are multiple covariates. In this paper, we develop a new data reduction approach for the density regression problem using conditional support points. After obtaining the representative data, we exploit the penalized likelihood method as the downstream estimation strategy. Based on the connections among the continuous ranked probability score, the energy distance, the $L_2$ discrepancy and the symmetrized Kullback-Leibler distance, we investigate the distributional convergence of the representative points and establish the rate of convergence of the density regression estimator. The usefulness of the methodology is illustrated by modeling the conditional distribution of power output given multivariate environmental factors using a large scale wind turbine data set. Supplementary materials for this article are available online.