Dimension Reduction for Conditional Density Estimation with Applications to High-Dimensional Causal Inference

TL;DR

This paper introduces a new efficient method for high-dimensional conditional density estimation that reduces dimensionality without restrictive assumptions, improving causal inference and variable selection.

Contribution

It develops a novel dependence measure and cross-validation technique for data-driven variable selection in high-dimensional nonparametric density estimation.

Findings

Effective variable selection for propensity scores.

Improved estimation of treatment effects.

Validated through simulations and real data analysis.

Abstract

We propose a novel and computationally efficient approach for nonparametric conditional density estimation in high-dimensional settings that achieves dimension reduction without imposing restrictive distributional or functional form assumptions. To uncover the underlying sparsity structure of the data, we develop an innovative conditional dependence measure and a modified cross-validation procedure that enables data-driven variable selection, thereby circumventing the need for subjective threshold selection. We demonstrate the practical utility of our dimension-reduced conditional density estimation by applying it to doubly robust estimators for average treatment effects. Notably, our proposed procedure is able to select relevant variables for nonparametric propensity score estimation and also inherently reduce the dimensionality of outcome regressions through a refined ignorability condition. We evaluate the finite-sample properties of our approach through comprehensive simulation studies and an empirical study on the effects of 401(k) eligibility on savings using SIPP data.