Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression

TL;DR

This paper introduces a novel method for analyzing treatment effects on the entire outcome distribution using kernel embeddings and U-statistics, providing deeper insights than average effects alone.

Contribution

It formalizes the concept of conditional distributional treatment effects (CoDiTE) and develops a kernel-based framework with hypothesis testing and regression for higher-order distributional analysis.

Findings

Effective in detecting distributional effects in synthetic and real data

Generalizes CATE to higher moments of the outcome distribution

Provides a hypothesis test for the presence of distributional effects

Abstract

We propose to analyse the conditional distributional treatment effect (CoDiTE), which, in contrast to the more common conditional average treatment effect (CATE), is designed to encode a treatment's distributional aspects beyond the mean. We first introduce a formal definition of the CoDiTE associated with a distance function between probability measures. Then we discuss the CoDiTE associated with the maximum mean discrepancy via kernel conditional mean embeddings, which, coupled with a hypothesis test, tells us whether there is any conditional distributional effect of the treatment. Finally, we investigate what kind of conditional distributional effect the treatment has, both in an exploratory manner via the conditional witness function, and in a quantitative manner via U-statistic regression, generalising the CATE to higher-order moments. Experiments on synthetic, semi-synthetic and real datasets demonstrate the merits of our approach.