Heterogeneous Treatment Effect Estimation based on a Partially Linear Nonparametric Bayes Model

TL;DR

This paper introduces a novel partially linear nonparametric Bayes model that uses Gaussian processes to estimate heterogeneous treatment effects, providing a flexible and consistent approach for CATE estimation.

Contribution

It extends existing Gaussian process models by explicitly modeling heterogeneity in treatment effects within a semiparametric framework.

Findings

The proposed model accurately estimates CATE in synthetic data experiments.

The posterior distribution derived is shown to be consistent.

Numerical experiments demonstrate the model's effectiveness.

Abstract

Recently, conditional average treatment effect (CATE) estimation has been attracting much attention due to its importance in various fields such as statistics, social and biomedical sciences. This study proposes a partially linear nonparametric Bayes model for the heterogeneous treatment effect estimation. A partially linear model is a semiparametric model that consists of linear and nonparametric components in an additive form. A nonparametric Bayes model that uses a Gaussian process to model the nonparametric component has already been studied. However, this model cannot handle the heterogeneity of the treatment effect. In our proposed model, not only the nonparametric component of the model but also the heterogeneous treatment effect of the treatment variable is modeled by a Gaussian process prior. We derive the analytic form of the posterior distribution of the CATE and prove that the posterior has the consistency property. That is, it concentrates around the true distribution. We show the effectiveness of the proposed method through numerical experiments based on synthetic data.