Uncertainty Quantification in Heterogeneous Treatment Effect Estimation with Gaussian-Process-Based Partially Linear Model
This work addresses the need for reliable decision-making in causal inference by providing a method for uncertainty quantification in treatment effect estimation, though it appears incremental as it builds on existing semiparametric models with Bayesian enhancements.
The authors tackled the problem of estimating heterogeneous treatment effects with uncertainty quantification in small sample settings, proposing a Bayesian Gaussian-process-based partially linear model that enables analytical posterior computation and shows accurate estimation and effective uncertainty quantification in experiments.
Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in treatment effect estimation to support decision-making in a relatively small sample size setting. Our proposed model places Gaussian process priors on the nonparametric components of a semiparametric model called a partially linear model. This model formulation has three advantages. First, we can analytically compute the posterior distribution of a treatment effect without relying on the computationally demanding posterior approximation. Second, we can guarantee that the posterior distribution concentrates around the true one as the sample size goes to infinity. Third, we can incorporate prior knowledge about a treatment effect into the prior distribution, improving the estimation efficiency. Our experimental results show that even in the small sample size setting, our method can accurately estimate the heterogeneous treatment effects and effectively quantify its estimation uncertainty.