Reproduce “Uncertainty Quantification in Heterogeneous Treatment Effect Estimation with Gaussian-Process-Based Partially Linear Model” on OpenResearch

About this paper

Shunsuke Horii, Yoichi Chikahara

A Bayesian framework leverages a Gaussian-process-based partially linear model to quantify uncertainty in heterogeneous treatment effect (HTE) estimation, demonstrating superior accuracy and more reliable uncertainty quantification than frequentist methods, especially in small sample sizes. The method provides an analytical posterior distribution for the Conditional Average Treatment Effect (CATE), offering stronger theoretical guarantees.

Key insights

• The analytical computation of the posterior predictive distribution for CATE implicitly handles confounding bias by marginalizing out the nuisance function, eliminating the need for explicit propensity score modeling.
• Bayesian methods, exemplified by the proposed framework and BCF, provide more reliable uncertainty quantification (higher coverage ratios) than frequentist approaches, particularly in small sample size regimes.
• The framework's design, utilizing GP priors on a partially linear model, balances flexibility for complex nonlinearities with sample-size efficiency, critical for effective HTE estimation in data-limited settings.

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