Title: Direct Bias-Correction Term Estimation for Average Treatment Effect Estimation
Primary area: causal reasoning
Keywords: average treatment effect estimation, covariate balancing, inverse probability weighting estimator

Abstract: This study considers the estimation of the average treatment effect (ATE). For ATE estimation, we estimate the propensity score through direct bias-correction term estimation. Let $\{(X_i, D_i, Y_i)\}_{i=1}^{n}$ be the observations, where $X_i \in \mathbb{R}^K$ denotes $K$-dimensional covariates, $D_i \in \{0, 1\}$ denotes a binary treatment assignment indicator, and $Y_i \in \mathbb{R}$ is an outcome. In ATE estimation, the bias-correction term $h_0(X_i, D_i) \coloneqq \frac{{1}[D_i = 1]}{e_0(X_i)} - \frac{{1}[D_i = 0]}{1 - e_0(X_i)}$ plays an important role, where $e_0(X_i)$ is the propensity score, the probability of being assigned treatment $1$. In this study, we propose estimating $h_0$ (or equivalently $e_0$) by directly minimizing the prediction error for $h_0$ without knowing $h_0$ in advance. We present a general framework for this direct bias-correction term estimation approach from the perspective of Bregman divergence minimization, which also generalizes the Riesz regression and covariate balancing.