Targeted Regularization for Causal Effect Estimation with Exponential Dispersion Family Outcomes

Abstract

Neural Networks (NNs) for causal effect estimation have shown strong empirical performance, yet endowing them with desirable semiparametric properties -- doubly robustness and fast convergence rates -- remains challenging. A common approach to address this is targeted regularization, which modifies the objective function of NNs. However, existing work on neural causal effect estimation is largely limited to continuous outcomes, restricting its applicability to settings involving binary, count, or other skewed outcomes commonly encountered in practice. We propose a unified targeted regularization framework for the Exponential Dispersion Family (EDF) to address this limitation. Specifically, we first derive the von Mises expansion of the average dose function of canonical functions (ADCF) for discrete treatments and of the sieve-projected ADCF for continuous treatments. Second, we use this expansion to construct a unified targeted regularization, that corrects first-order bias at the distributional level. We integrate this objective into a NN architecture that jointly estimates the outcome model, propensity score model, and fluctuation parameter end-to-end. Experimental results demonstrate the effectiveness of our method.