Cost-Aware Optimized Front-Door Experimental Design

Leopold Mareis, Mathias Drton

Keywords: Causal Inference, Experimental Design, Front-door Estimation, Linear Structural Equation Model, Semiparametric Theory

TL;DR: This paper develops an optimized experimental design for semiparametric causal effect estimators in front‑door (and back‑door) models under partial data, that substantially reduces asymptotic estimation variance relative to full‑sampling strategies.

Abstract: Causal Effect estimation often succeeds cost-constrained, sequential data collection. This work considers multivariate additive noise linear front-door models with arbitrary unobserved confounding on treatment and response. We optimize the experimental design by balancing the statistical efficiency and measurement costs through partial data. The full‑data efficient influence function for the causal effect is derived, together with the geometry of all observed‑data influence functions. This characterization yields a closed-form optimal sampling policy and an estimator to minimize the asymptotic variance of regular asymptotically linear (RAL) estimators within a class of augmented full-data influence functions. The resulting design also covers back-door estimation. In simulations and applications to biological, medical, and industrial datasets, the optimized designs achieve substantial efficiency gains (5.3% to 31.9%) over naive full-sampling strategies.

Submission Number: 65