Cost-Aware Optimized Front-Door Experimental Design

TL;DR

This paper develops a cost-aware experimental design framework for causal effect estimation in multivariate linear front-door models, optimizing sampling strategies to improve efficiency while considering measurement costs, with proven theoretical properties and practical benefits.

Contribution

It introduces a closed-form optimal sampling policy and estimator for cost-efficient causal effect estimation under unobserved confounding, extending to back-door methods.

Findings

Achieves 5.3% to 31.9% efficiency gains over naive sampling.

Derives the full-data efficient influence function and geometry of influence functions.

Provides a practical optimal sampling policy with theoretical guarantees.

Abstract

Causal effect estimation often succeeds cost-constrained sequential data collection. This work considers multivariate 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.