Cost-Aware Optimized Front-Door Experimental Design

2026-03-23

AI Summary

This work proposes an efficient causal effect estimation method for multivariate linear front-door models under measurement cost constraints and unobserved confounding. By deriving, for the first time, the geometric structure of the influence functions under both full-data and observed-data regimes, the authors develop an optimal sampling and estimation framework grounded in influence function theory, regular asymptotically linear estimators, and convex optimization. This framework yields a closed-form optimal sampling strategy and naturally subsumes back-door adjustment as a special case. Empirical evaluations on multiple real-world datasets from biology, medicine, and industrial domains demonstrate that the proposed approach achieves estimation efficiency gains ranging from 5.3% to 31.9% compared to naive full-sampling strategies.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web measurements

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.

Problem

• causal effect estimation
• front-door model
• experimental design
• measurement cost
• unobserved confounding

Innovation

• front-door adjustment
• cost-aware experimental design
• influence function
• causal effect estimation
• optimal sampling