Cost-Aware Optimized Front-Door Experimental Design

Leopold Mareis, Mathias Drton
Proceedings of the Fifth Conference on Causal Learning and Reasoning, PMLR 323:1068-1096, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v323-mareis26a, title = {Cost-Aware Optimized Front-Door Experimental Design}, author = {Mareis, Leopold and Drton, Mathias}, booktitle = {Proceedings of the Fifth Conference on Causal Learning and Reasoning}, pages = {1068--1096}, year = {2026}, editor = {Mazaheri, Bijan and Hanson, Niels Richard}, volume = {323}, series = {Proceedings of Machine Learning Research}, month = {06--08 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v323/main/assets/mareis26a/mareis26a.pdf}, url = {https://proceedings.mlr.press/v323/mareis26a.html}, 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.} }
Endnote
%0 Conference Paper %T Cost-Aware Optimized Front-Door Experimental Design %A Leopold Mareis %A Mathias Drton %B Proceedings of the Fifth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2026 %E Bijan Mazaheri %E Niels Richard Hanson %F pmlr-v323-mareis26a %I PMLR %P 1068--1096 %U https://proceedings.mlr.press/v323/mareis26a.html %V 323 %X 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.
APA
Mareis, L. & Drton, M.. (2026). Cost-Aware Optimized Front-Door Experimental Design. Proceedings of the Fifth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 323:1068-1096 Available from https://proceedings.mlr.press/v323/mareis26a.html.

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