A Geometric Approach to Optimal Experimental Design

Gavin Kerrigan, Christian A. Naesseth, Tom Rainforth
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3277-3285, 2026.

Abstract

We introduce a novel geometric framework for optimal experimental design (OED). Traditional OED approaches, such as those based on mutual information, rely explicitly on probability densities, leading to restrictive invariance properties. To address these limitations, we propose the mutual transport dependence (MTD), a measure of statistical dependence grounded in optimal transport theory which provides a geometric objective for optimizing designs. Unlike conventional approaches, the MTD can be tailored to specific downstream estimation problems by choosing appropriate geometries on the underlying spaces. We demonstrate that our framework produces high-quality designs while offering a flexible alternative to standard information-theoretic techniques.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-kerrigan26b, title = { A Geometric Approach to Optimal Experimental Design }, author = {Kerrigan, Gavin and Naesseth, Christian A. and Rainforth, Tom}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3277--3285}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/kerrigan26b/kerrigan26b.pdf}, url = {https://proceedings.mlr.press/v300/kerrigan26b.html}, abstract = { We introduce a novel geometric framework for optimal experimental design (OED). Traditional OED approaches, such as those based on mutual information, rely explicitly on probability densities, leading to restrictive invariance properties. To address these limitations, we propose the mutual transport dependence (MTD), a measure of statistical dependence grounded in optimal transport theory which provides a geometric objective for optimizing designs. Unlike conventional approaches, the MTD can be tailored to specific downstream estimation problems by choosing appropriate geometries on the underlying spaces. We demonstrate that our framework produces high-quality designs while offering a flexible alternative to standard information-theoretic techniques. } }
Endnote
%0 Conference Paper %T A Geometric Approach to Optimal Experimental Design %A Gavin Kerrigan %A Christian A. Naesseth %A Tom Rainforth %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-kerrigan26b %I PMLR %P 3277--3285 %U https://proceedings.mlr.press/v300/kerrigan26b.html %V 300 %X We introduce a novel geometric framework for optimal experimental design (OED). Traditional OED approaches, such as those based on mutual information, rely explicitly on probability densities, leading to restrictive invariance properties. To address these limitations, we propose the mutual transport dependence (MTD), a measure of statistical dependence grounded in optimal transport theory which provides a geometric objective for optimizing designs. Unlike conventional approaches, the MTD can be tailored to specific downstream estimation problems by choosing appropriate geometries on the underlying spaces. We demonstrate that our framework produces high-quality designs while offering a flexible alternative to standard information-theoretic techniques.
APA
Kerrigan, G., Naesseth, C.A. & Rainforth, T.. (2026). A Geometric Approach to Optimal Experimental Design . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3277-3285 Available from https://proceedings.mlr.press/v300/kerrigan26b.html.

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