A Geometric Approach to Optimal Experimental Design
This work provides a novel method for researchers in statistics and machine learning dealing with experimental design, though it appears incremental as it builds on existing optimal transport theory.
The paper tackles the limitations of traditional optimal experimental design approaches by introducing a geometric framework based on mutual transport dependence, which offers flexibility and produces high-quality designs.
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.