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.

翻译：我们提出了一种新颖的几何框架用于最优实验设计。传统的实验设计方法，例如基于互信息的方法，明确依赖于概率密度，导致其不变性性质受到限制。为解决这些局限性，我们提出了互传输依赖度，这是一种基于最优传输理论的统计依赖性度量，为优化设计提供了几何目标。与传统方法不同，互传输依赖度可通过在底层空间选择适当的几何结构，针对特定的下游估计问题进行定制。我们证明，该框架能够生成高质量的设计，同时为标准信息论技术提供了一种灵活的替代方案。