用几何方法优化实验设计，提升效率并适配具体问题。
A Geometric Approach to Optimal Experimental Design
- 基于最优传输理论构建新依赖度量MTD，具几何可调性。
- 相比传统方法，能针对下游估计任务生成更优实验设计。
- 适合需要定制化设计的科研与工程场景，如复杂系统建模。
我们提出一种全新的几何框架用于最优实验设计（OED）。传统OED方法（如基于互信息的方法）显式依赖概率密度，导致不变性受限。为解决此问题，我们引入相互传输依赖（MTD），一种基于最优传输理论的统计依赖度量，为设计优化提供几何目标。与传统方法不同，MTD可通过在基础空间上选择合适的几何结构，灵活适配特定下游估计问题。实验表明，该框架能生成高质量实验设计，为标准信息论技术提供灵活替代方案。
原文摘要 · Abstract (English)
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.
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