A Geometric Approach to Optimal Experimental Design

2025-10-16

AI Summary

Conventional optimal experimental design (OED) relies on probabilistic density modeling, rendering it non-invariant under coordinate transformations and ill-suited for task-specific parameter estimation. Method: We propose the first geometric OED framework grounded in optimal transport theory, introducing mutual transport dependence (MTD)—a density-free, geometry-customizable statistical dependence measure. This enables geometric modeling of experimental design and end-to-end differentiable optimization. Contribution/Results: Our framework overcomes the invariance limitations of information-theoretic OED approaches and supports task-adaptive design. Experiments across diverse parameter estimation tasks demonstrate significant improvements over classical OED baselines, with enhanced flexibility, scalability, and robustness.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Proposes geometric framework for optimal experimental design
• Addresses limitations of probability-based traditional approaches
• Introduces transport-based dependence measure for flexible design optimization

Innovation

• Geometric framework for optimal experimental design
• Mutual transport dependence based on optimal transport
• Flexible design optimization with customizable geometries