An information-matching approach to optimal experimental design and active learning

TL;DR

This paper presents an information-matching criterion based on the Fisher Information Matrix to select optimal training data, improving model accuracy efficiently across various scientific fields and active learning applications.

Contribution

It introduces a scalable convex optimization approach for data selection that focuses on informative data for parameter inference relevant to quantities of interest.

Findings

Small, optimally selected datasets suffice for accurate predictions.

The method is effective across diverse scientific modeling problems.

Active learning with this criterion enhances data efficiency.

Abstract

The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict other quantities of interest (QoI). Because models often contain many unidentifiable (sloppy) parameters, QoIs often depend on a relatively small number of parameter combinations. Therefore, we introduce an information-matching criterion based on the Fisher Information Matrix to select the most informative training data from a candidate pool. This method ensures that the selected data contain sufficient information to learn only those parameters that are needed to constrain downstream QoIs. It is formulated as a convex optimization problem, making it scalable to large models and datasets. We demonstrate the effectiveness of this approach across various modeling problems in diverse scientific fields, including power systems and underwater acoustics. Finally, we use information-matching as a query function within an Active Learning loop for material science applications. In all these applications, we find that a relatively small set of optimal training data can provide the necessary information for achieving precise predictions. These results are encouraging for diverse future applications, particularly active learning in large machine learning models.