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

arXiv: https://arxiv.org/abs/2411.02740 · HTML: https://mlsanity.com/paper/2411.02740/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 87 references that are in the map.
- First posted on arXiv 5 Nov 2024.

## Builds on (most cited first, 6 of 6)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Globally Convergent Type-I Anderson Acceleration for Non-Smooth Fixed-Point Iterations](https://mlsanity.com/paper/1808.03971/) (2018)
- [Operator splitting for a homogeneous embedding of the linear complementarity problem](https://mlsanity.com/paper/2004.02177/) (2020)
- [Enabling Research through the SCIP Optimization Suite 8.0](https://mlsanity.com/paper/2303.07101/) (2023)
- [Uncertainty Prediction for Machine Learning Models of Material Properties](https://mlsanity.com/paper/2107.07997/) (2021)

## Built on by (most cited first, 1 of 1)

- [Inverse design of bespoke interatomic potentials via active learning by information-matching](https://mlsanity.com/paper/2606.08148/) (2026)

## Abstract (arXiv)

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.