Nonlinear Bayesian optimal experimental design using logarithmic Sobolev inequalities

TL;DR

This paper introduces a computationally efficient greedy method for nonlinear Bayesian experimental design that maximizes mutual information using novel bounds from log-Sobolev inequalities, outperforming existing strategies.

Contribution

The paper develops a new approach to approximate mutual information in nonlinear settings using log-Sobolev inequalities, enabling scalable experimental design.

Findings

Outperforms random selection strategies.

Better than Gaussian approximations.

More efficient than nested Monte Carlo estimators.

Abstract

We study the problem of selecting $k$ experiments from a larger candidate pool, where the goal is to maximize mutual information (MI) between the selected subset and the underlying parameters. Finding the exact solution is to this combinatorial optimization problem is computationally costly, not only due to the complexity of the combinatorial search but also the difficulty of evaluating MI in nonlinear/non-Gaussian settings. We propose greedy approaches based on new computationally inexpensive lower bounds for MI, constructed via log-Sobolev inequalities. We demonstrate that our method outperforms random selection strategies, Gaussian approximations, and nested Monte Carlo (NMC) estimators of MI in various settings, including optimal design for nonlinear models with non-additive noise.