On submodularity of the expected information gain

2025/05/07 by Maio, Steven, Alexanderian, Alen
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2505.04145

Abstract

We consider finite-dimensional linear Gaussian Bayesian inverse problems with uncorrelated sensor measurements. In this setting, it is known that the expected information gain, quantified by the expected Kullback-Leibler divergence from the posterior measure to the prior measure, is submodular. We present a simple alternative proof of this fact tailored to a weighted inner product space setting arising from discretization of infinite-dimensional inverse problems constrained by partial differential equations (PDEs).

Citations

• Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review
• On Bayesian A- and D-optimal experimental designs in infinite dimensions
• A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversion
• An analysis of approximations for maximizing submodular set functions—I

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