Nonlinear Bayesian optimal experimental design using logarithmic Sobolev inequalities
This work addresses a computational bottleneck in optimal experimental design for researchers in statistics and machine learning, though it appears incremental as it builds on existing greedy and bound-based approaches.
The paper tackles the combinatorial optimization problem of selecting experiments to maximize mutual information in nonlinear/non-Gaussian settings, proposing greedy methods based on logarithmic Sobolev inequalities that outperform random selection, Gaussian approximations, and nested Monte Carlo estimators.
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.