Nonlinear Bayesian optimal experimental design using logarithmic Sobolev
  inequalities
Fengyi Li Ayoub Belhadji Youssef Marzouk
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.