Probabilistic Bayesian optimal experimental design using conditional normalizing flows
<|reference_start|>Probabilistic Bayesian optimal experimental design using conditional normalizing flows: Bayesian optimal experimental design (OED) seeks to conduct the most informative experiment under budget constraints to update the prior knowledge of a system to its posterior from the experimental data in a Bayesian framework. Such problems are computationally challenging because of (1) expensive and repeated evaluation of some optimality criterion that typically involves a double integration with respect to both the system parameters and the experimental data, (2) suffering from the curse-of-dimensionality when the system parameters and design variables are high-dimensional, (3) the optimization is combinatorial and highly non-convex if the design variables are binary, often leading to non-robust designs. To make the solution of the Bayesian OED problem efficient, scalable, and robust for practical applications, we propose a novel joint optimization approach. This approach performs simultaneous (1) training of a scalable conditional normalizing flow (CNF) to efficiently maximize the expected information gain (EIG) of a jointly learned experimental design (2) optimization of a probabilistic formulation of the binary experimental design with a Bernoulli distribution. We demonstrate the performance of our proposed method for a practical MRI data acquisition problem, one of the most challenging Bayesian OED problems that has high-dimensional (320 $\times$ 320) parameters at high image resolution, high-dimensional (640 $\times$ 386) observations, and binary mask designs to select the most informative observations.<|reference_end|>
@article{orozco2024probabilistic,
    title={Probabilistic Bayesian optimal experimental design using conditional
  normalizing flows},
    author={Rafael Orozco, Felix J. Herrmann, Peng Chen},
    journal={arXiv preprint arXiv:2402.18337},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.18337},
    primaryClass={cs.LG cs.CV}
}