Probabilistic Bayesian optimal experimental design using conditional normalizing flows

• URL: http://arxiv.org/abs/2402.18337v1
• Date: Wed, 28 Feb 2024 13:59:20 GMT
• Title: Probabilistic Bayesian optimal experimental design using conditional normalizing flows
• Authors: Rafael Orozco, Felix J. Herrmann, Peng Chen
• Abstract summary: Bayesian optimal experimental design (OED) seeks to conduct the most informative experiment under budget constraints. We propose a novel joint optimization approach to make the solution of the OED problem efficient, scalable, and robust for practical applications. We demonstrate the performance proposed method for a practical MRI OED problem that has high-dimensional (320 $times 320) parameters at high image resolution, high-dimensional (640 $times 386) observations, and binary designs to select the most informative observations.
• Score: 2.7689411149700685
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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