Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
126 tokens/sec
GPT-4o
47 tokens/sec
Gemini 2.5 Pro Pro
43 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Probabilistic Bayesian optimal experimental design using conditional normalizing flows (2402.18337v1)

Published 28 Feb 2024 in cs.LG and cs.CV

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.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (20)
  1. Dennis V Lindley. On a measure of the information provided by an experiment. The Annals of Mathematical Statistics, 27(4):986–1005, 1956.
  2. Variational bayesian optimal experimental design. Advances in Neural Information Processing Systems, 32, 2019.
  3. The frontier of simulation-based inference. Proceedings of the National Academy of Sciences, 117(48):30055–30062, 2020.
  4. Nice: Non-linear independent components estimation. arXiv preprint arXiv:1410.8516, 2014.
  5. Minimizing the expected posterior entropy yields optimal summary statistics. arXiv preprint arXiv:2206.02340, 2022.
  6. A unified stochastic gradient approach to designing bayesian-optimal experiments. In International Conference on Artificial Intelligence and Statistics, pages 2959–2969. PMLR, 2020.
  7. Bayesflow: Learning complex stochastic models with invertible neural networks. IEEE transactions on neural networks and learning systems, 33(4):1452–1466, 2020.
  8. Guided image generation with conditional invertible neural networks. arXiv preprint arXiv:1907.02392, 2019.
  9. On the universality of coupling-based normalizing flows. arXiv preprint arXiv:2402.06578, 2024.
  10. Learning-based optimization of the under-sampling pattern in mri. In Information Processing in Medical Imaging: 26th International Conference, IPMI 2019, Hong Kong, China, June 2–7, 2019, Proceedings 26, pages 780–792. Springer, 2019.
  11. Estimating or propagating gradients through stochastic neurons for conditional computation. arXiv preprint arXiv:1308.3432, 2013.
  12. fastmri: An open dataset and benchmarks for accelerated mri. arXiv preprint arXiv:1811.08839, 2018.
  13. End-to-end sequential sampling and reconstruction for mr imaging. In Proceedings of the Machine Learning for Health Conference, 2021.
  14. Invertiblenetworks. jl: A julia package for scalable normalizing flows. arXiv preprint arXiv:2312.13480, 2023.
  15. Extending loupe for k-space under-sampling pattern optimization in multi-coil mri. In Machine Learning for Medical Image Reconstruction: Third International Workshop, MLMIR 2020, Held in Conjunction with MICCAI 2020, Lima, Peru, October 8, 2020, Proceedings 3, pages 91–101. Springer, 2020.
  16. Image formation in diffusion mri: a review of recent technical developments. Journal of Magnetic Resonance Imaging, 46(3):646–662, 2017.
  17. A fast and scalable computational framework for large-scale high-dimensional bayesian optimal experimental design. SIAM/ASA Journal on Uncertainty Quantification, 11(1):235–261, 2023.
  18. Design amortization for bayesian optimal experimental design. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pages 8220–8227, 2023.
  19. Sequential experimental design for x-ray ct using deep reinforcement learning. arXiv preprint arXiv:2307.06343, 2023.
  20. Edge-promoting adaptive bayesian experimental design for x-ray imaging. SIAM Journal on Scientific Computing, 44(3):B506–B530, 2022.
Citations (4)

Summary

We haven't generated a summary for this paper yet.