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Greedy inference with structure-exploiting lazy maps

Michael Brennan 1 Daniele Bigoni 1 Olivier Zahm 2 Alessio Spantini 1 Youssef Marzouk 1
2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : We propose a framework for solving high-dimensional Bayesian inference problems using \emph{structure-exploiting} low-dimensional transport maps or flows. These maps are confined to a low-dimensional subspace (hence, lazy), and the subspace is identified by minimizing an upper bound on the Kullback--Leibler divergence (hence, structured). Our framework provides a principled way of identifying and exploiting low-dimensional structure in an inference problem. It focuses the expressiveness of a transport map along the directions of most significant discrepancy from the posterior, and can be used to build deep compositions of lazy maps, where low-dimensional projections of the parameters are iteratively transformed to match the posterior. We prove weak convergence of the generated sequence of distributions to the posterior, and we demonstrate the benefits of the framework on challenging inference problems in machine learning and differential equations, using inverse autoregressive flows and polynomial maps as examples of the underlying density estimators.
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https://hal.inria.fr/hal-02147706
Contributor : Olivier Zahm Connect in order to contact the contributor
Submitted on : Tuesday, June 4, 2019 - 10:15:44 PM
Last modification on : Tuesday, October 19, 2021 - 11:25:54 AM

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  • HAL Id : hal-02147706, version 1
  • ARXIV : 1906.00031

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Michael Brennan, Daniele Bigoni, Olivier Zahm, Alessio Spantini, Youssef Marzouk. Greedy inference with structure-exploiting lazy maps. NeurIPS '20 - 34th International Conference on Neural Information Processing Systems, Dec 2020, Virtual, Canada. pp.8330-8342. ⟨hal-02147706⟩

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