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Greedy inference with layers of lazy maps

Daniele Bigoni 1 Olivier Zahm 2 Alessio Spantini 1 Youssef Marzouk 1
2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
UGA [2016-2019] - Université Grenoble Alpes [2016-2019], Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019], LJK - Laboratoire Jean Kuntzmann , Inria Grenoble - Rhône-Alpes
Abstract : We propose a framework for the greedy approximation of high-dimensional Bayesian inference problems, through the composition of multiple \emph{low-dimensional} transport maps or flows. Our framework operates recursively on a sequence of ``residual'' distributions, given by pulling back the posterior through the previously computed transport maps. The action of each map is confined to a low-dimensional subspace that we identify by minimizing an error bound. At each step, our approach thus identifies (i) a relevant subspace of the residual distribution, and (ii) a low-dimensional transformation between a restriction of the residual onto this subspace and a standard Gaussian. We prove weak convergence of the approach to the posterior distribution, and we demonstrate the algorithm on a range of challenging inference problems in differential equations and spatial statistics.
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Contributor : Olivier Zahm <>
Submitted on : Tuesday, June 4, 2019 - 10:15:44 PM
Last modification on : Wednesday, October 14, 2020 - 4:19:57 AM

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



Daniele Bigoni, Olivier Zahm, Alessio Spantini, Youssef Marzouk. Greedy inference with layers of lazy maps. 2019. ⟨hal-02147706⟩



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