# Greedy inference with layers of lazy maps

2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, 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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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-02147706
Contributor : Olivier Zahm <>
Submitted on : Tuesday, June 4, 2019 - 10:15:44 PM
Last modification on : Wednesday, June 5, 2019 - 11:26:58 AM

### Identifiers

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

### Citation

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

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