Repository: Freie Universität Berlin, Math Department

Affine invariant interacting Langevin dynamics for Bayesian inference

Garbuno Inigo, A. and Nüsken, N. and Reich, S. (2019) Affine invariant interacting Langevin dynamics for Bayesian inference. SFB 1114 Preprint in arXiv:1912.02859 . pp. 1-29. (Unpublished)

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Official URL: https://arxiv.org/pdf/1912.02859.pdf

Abstract

We propose a computational method (with acronym ALDI) for sampling from a given target distribution based on first-order (overdamped) Langevin dynamics which satisfies the property of affine invariance. The central idea of ALDI is to run an ensemble of particles with their empirical covariance serving as a preconditioner for their underlying Langevin dynamics. ALDI does not require taking the inverse or square root of the empirical covariance matrix, which enables application to high-dimensional sampling problems. The theoretical properties of ALDI are studied in terms of non-degeneracy and ergodicity. Furthermore, we study its connections to diffusions on Riemannian manifolds and Wasserstein gradient flows. Bayesian inference serves as a main application area for ALDI. In case of a forward problem with additive Gaussian measurement errors, ALDI allows for a gradient-free implementation in the spirit of the ensemble Kalman filter. A computational comparison between gradient-free and gradient-based ALDI is provided for a PDE constrained Bayesian inverse problem.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:2394
Deposited By: Monika Drueck
Deposited On:05 Feb 2020 14:32
Last Modified:05 Feb 2020 14:32

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