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High-Dimensional Gaussian Sampling: A Review and a Unifying Approach Based on a Stochastic Proximal Point Algorithm

Efficient sampling from a high-dimensional Gaussian distribution is an old but high-stakes issue. Vanilla Cholesky samplers imply a computational cost and memory requirements that can rapidly become prohibitive in high dimensions. To tackle these issues, multiple methods have been proposed from different communities ranging from iterative numerical linear algebra to Markov chain Monte Carlo (MCMC) approaches. Surprisingly, no complete review and comparison of these methods has been conducted. This paper aims to review all these approaches by pointing out their differences, close relations, benefits, and limitations. In addition to reviewing the state of the art, this paper proposes a unifying Gaussian simulation framework by deriving a stochastic counterpart of the celebrated proximal point algorithm in optimization. This framework offers a novel and unifying revisiting of most of the existing MCMC approaches while also extending them. Guidelines to choosing the appropriate Gaussian simulation method for a given sampling problem in high dimensions are proposed and illustrated with numerical examples.

Ketersediaan

Informasi Detail

Judul Seri

SIAM REVIEW; Vol.64 No.1 March 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 3-56

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

GAUSSIAN DISTRIBUTION
MARKOV CHAIN MONTE CARLO
LINEAR SYSTEM
PROXIMAL POINT ALGORITHM
HIGH-DIMENSIONAL SAMPLING

Info Detail Spesifik

https://doi.org/10.1137/20M1371026

Pernyataan Tanggungjawab

Maxime Vono, Nicolas Dobigeon, Pierre Chainais

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