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

DOI10.1137/20M1371026OpenAlexW3090043041MaRDI QIDQ5025734

Pierre Chainais, Maxime Vono, Nicolas Dobigeon

Publication date: 3 February 2022

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.01510

zbMATH Keywords

linear systemMarkov chain Monte CarloGaussian distributionproximal point algorithmhigh-dimensional sampling

Mathematics Subject Classification ID

Related Items (2)

The Split Gibbs Sampler Revisited: Improvements to Its Algorithmic Structure and Augmented Target Distribution ⋮ Horseshoe Priors for Edge-Preserving Linear Bayesian Inversion

Uses Software

• GMRFLib
• tmvtnorm
• Stan
• Krylstat
• PRMLT

Cites Work

• Fast Sampling of Gaussian Markov Random Fields
• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
• Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
• A unified primal-dual algorithm framework based on Bregman iteration
• Iterative numerical methods for sampling from high dimensional Gaussian distributions
• Gaussian process for nonstationary time series prediction
• Monotone (nonlinear) operators in Hilbert space
• A dual algorithm for the solution of nonlinear variational problems via finite element approximation
• Exponential convergence of Langevin distributions and their discrete approximations
• A Krylov subspace method for covariance approximation and simulation of random processes and fields
• Honest exploration of intractable probability distributions via Markov chain Monte Carlo.
• A first-order primal-dual algorithm for convex problems with applications to imaging
• A fast divide-and-conquer algorithm for computing the spectra of real symmetric tridiagonal matrices
• Numerical approximation of the product of the square root of a matrix with a vector
• Efficient sampling methods for truncated multivariate normal and Student-\(t\) distributions subject to linear inequality constraints
• Accelerated Gibbs sampling of normal distributions using matrix splittings and polynomials
• A proximal point analysis of the preconditioned alternating direction method of multipliers
• Matrix Algorithms
• A Majorized ADMM with Indefinite Proximal Terms for Linearly Constrained Convex Composite Optimization
• Preconditioned Krylov Subspace Methods for Sampling Multivariate Gaussian Distributions
• Sampling Gaussian Distributions in Krylov Spaces with Conjugate Gradients
• A restarted Lanczos approximation to functions of a symmetric matrix
• A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science
• Improving Stochastic Relaxation for Gussian Random Fields
• Markov Random Field Modeling in Image Analysis
• The Bayesian Lasso
• Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
• Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
• Monotone Operators and the Proximal Point Algorithm
• Iterative Solution Methods
• A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem
• Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix
• Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems Using MCMC
• Split-and-Augmented Gibbs Sampler—Application to Large-Scale Inference Problems
• Gaussian Markov Random Fields
• Decomposable graphical Gaussian model determination
• Asymptotically Exact Data Augmentation: Models, Properties, and Algorithms
• An Algorithm for the Inversion of Finite Toeplitz Matrices
• A Variational Approach for Bayesian Blind Image Deconvolution
• Fast Image Recovery Using Variable Splitting and Constrained Optimization
• Random Phase Textures: Theory and Synthesis
• An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems
• Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables
• Convergence in Variance of Chebyshev Accelerated Gibbs Samplers
• Bayesian Approach to Inverse Problems
• Proximité et dualité dans un espace hilbertien
• On the Generation of Normal Random Vectors
• Methods of conjugate gradients for solving linear systems
• An invariant form for the prior probability in estimation problems
• Convex analysis and monotone operator theory in Hilbert spaces
• Monte Carlo strategies in scientific computing
• Bayesian semiparametric regression analysis of multicategorical time-space data
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