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40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015

作者： Repetti, Audrey Chouzenoux, Emilie Pesquet, Jean-Christophe Université Paris-Est Lab. d'Informatique Gaspard Monge UMR CNRS 8049 Champs-sur-Marne Marne-la-Vallée France

ISBN: (纸本)9781467369978

Primal-dual proximal optimization methods have recently gained much interest for dealing with very large-scale data sets encoutered in many application fields such as machine learning, computer vision and inverse problems [1-3]. In this work, we propose a novel random block-coordinate version of such algorithms allowing us to solve a wide array of convex variational problems. One of the main advantages of the proposed algorithm is its ability to solve composite problems involving large-size matrices without requiring any inversion. In addition, the almost sure convergence to an optimal solution to the problem is guaranteed. We illustrate the good performance of our method on a mesh denoising application. © 2015 IEEE.

关键词： block-coordinate algorithm convex optimization denoising inverse problems mesh processing nonsmooth optimization primal-dual algorithm proximity operator stochastic algorithm

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A random block-coordinate primal-dual proximal algorithm with application to 3D mesh denoising

A random block-coordinate primal-dual proximal algorithm wit...

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： A. Repetti E. Chouzenoux J. C. Pesquet Lab. d'Inf. Gaspard Monge Univ. Paris-Est Marne-la-Vallee France

ISBN: (纸本)9781467369985

关键词： block-coordinate algorithm convex optimization denoising inverse problems mesh processing nonsmooth optimization primal-dual algorithm proximity operator stochastic algorithm Noise reduction Inverse method Convex function Medical Subject Headings

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STOCHASTIC QUASI-FEJER block-coordinate FIXED POINT ITERATIONS WITH RANDOM SWEEPING

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SIAM JOURNAL ON OPTIMIZATION 2015年第2期25卷 1221-1248页

作者： Combettes, Patrick L. Pesquet, Jean-Christophe Univ Paris 06 Sorbonne Univ UMR 7598 Lab Jacques Louis Lions F-75005 Paris France Univ Paris Est CNRS UMR 8049 Lab Informat Gaspard Monge F-77454 Marne La Vallee 2 France

This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces. The asymptotic analysis relies on a notion of stochastic quasi-Fejer monotonicity, which is thoroughly investigated. The iterative methods under consideration feature random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and they allow for stochastic errors in the evaluation of the operators. algorithms using quasi-nonexpansive operators or compositions of averaged nonexpansive operators are constructed, and weak and strong convergence results are established for the sequences they generate. As a by-product, novel block-coordinate operator splitting methods are obtained for solving structured monotone inclusion and convex minimization problems. In particular, the proposed framework leads to random block-coordinate versions of the Douglas-Rachford and forward-backward algorithms and of some of their variants. In the standard case of m = 1 block, our results remain new as they incorporate stochastic perturbations.

关键词： arbitrary sampling block-coordinate algorithm fixed-point algorithm monotone operator splitting primal-dual algorithm stochastic quasi-Fejer sequence stochastic algorithm structured convex minimization problem

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Stochastic quasi-Fejer block-coordinate fixed point iterations with random sweeping II: mean-square and linear convergence

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MATHEMATICAL PROGRAMMING 2019年第1-2期174卷 433-451页

作者： Combettes, Patrick L. Pesquet, Jean-Christophe North Carolina State Univ Dept Math Raleigh NC 27695 USA Univ Paris Saclay CentraleSupelec Ctr Visual Comp F-92295 Chatenay Malabry France

Combettes and Pesquet (SIAM J Optim 25:1221-1248,2015) investigated the almost sure weak convergence of block-coordinate fixed point algorithms and discussed their applications to nonlinear analysis and optimization. This algorithmic framework features random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and it allows for stochastic errors in the evaluation of the operators. The present paper establishes results on the mean-square and linear convergence of the iterates. Applications to monotone operator splitting and proximal optimization algorithms are presented.

关键词： block-coordinate algorithm Fixed-point algorithm Mean-square convergence Monotone operator splitting Linear convergence Stochastic algorithm

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LINEAR CONVERGENCE OF STOCHASTIC block-coordinate FIXED POINT algorithmS 26

LINEAR CONVERGENCE OF STOCHASTIC BLOCK-COORDINATE FIXED POIN...

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26th European Signal Processing Conference (EUSIPCO)

作者： Combettes, Patrick L. Pesquet, Jean-Christophe North Carolina State Univ Dept Math Box 8205 Raleigh NC 27695 USA Univ Paris Saclay Cent Supelec INRIA Ctr Visual Comp Gif Sur Yvette France

ISBN: (纸本)9789082797015

Recent random block-coordinate fixed point algorithms are particularly well suited to large-scale optimization in signal and image processing. These algorithms feature random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and they allow for stochastic errors in the evaluation of the operators. The present paper provides new linear convergence results. These convergence rates are compared to those of standard deterministic algorithms both theoretically and experimentally in an image recovery problem.

关键词： block-coordinate algorithm fixed-point algorithm linear convergence stochastic algorithm

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A Distributed block-Split Gibbs Sampler with Hypergraph Structure for High-Dimensional Inverse Problems

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2024年第3期33卷 814-832页

作者： Thouvenin, Pierre-Antoine Repetti, Audrey Chainais, Pierre Univ Lille CNRS Cent Lille UMR 9189CRIStAL Lille France Heriot Watt Univ Sch Math & Comp Sci Edinburgh Scotland Heriot Watt Univ Sch Engn & Phys Sci Edinburgh Scotland

Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods hardly scale to high dimensional problems, they have recently been paired with optimization techniques, such as proximal and splitting approaches, to address this issue. Such approaches pave the way to distributed samplers, splitting computations to make inference more scalable and faster. We introduce a distributed Split Gibbs sampler (SGS) to efficiently solve such problems involving distributions with multiple smooth and non-smooth functions composed with linear operators. The proposed approach leverages a recent approximate augmentation technique reminiscent of primal-dual optimization methods. It is further combined with a block-coordinate approach to split the primal and dual variables into blocks, leading to a distributed block-coordinate SGS. The resulting algorithm exploits the hypergraph structure of the involved linear operators to efficiently distribute the variables over multiple workers under controlled communication costs. It accommodates several distributed architectures, such as the Single Program Multiple Data and client-server architectures. Experiments on a large image deblurring problem show the performance of the proposed approach to produce high quality estimates with credibility intervals in a small amount of time. Supplementary material to reproduce the experiments is available online.

关键词： Bayesian inference block-coordinate algorithm Distributed architecture High dimensional imaging inverse problems MCMC algorithm

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