366 citations · 1.8k across the 46 of their papers we have counts for
16 papers · 1 filter
Model Consistency for Learning with Mirror-Stratifiable Regularizers
Jalal Fadili, Guillaume Garrigos, Jérome Malick +1
Low-complexity non-smooth convex regularizers are routinely used to impose some structure (such as sparsity or low-rank) on the coefficients for linear predictors in supervised lea…
A Low-Rank Approach to Off-The-Grid Sparse Deconvolution
Paul Catala, Vincent Duval, Gabriel Peyré
We propose a new solver for the sparse spikes deconvolution problem over the space of Radon measures. A common approach to off-the-grid deconvolution considers semidefinite (SDP) r…
Sensitivity Analysis for Mirror-Stratifiable Convex Functions
Jalal Fadili, Jérôme Malick, Gabriel Peyré
This paper provides a set of sensitivity analysis and activity identification results for a class of convex functions with a strong geometric structure, that we coined "mirror-stra…
A Multi-step Inertial Forward--Backward Splitting Method for Non-convex Optimization
Jingwei Liang, Jalal Fadili, Gabriel Peyré
In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower s…
Stochastic Optimization for Large-scale Optimal Transport
Genevay Aude, Marco Cuturi, Gabriel Peyré +1
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited becau…
Unbalanced Optimal Transport: Dynamic and Kantorovich Formulation
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer +1
This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative…
Activity Identification and Local Linear Convergence of Forward--Backward-type methods
Jingwei Liang, Jalal Fadili, Gabriel Peyré
In this paper, we consider a class of Forward--Backward (FB) splitting methods that includes several variants (e.g. inertial schemes, FISTA) for minimizing the sum of two proper co…
Activity Identification and Local Linear Convergence of Douglas--Rachford/ADMM under Partial Smoothness
Jingwei Liang, Jalal Fadili, Gabriel Peyré +1
Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to…
Local Linear Convergence of Forward-Backward under Partial Smoothness
Jingwei Liang, Jalal Fadili, Gabriel Peyré
In this paper, we consider the Forward--Backward proximal splitting algorithm to minimize the sum of two proper convex functions, one of which having a Lipschitz continuous gradien…
Low Complexity Regularization of Linear Inverse Problems
Samuel Vaiter, Gabriel Peyré, Jalal M. Fadili
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possi…
Model Consistency of Partly Smooth Regularizers
Samuel Vaiter, Gabriel Peyré, Jalal M. Fadili
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions confo…
Convergence Rates with Inexact Non-expansive Operators
Jingwei Liang, Jalal Fadili, Gabriel Peyré
In this paper, we present a convergence rate analysis for the inexact Krasnosel'skii-Mann iteration built from nonexpansive operators. Our results include two main parts: we first…
Geodesics on Shape Spaces with Bounded Variation and Sobolev Metrics
G. Nardi, G. Peyré, F. -X. Vialard
This paper studies the space of planar curves endowed with the Finsler metric over its tangent space of displacement vector fields. Such a space is of interest for ap…
Exact Support Recovery for Sparse Spikes Deconvolution
Vincent Duval, Gabriel Peyré
This paper studies sparse spikes deconvolution over the space of measures. We focus our attention to the recovery properties of the support of the measure, i.e. the location of the…
Risk estimation for matrix recovery with spectral regularization
Charles-Alban Deledalle, Samuel Vaiter, Gabriel Peyré +2
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of…
Generalized Forward-Backward Splitting
Hugo Raguet, Jalal Fadili, Gabriel Peyré
This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form , where has a Lipschitz-continuous…