Search Results for author: Samuel Vaiter

Found 19 papers, 8 papers with code

The derivatives of Sinkhorn-Knopp converge

no code implementations26 Jul 2022 Edouard Pauwels, Samuel Vaiter

We show that the derivatives of the Sinkhorn-Knopp algorithm, or iterative proportional fitting procedure, converge towards the derivatives of the entropic regularization of the optimal transport problem with a locally uniform linear convergence rate.

Automatic differentiation of nonsmooth iterative algorithms

no code implementations31 May 2022 Jérôme Bolte, Edouard Pauwels, Samuel Vaiter

Is there a limiting object for nonsmooth piggyback automatic differentiation (AD)?

A framework for bilevel optimization that enables stochastic and global variance reduction algorithms

1 code implementation31 Jan 2022 Mathieu Dagréou, Pierre Ablin, Samuel Vaiter, Thomas Moreau

However, computing the gradient of the value function involves solving a linear system, which makes it difficult to derive unbiased stochastic estimates.

Bilevel Optimization

Supervised learning of analysis-sparsity priors with automatic differentiation

no code implementations15 Dec 2021 Hashem Ghanem, Joseph Salmon, Nicolas Keriven, Samuel Vaiter

In most situations, this dictionary is not known, and is to be recovered from pairs of ground-truth signals and measurements, by minimizing the reconstruction error.

Denoising Image Reconstruction

A theory of optimal convex regularization for low-dimensional recovery

no code implementations7 Dec 2021 Yann Traonmilin, Rémi Gribonval, Samuel Vaiter

To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constraint.

On the Universality of Graph Neural Networks on Large Random Graphs

1 code implementation NeurIPS 2021 Nicolas Keriven, Alberto Bietti, Samuel Vaiter

In the large graph limit, GNNs are known to converge to certain "continuous" models known as c-GNNs, which directly enables a study of their approximation power on random graph models.

Stochastic Block Model

Model identification and local linear convergence of coordinate descent

no code implementations22 Oct 2020 Quentin Klopfenstein, Quentin Bertrand, Alexandre Gramfort, Joseph Salmon, Samuel Vaiter

For composite nonsmooth optimization problems, Forward-Backward algorithm achieves model identification (e. g. support identification for the Lasso) after a finite number of iterations, provided the objective function is regular enough.

Convergence and Stability of Graph Convolutional Networks on Large Random Graphs

1 code implementation NeurIPS 2020 Nicolas Keriven, Alberto Bietti, Samuel Vaiter

We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel.

Automated data-driven selection of the hyperparameters for Total-Variation based texture segmentation

no code implementations20 Apr 2020 Barbara Pascal, Samuel Vaiter, Nelly Pustelnik, Patrice Abry

This work extends the Stein's Unbiased GrAdient estimator of the Risk of Deledalle et al. to the case of correlated Gaussian noise, deriving a general automatic tuning of regularization parameters.

Sparse and Smooth: improved guarantees for Spectral Clustering in the Dynamic Stochastic Block Model

no code implementations7 Feb 2020 Nicolas Keriven, Samuel Vaiter

Existing results show that, in the relatively sparse case where the expected degree grows logarithmically with the number of nodes, guarantees in the static case can be extended to the dynamic case and yield improved error bounds when the DSBM is sufficiently smooth in time, that is, the communities do not change too much between two time steps.

Stochastic Block Model

Linear Support Vector Regression with Linear Constraints

1 code implementation6 Nov 2019 Quentin Klopfenstein, Samuel Vaiter

This paper studies the addition of linear constraints to the Support Vector Regression (SVR) when the kernel is linear.

regression

Block based refitting in $\ell_{12}$ sparse regularisation

no code implementations22 Oct 2019 Charles-Alban Deledalle, Nicolas Papadakis, Joseph Salmon, Samuel Vaiter

This is done through the use of refitting block penalties that only act on the support of the estimated solution.

Image Restoration

Dual Extrapolation for Sparse Generalized Linear Models

1 code implementation12 Jul 2019 Mathurin Massias, Samuel Vaiter, Alexandre Gramfort, Joseph Salmon

Generalized Linear Models (GLM) form a wide class of regression and classification models, where prediction is a function of a linear combination of the input variables.

Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence

no code implementations8 Dec 2016 Charles-Alban Deledalle, Nicolas Papadakis, Joseph Salmon, Samuel Vaiter

Though, it is of importance when tuning the regularization parameter as it allows fixing an upper-bound on the grid for which the optimal parameter is sought.

Denoising

Low Complexity Regularization of Linear Inverse Problems

no code implementations7 Jul 2014 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 possibly noisy, measurements of it.

Model Consistency of Partly Smooth Regularizers

no code implementations5 May 2014 Samuel Vaiter, Gabriel Peyré, Jalal M. Fadili

We show that a generalized "irrepresentable condition" implies stable model selection under small noise perturbations in the observations and the design matrix, when the regularization parameter is tuned proportionally to the noise level.

Model Selection

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