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no code implementations • 26 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.

1 code implementation • 27 Jun 2022 • Thomas Moreau, Mathurin Massias, Alexandre Gramfort, Pierre Ablin, Pierre-Antoine Bannier, Benjamin Charlier, Mathieu Dagréou, Tom Dupré La Tour, Ghislain Durif, Cassio F. Dantas, Quentin Klopfenstein, Johan Larsson, En Lai, Tanguy Lefort, Benoit Malézieux, Badr Moufad, Binh T. Nguyen, Alain Rakotomamonjy, Zaccharie Ramzi, Joseph Salmon, Samuel Vaiter

Numerical validation is at the core of machine learning research as it allows to assess the actual impact of new methods, and to confirm the agreement between theory and practice.

no code implementations • 31 May 2022 • Jérôme Bolte, Edouard Pauwels, Samuel Vaiter

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

1 code implementation • 31 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.

no code implementations • 15 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.

no code implementations • 7 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.

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.

1 code implementation • 4 May 2021 • Quentin Bertrand, Quentin Klopfenstein, Mathurin Massias, Mathieu Blondel, Samuel Vaiter, Alexandre Gramfort, Joseph Salmon

Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques.

no code implementations • 22 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.

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.

no code implementations • 20 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.

1 code implementation • ICML 2020 • Quentin Bertrand, Quentin Klopfenstein, Mathieu Blondel, Samuel Vaiter, Alexandre Gramfort, Joseph Salmon

Our approach scales to high-dimensional data by leveraging the sparsity of the solutions.

no code implementations • 7 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.

1 code implementation • 6 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.

no code implementations • 22 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.

1 code implementation • 12 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.

no code implementations • 8 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.

no code implementations • 7 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.

no code implementations • 5 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.

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