249 citations · 744 across the 13 of their papers we have counts for
9 papers · 1 filter
Sharper Exponential Convergence Rates for Sinkhorn's Algorithm in Continuous Settings
Lénaïc Chizat, Alex Delalande, Tomas Vaškevičius
We study the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems when at least one of the probability measures, , admits a densit…
Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterations
Lénaïc Chizat, Tomas Vaškevičius
We study the computation of doubly regularized Wasserstein barycenters, a recently introduced family of entropic barycenters governed by inner and outer regularization strengths. P…
Faster Wasserstein Distance Estimation with the Sinkhorn Divergence
Lenaic Chizat, Pierre Roussillon, Flavien Léger +2
The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimat…
Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss
Lenaic Chizat, Francis Bach
Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towar…
Sparse Optimization on Measures with Over-parameterized Gradient Descent
Lenaic Chizat
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training.…
On Lazy Training in Differentiable Programming
Lenaic Chizat, Edouard Oyallon, Francis Bach
In a series of recent theoretical works, it was shown that strongly over-parameterized neural networks trained with gradient-based methods could converge exponentially fast to zero…
On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport
Lenaic Chizat, Francis Bach
Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural netw…
Scaling Algorithms for Unbalanced Transport Problems
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer +1
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only…
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…