147 citations · 439 across the 10 of their papers we have counts for
10 papers
Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark
Alexander Korotin, Lingxiao Li, Aude Genevay +3
Despite the recent popularity of neural network-based solvers for optimal transport (OT), there is no standard quantitative way to evaluate their performance. In this paper, we add…
Large-Scale Wasserstein Gradient Flows
Petr Mokrov, Alexander Korotin, Lingxiao Li +3
Wasserstein gradient flows provide a powerful means of understanding and solving many diffusion equations. Specifically, Fokker-Planck equations, which model the diffusion of proba…
Improving Approximate Optimal Transport Distances using Quantization
Gaspard Beugnot, Aude Genevay, Kristjan Greenewald +1
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming a…
Continuous Regularized Wasserstein Barycenters
Lingxiao Li, Aude Genevay, Mikhail Yurochkin +1
Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in pr…
Differentiable Deep Clustering with Cluster Size Constraints
Aude Genevay, Gabriel Dulac-Arnold, Jean-Philippe Vert
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as -means -- rely on the euclidean distance as a similarity measure, which is ofte…
Sample Complexity of Sinkhorn divergences
Aude Genevay, Lénaic Chizat, Francis Bach +2
Optimal transport (OT) and maximum mean discrepancies (MMD) are now routinely used in machine learning to compare probability measures. We focus in this paper on \emph{Sinkhorn div…
Wasserstein Measure Coresets
Sebastian Claici, Aude Genevay, Justin Solomon
The proliferation of large data sets and Bayesian inference techniques motivates demand for better data sparsification. Coresets provide a principled way of summarizing a large dat…
GAN and VAE from an Optimal Transport Point of View
Aude Genevay, Gabriel Peyré, Marco Cuturi
This short article revisits some of the ideas introduced in arXiv:1701.07875 and arXiv:1705.07642 in a simple setup. This sheds some lights on the connexions between Variational Au…
Learning Generative Models with Sinkhorn Divergences
Aude Genevay, Gabriel Peyré, Marco Cuturi
The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dime…
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…