3 citations · 3 across the 11 of their papers we have counts for
12 papers
Fluctuations of the quadratic matching cost on the flat torus: dimensions two, three and four
Shi Feng, Gilles Mordant
We establish sharp variance asymptotics and limiting distributions for the quadratic optimal matching cost between the uniform measure and an empirical measure counterpart on the f…
Convergence of the Sinkhorn Riemannian metric for finitely supported measures
Gilles Mordant, Liane Xu
The Sinkhorn Riemannian metric characterizes the local behavior of the Sinkhorn divergence, a debiased version of entropy-regularized optimal transport. Although the Sinkhorn diver…
On the discretization of the object space in inverse problems with application to cryo-electron microscopy
Gilles Mordant, Luke Evans, David Silva-Sánchez +2
In many inverse problems, the aim is to recover a probability distribution on a latent (or object state) space from indirect, noisy observations. When the observations can be model…
Empirical optimal transport potentials: fast rates and a functional central limit theorem
Alberto González-Sanz, Gilles Mordant, Shunan Sheng
Optimal transport potentials are fundamental objects in statistics, economics, and machine learning: their gradients generate optimal transport maps, while the potentials themselve…
The Catastrophic Failure of The k-Means Algorithm in High Dimensions, and How Hartigan's Algorithm Avoids It
Roy R. Lederman, David Silva-Sánchez, Ziling Chen +3
Lloyd's k-means algorithm is one of the most widely used clustering methods. We prove that in high-dimensional, high-noise settings, the algorithm exhibits catastrophic failure: wi…
Estimation of Algebraic Sets: Extending PCA Beyond Linearity
Alberto González-Sanz, Gilles Mordant, Álvaro Samperio +1
An algebraic set is defined as the zero locus of a system of real polynomial equations. In this paper we address the problem of recovering an unknown algebraic set fr…
The entropic optimal (self-)transport problem: Limit distributions for decreasing regularization with application to score function estimation
Gilles Mordant
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution f…
Infinitesimal behavior of Quadratically Regularized Optimal Transport and its relation with the Porous Medium Equation
Alejandro Garriz-Molina, Alberto González-Sanz, Gilles Mordant
The quadratically regularized optimal transport problem has recently been considered in various applications where the coupling needs to be \emph{sparse}, i.e., the density of the…
Regularised optimal self-transport is approximate Gaussian mixture maximum likelihood
Gilles Mordant
We investigate the link between regularised self-transport problems and maximum likelihood estimation in Gaussian mixture models (GMM). This link suggests that self-transport follo…
Manifold Learning with Sparse Regularised Optimal Transport
Stephen Zhang, Gilles Mordant, Tetsuya Matsumoto +1
Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high…
Quadratically Regularized Optimal Transport: nearly optimal potentials and convergence of discrete Laplace operators
Gilles Mordant, Stephen Zhang
We consider the conjecture proposed in Matsumoto, Zhang and Schiebinger (2022) suggesting that optimal transport with quadratic regularisation can be used to construct a graph whos…
About limiting spectral distributions of block-rescaled empirical covariance matrices
Gilles Mordant
We establish that the limiting spectral distribution of a block-rescaled empirical covariance matrix is an arcsine law when the ratio between the dimension and the underlying sampl…