11 papers
PCA of probability measures: Sparse and Dense sampling regimes
Gachon Erell, Jérémie Bigot, Elsa Cazelles
A common approach to perform PCA on probability measures is to embed them into a Hilbert space where standard functional PCA techniques apply. While convergence rates for estimatin…
On the Wasserstein Geodesic Principal Component Analysis of probability measures
Nina Vesseron, Elsa Cazelles, Alice Le Brigant +1
This paper focuses on Geodesic Principal Component Analysis (GPCA) on a collection of probability distributions using the Otto-Wasserstein geometry. The goal is to identify geodesi…
On the sequential convergence of Lloyd's algorithms
Léo Portales, Elsa Cazelles, Edouard Pauwels
Lloyd's algorithm is an iterative method that solves the quantization problem, i.e. the approximation of a target probability measure by a discrete one, and is particularly used in…
Statistical Estimation of Monge Transport Maps via Brenier Potentials
Elsa Cazelles, Edouard Pauwels, Léo Portales
We introduce and analyze a statistical estimator for Monge transport maps: solutions to the quadratic optimal transport problem in Euclidean space. For absolutely continuous source…
Enhancing time-frequency resolution with optimal transport and barycentric fusion of multiple spectrogram
David Valdivia, Elsa Cazelles, Cédric Févotte
Time-frequency representations, such as the short-time Fourier transform (STFT), are fundamental tools for analyzing non-stationary signals. However, their ability to achieve sharp…
Scalable Learning from Probability Measures with Mean Measure Quantization
Erell Gachon, Elsa Cazelles, Jérémie Bigot
We consider statistical learning problems in which data are observed as a set of probability measures. Optimal transport (OT) is a popular tool to compare and manipulate such objec…