10 citations · 17 across the 16 of their papers we have counts for
18 papers
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…
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 the Euclidean space. For absolutely continuous so…
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…
Efficient Gaussian process learning via subspace projections
Elsa Cazelles, Felipe Tobar
We propose a novel training objective for GPs constructed using lower-dimensional linear projections of the data, referred to as \emph{projected likelihood} (PL). We provide a clos…
Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicing
Clément Bonet, Elsa Cazelles, Lucas Drumetz +1
The Busemann function has recently found much interest in a variety of geometric machine learning problems, as it naturally defines projections onto geodesic rays of Riemannian man…
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…
Sample complexity of optimal transport barycenters with discrete support
Léo Portales, Edouard Pauwels, Elsa Cazelles
Computational implementation of optimal transport barycenters for a set of target probability measures requires a form of approximation, a widespread solution being empirical appro…
Audio signal interpolation using optimal transportation of spectrograms
David Valdivia, Marien Renaud, Elsa Cazelles +1
We present a novel approach for generating an artificial audio signal that interpolates between given source and target sounds. Our approach relies on the computation of Wasserstei…
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…
Low dimensional representation of multi-patient flow cytometry datasets using optimal transport for minimal residual disease detection in leukemia
Erell Gachon, Jérémie Bigot, Elsa Cazelles +4
Representing and quantifying Minimal Residual Disease (MRD) in Acute Myeloid Leukemia (AML), a type of cancer that affects the blood and bone marrow, is essential in the prognosis…
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…
Computationally-efficient initialisation of GPs: The generalised variogram method
Felipe Tobar, Elsa Cazelles, Taco de Wolff
We present a computationally-efficient strategy to initialise the hyperparameters of a Gaussian process (GP) avoiding the computation of the likelihood function. Our strategy can b…
A novel notion of barycenter for probability distributions based on optimal weak mass transport
Elsa Cazelles, Felipe Tobar, Joaquín Fontbona
We introduce weak barycenters of a family of probability distributions, based on the recently developed notion of optimal weak transport of mass by Gozlanet al. (2017) and Backhoff…
The Wasserstein-Fourier Distance for Stationary Time Series
Elsa Cazelles, Arnaud Robert, Felipe Tobar
We propose the Wasserstein-Fourier (WF) distance to measure the (dis)similarity between time series by quantifying the displacement of their energy across frequencies. The WF dista…
Data-driven regularization of Wasserstein barycenters with an application to multivariate density registration
Jérémie Bigot, Elsa Cazelles, Nicolas Papadakis
We present a framework to simultaneously align and smooth data in the form of multiple point clouds sampled from unknown densities with support in a d-dimensional Euclidean space.…
Central limit theorems for entropy-regularized optimal transport on finite spaces and statistical applications
Jérémie Bigot, Elsa Cazelles, Nicolas Papadakis
The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the…
Log-PCA versus Geodesic PCA of histograms in the Wasserstein space
Elsa Cazelles, Vivien Seguy, Jérémie Bigot +2
This paper is concerned by the statistical analysis of data sets whose elements are random histograms. For the purpose of learning principal modes of variation from such data, we c…
Penalized Barycenters in the Wasserstein Space
Jérémie Bigot, Elsa Cazelles, Nicolas Papadakis
In this paper, a regularization of Wasserstein barycenters for random measures supported on is introduced via convex penalization. The existence and uniqueness of…