4 papers · 1 filter
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…
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…