Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:00 pm
Date: 19th January
Place: 3001

Elsa CAZELLES (CNRS- IRIT) – Principal component analysis for probability distributions: a review

 Abstract: 

I will present different ways of conducting principal component analysis of datasets whose elements are probability distributions. For that purpose, I will consider the Riemannian-like structure of the space of probability distributions (with moments of order 2) endowed with the Wasserstein metric. The nice geometric properties (such as the existence of geodesics) of the Wasserstein space do not, however, allow applying classical statistical learning tools such as PCA for Hilbert spaces. Using techniques borrowed from Riemannian geometry, I will present different tools to produce a meaningful second order statistical analysis of a dataset of probability measures, focusing on the one-dimensional case, the Gaussian case, and the linearization of the Wasserstein metric.

Organizers:

Anna KORBA (CREST), Vincent DIVOL (CREST) , Jaouad MOURTADA (CREST)

Sponsors:
CREST-CMAP