N&O seminar: Edouard Pauwels 'Moment based data analysis'

N&O seminar by Edouard Pauwels (IRIT, Universite Toulouse 3)
Title: Moment based data analysis

Inference of geometric or topological properties from data is an active
research field which includes, for example, nonlinear dimension
reduction, manifold estimation, or topological data analysis. To answer
these questions, we propose to use the Christoffel-Darboux kernel,
related to the theory of orthogonal polynomials. I will first present a
general construction and some properties. I will then illustrate with an
example the ability of this object to capture geometric information
about a probability measure, seen as a population measure. In a
statistical framework I will propose preliminary results on statistical
error bounds when working only with a finite sample. Finally, I will
illustrate these results on simulations and real data. One of the
advantages of this approach lies in the fact that it gives rise to
conceptually very simple estimators based solely on the knowledge of
moments.