Moment based data analysis ---- Edouard Pauwels

This is an interesting talk in the N&O seminar hosted by Daniel Dadush at CWI.

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.

Edouard Pauwels is an assistant professor at IRIT, Universite Toulouse 3.