Title: The empirical Christoffel function with applications in data analysis,
Abstract: We illustrate the potential applications in machine learning of the
Christoffel function, or more precisely, its empirical counterpart associated
with a counting measure uniformly supported on a finite set of points. Firstly,
we provide a thresholding scheme which allows to approximate the support of a
measure from a finite subset of its moments with strong asymptotic guaranties.
Secondly, we provide a consistency result which relates the empirical
Christoffel function and its population counterpart in the limit of large
samples. Finally, we illustrate the relevance of our results on simulated and
real world datasets for several applications in statistics and machine
learning: (a) density and support estimation from finite samples, (b) outlier
and novelty detection and (c) affine matching.