The empirical Christoffel function with applications in data analysis
Résumé
We illustrate the potential applications in machine learning of theChristoffel function, or more precisely, its empirical counterpart associatedwith a counting measure uniformly supported on a finite set of points.Firstly, we provide a thresholding scheme which allows to approximatethe support of a measure from a finite subset of its moments with strongasymptotic guaranties. Secondly, we provide a consistency result whichrelates the empirical Christoffel function and its population counterpartin the limit of large samples. Finally, we illustrate the relevance of ourresults on simulated and real world datasets for several applications instatistics and machine learning: (a) density and support estimation fromfinite samples, (b) outlier and novelty detection and (c) affine matching