Vincent Divol

Spectral stability of empirical metric-measure Laplacians

The variance of nonparametric estimators is typically insensitive to the regularity of the object being estimated. We establish such a property for the spectra of graph Laplacian matrices at a fixed bandwidth $h>0$. Specifically, given $n$ i.i.d. samples from a probability measure $\mu$ on a Polish metric space, we com...