Polylogarithmic Sparsity of Randomly Reweighted NPMLEs for Gaussian Mixtures

Excerpt

arXiv:2610.01088v1 Announce Type: cross Abstract: The nonparametric maximum likelihood estimator (NPMLE) of a Gaussian location mixture maximizes the likelihood over the infinite-dimensional space of mixing distributions. The maximizing mixing distribution can be nonunique, and the classical bound on its number of atoms grows linearly with the sample size $n$. We show that a vanishingly small random perturbation of the likelihood yields exact polylogarithmic sparsity. The resulting randomly rewe