On the best approximation by finite Gaussian mixtures

arXiv:2404.08913v1 Announce Type: cross
Abstract: We consider the problem of approximating a general Gaussian location mixture by finite mixtures. The minimum order of finite mixtures that achieve a prescribed accuracy (measured by various $f$-divergences) is determined within constant factors for the family of mixing distributions with compactly support or appropriate assumptions on the tail probability including subgaussian and subexponential. While the upper bound is achieved using the technique of local moment matching, the lower bound is established by relating the …

abstract accuracy approximation arxiv assumptions cs.it cs.lg family general location math.it math.st stat.ml stat.th support type