Risk Bounds for Mixture Density Estimation on Compact Domains via the $h$-Lifted Kullback--Leibler Divergence

arXiv:2404.12586v1 Announce Type: cross
Abstract: We consider the problem of estimating probability density functions based on sample data, using a finite mixture of densities from some component class. To this end, we introduce the $h$-lifted Kullback--Leibler (KL) divergence as a generalization of the standard KL divergence and a criterion for conducting risk minimization. Under a compact support assumption, we prove an $\mc{O}(1/{\sqrt{n}})$ bound on the expected estimation error when using the $h$-lifted KL divergence, which extends the results of Rakhlin …

abstract arxiv class compact cs.lg data divergence domains functions probability risk sample standard stat.ml type via