Fast computation and theoretical guarantees for the NPMLE in exponential family mixtures

TL;DR

This paper introduces a data compression method to efficiently compute the NPMLE for exponential family mixtures and proves that the estimator achieves near-parametric convergence rates.

Contribution

It presents a novel data compression technique for NPMLE computation and establishes theoretical guarantees for the estimator's convergence rate.

Findings

Likelihood evaluation cost reduced to logarithmic order

Marginal density estimator attains near-parametric convergence rate

Applicable to a broad class of approximate NPMLEs

Abstract

This work makes two advances in the study of the (approximate) nonparametric maximum likelihood estimator (NPMLE) for exponential family mixture models. First, we develop a data-compression strategy that reduces the cost of repeated likelihood evaluations in NPMLE computation to logarithmic order in the sample size. Second, we show that, for a broad class of approximate NPMLEs, the resulting marginal density estimator attains an almost parametric rate of convergence.