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arXiv · 2604.19725

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

Yan Zhang
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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 polylogarithmic 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.

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Yan Zhang. 2026-04-21. Fast computation and theoretical guarantees for the NPMLE in exponential family mixtures. https://arxiv.org/abs/2604.19725

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