🤖 AI Summary
This work addresses the high computational cost and lack of convergence rate guarantees associated with nonparametric maximum likelihood estimation (NPMLE) in exponential family mixture models. The authors propose a data-compression-based acceleration strategy that, for the first time, reduces the likelihood evaluation complexity of NPMLE to logarithmic order. They establish rigorous statistical theory for the resulting approximate estimator, demonstrating that the proposed method achieves near-parametric convergence rates for marginal density estimation while substantially lowering computational overhead.
📝 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.