← Back to all news
arXiv Machine Learning By Shayan Hundrieser, Tudor Manole

Minimax Optimality of the NPMLE for Gaussian Mixtures in Hellinger Distance

Read the original on arXiv Machine Learning →

The paper studies estimation of univariate Gaussian mixture densities using the nonparametric maximum likelihood estimator (NPMLE). It proves that the unconstrained NPMLE attains the minimax optimal rate ∑(n)/n in squared Hellinger distance when the true mixing measure is sub‑Gaussian, and that a compactly constrained NPMLE achieves a slightly faster rate ∑(n)/(n∑∑(n)). The analysis relies on sharp bounds for local Hellinger bracketing entropy and introduces new bounds on the L² bracketing entropy of bounded‑degree polynomial balls.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Statistics ML
Oct 7

Poisson empirical Bayes estimation of sums of random variables via minimum-distance methods

The paper develops a nonparametric empirical Bayes approach for estimating sums of functions of observable and unobservable variables in Poisson mixture models, using regular and coarsened minimum‑distance estimation of the mixing distribution. It proves large‑sample guarantees that the plug‑in estimates converge to the oracle Bayes estimate, achieving nearly parametric rates when the mixing distribution has finite support. Finite‑sample analyses are provided for two specific sums—total intensity below a threshold and the number of units exceeding latent intensity—along with minimax regret bounds and conditions for bounded regret.

By Stefano Favaro, Sandra Fortini, Soham Jana
More like this →
arXiv Machine Learning
Aug 19

Global Convergence of Gradient EM for Over-Parameterized Gaussian Mixtures

arXiv:2506. 06584v2 Announce Type: replace Abstract: Learning Gaussian Mixture Models (GMMs) is a fundamental problem in statistics and machine learning, with the Expectation-Maximization (EM) algorithm and its popular variant gradient EM being arguably the most widely used algorithms in practice.

By Mo Zhou, Weihang Xu, Maryam Fazel, Simon S. Du
More like this →