Learning Gaussian mixture models (GMMs) using the Expectation-Maximization (EM) algorithm and its gradient-based variants is a fundamental problem in machine learning. It is known that randomly initia...
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
The paper introduces a highly efficient variational approximation for Gaussian Mixture Models (GMMs) with arbitrary covariances, integrated with mixtures of factor analyzers. This method reduces the per‑iteration runtime from ≠O(NCD^2) to a complexity that scales linearly with dimensionality D and sublinearly with the product NC. Experiments demonstrate sublinear scaling across the entire optimization, order‑of‑magnitude speed‑ups on large benchmarks, training of GMMs with over 10 billion parameters in under nine hours on a single CPU, and competitive zero‑shot image denoising performance.
By Sebastian Salwig, Till Kahlke, Florian Hirschberger, Dennis Forster, J\"org L\"ucke
arXiv:2606. 19876v1 Announce Type: new Abstract: The score matching problem is a central training objective in modern generative modeling, diffusion models, fitting unnormalized statistical models, and inverse problems.
By Alexander Tyurin
arXiv:2409. 09903v3 Announce Type: replace-cross Abstract: Softmax Mixture Models (SMMs) are discrete $K$-component mixture models for the probabilities of selecting one of $p$ candidate feature vectors $X_1,\ldots,X_p\in\mathbb{R}^L$ in heterogeneous populations and are widely used in econometrics and scientific applications.
By Xin Bing, Florentina Bunea, Jonathan Niles-Weed, Marten Wegkamp
arXiv:2603.19657v2 Announce Type: replace-cross
Abstract: We study model-order selection and component-mean estimation for multidimensional Gaussian mixture models with a known common covariance matr...
By Xinyu Liu, Hai Zhang