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: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
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
arXiv:2610. 07551v1 Announce Type: cross Abstract: Learning Gaussian mixture models (GMMs) using the Expectation-Maximization (EM) algorithm and its gradient-based variants is a fundamental problem in machine learning.
By Yiran Zhang, Mo Zhou, Weihang Xu, Maryam Fazel, Simon S. Du
arXiv:2609.00773v1 Announce Type: cross
Abstract: High-dimensional clustering is challenging when component distributions are both heavy-tailed and directionally asymmetric. We propose a deep skew-$t...
By Jinran Wu, You-Gan Wang, Geoffrey J. McLachlan
arXiv:2609.15723v1 Announce Type: new
Abstract: Traditional variance reduction methods (e.g., SPIDER, SARAH, STORM) have been extensively investigated for improving the convergence rates of stochasti...
By Wei Jiang, Sifan Yang, Yibo Wang, Lijun Zhang, Zechao Li
arXiv:2607. 03809v1 Announce Type: new Abstract: Normalising flows provide a powerful variational family for approximate inference, yet individual architectures often fail to generalise across heterogeneous posterior geometries.
By Benjamin Wiriyapong, Oktay Karakus, Can Eyupoglu, Kirill Sidorov
arXiv:2609. 26647v1 Announce Type: cross Abstract: We study statistical rates in entropic optimal transport in the semi-discrete regime where one measure has finite support and the other is subGaussian.
By Tomas Gonzalez, Gonzalo Mena
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:2607. 24518v1 Announce Type: new Abstract: Symmetric non-negative matrix factorization (SymNMF) recovers latent group structure from a dependence matrix, but its dense, quadratic-memory objective has confined prior work to moderate sizes.
By Lavinia Ghita, Dhruv Desai, Jake Goldberg, Roman Yokunda Enzmann
arXiv:2405. 18220v4 Announce Type: replace-cross Abstract: Tensor-based discrete density estimation requires flexible modeling and proper divergence criteria to enable effective learning; however, traditional approaches using $\alpha$-divergence face analytical challenges due to the $\alpha$-power terms in the objective function, which hinder the derivation of closed-form update rules.
By Kazu Ghalamkari, Jesper L{\o}ve Hinrich, Morten M{\o}rup
arXiv:2607. 15485v1 Announce Type: new Abstract: Score-based generative models exhibit a puzzling behavior: they often appear to cover all modes of a target multimodal distribution and yet may fail to learn the correct relative mode amplitudes, which can be interpreted as mixture weights.
By Andrew Dennehy, Ramchandran Muthukumar, Rebecca Willett, Nisha Chandramoorthy