arXiv Statistics ML
Diagonally-Weighted Generalized Method of Moments Estimation for Gaussian Mixture Modeling
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Sublinear Variational Optimization of Gaussian Mixture Models with Millions to Billions of Parameters
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.
arXiv Machine Learning
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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.
arXiv Machine Learning
Sep 1
Model Selection and Parameter Estimation for Multidimensional Gaussian Mixture Models with a Common Covariance Matrix
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Is $\sqrt{d}$ Separation Necessary for Gradient EM to Learn Gaussian Mixtures in High Dimensions?
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.
arXiv Statistics ML
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Deep Skew-t Mixture Models
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arXiv Machine Learning
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Solving Finite-sum Coupled Compositional Optimization via Multi-block-Single-probe Estimator
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...