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...
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.
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.
arXiv:2509. 22879v2 Announce Type: replace-cross Abstract: Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions.
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.
arXiv:2609.16622v1 Announce Type: cross Abstract: Parameter estimation in finite mixture models can exhibit highly heterogeneous convergence behavior: locally isolated components may be estimated sub...
arXiv:2507.20459v2 Announce Type: replace-cross Abstract: With direct computation of moments through order $L$ in $d$ dimensions, standard method of moments (MM) incurs $\Omega(d^L)$ computation and...
The paper studies the numerical solution of the Beurling‑LASSO (BLASSO) for estimating Gaussian mixture models (GMMs) with unknown numbers of components and unknown diagonal covariance matrices. It introduces a Conic Particle Gradient Descent (CPGD) algorithm that incorporates Riemannian gradient descent to respect the Fisher‑Rao geometry of Gaussian distributions. The authors provide theoretical convergence guarantees, including exponential local convergence under a non‑degeneracy condition related to component separation, and demonstrate through numerical experiments that CPGD is more robust to overspecification of components than the EM algorithm.
arXiv:2411. 05591v2 Announce Type: replace-cross Abstract: We systematically study several network-based Expectation-Maximization (EM) algorithms for the Gaussian mixture model within decentralized federated learning (DFL).
arXiv:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
arXiv:2610. 01088v1 Announce Type: cross Abstract: The nonparametric maximum likelihood estimator (NPMLE) of a Gaussian location mixture maximizes the likelihood over the infinite-dimensional space of mixing distributions.