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.
arXiv:2607. 17018v1 Announce Type: cross Abstract: We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM).
arXiv:2606. 11469v1 Announce Type: cross Abstract: We study the task of density estimation, where we hope to accurately estimate a probability density from $n$ samples.
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. 01576v3 Announce Type: replace Abstract: The explainable clustering problem was first posed by Moshkovitz et al.
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: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:2401. 10927v3 Announce Type: replace-cross Abstract: In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions in $\mathbb{R}^p$.
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.
arXiv:2411. 12438v2 Announce Type: replace-cross Abstract: We develop a new approach for clustering non-spherical (i.
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:2404.12613v4 Announce Type: replace-cross Abstract: In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the m...
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.