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:2504.05161v2 Announce Type: replace-cross
Abstract: Score estimation is the backbone of score-based generative models (SGMs), especially denoising diffusion probabilistic models (DDPMs). A key...
By Sinho Chewi, Alkis Kalavasis, Anay Mehrotra, Omar Montasser
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.
By Romane Giard, Yohann De Castro, Roland Denis, Cl\'ement Marteau
The paper introduces a generalized score matching objective for parameter estimation on convex subsets of ρ^d, derived from Minimum Probability Flow learning. It shows that this objective is a proper local scoring rule of second order, ensuring recovery of the true density when minimized, and proves convexity and consistency for exponential family models under standard conditions. Experiments demonstrate the method’s effectiveness on constrained domains where the partition function is intractable, including a generative modeling use‑case.
By Nishanth Shetty, Saisuchith Mahajan, Chandra Sekhar Seelamantula
arXiv:2608. 06250v1 Announce Type: cross Abstract: In overparameterised classification, training data can be linearly separable even when the underlying distribution is not.
By Alex Buna, Shirley Xiaoqi Liu, Patrick Rebeschini
arXiv:2609.05727v1 Announce Type: cross
Abstract: We develop Newton Matching, a unified framework for fine-tuning and sampling in generative modeling. The target is $\pi\propto\mu e^{\tau r}$, where...
By Zeyang Li, Yunan Wang, Paolo Giaretta, Navid Azizan