arXiv:2606. 19876v1 Announce Type: new Abstract: The score matching problem is a central training objective in modern generative modeling, diffusion models, fitting unnormalized statistical models, and inverse problems.
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: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...
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.
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.
arXiv:2608. 06250v1 Announce Type: cross Abstract: In overparameterised classification, training data can be linearly separable even when the underlying distribution is not.
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...
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.
arXiv:2608.23916v1 Announce Type: new Abstract: Denoising score matching trains diffusion models by regressing onto a conditional score, although generation ultimately requires the marginal score. Th...
arXiv:2609.05688v1 Announce Type: new Abstract: We study variance-preserving diffusion of the response in mixed linear regression (MLR) with unknown mixing weights. Our analysis separates the statist...
arXiv:2606. 16257v1 Announce Type: cross Abstract: Sampling from high-dimensional, non-log-concave distributions with unnormalized densities is a fundamental challenge in machine learning, particularly when the exact gradient of the potential is unavailable and must be approximated via stochastic gradients that exhibit high variance under a fixed budget of gradient computations per iteration.
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:2606. 06179v1 Announce Type: cross Abstract: Score-based diffusion models are typically trained by minimizing the $L^2$ score matching error, and standard theoretical analyses rely on this quantity to bound the sampling discrepancy between the learned and target distributions.