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: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: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...
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:2607. 24583v1 Announce Type: new Abstract: Large scale Bayesian nonparametrics (BNP) learner such as Stochastic Variational Inference (SVI) can handle datasets with large class number and large training size at fractional cost.
arXiv:2606. 15832v1 Announce Type: new Abstract: Empirical risk minimization on massive datasets naturally exhibits a nested double finite-sum structure, where $N=nm$ total samples are logically or physically partitioned into $n$ blocks of size $m$ (e.
arXiv:2402.11215v4 Announce Type: replace Abstract: The choice of batch size in minibatch stochastic gradient optimization is critical for both optimization and generalization performance in large-sc...
arXiv:2608. 06912v1 Announce Type: new Abstract: The top-$k$ operation is a fundamental building block of modern sparse computation, enabling token routing, expert activation, memory selection, and attention pruning.
arXiv:2607. 16261v1 Announce Type: cross Abstract: Modern optimizers combine gradients from the current mini-batch with historical optimization state, such as momentum or adaptive moments.
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:2610.28256v1 Announce Type: cross Abstract: Sparse variational Gaussian processes (SVGPs) are a widely used, principled approach to scalable Gaussian process modelling. Their success stems from...
arXiv:2608.06912v2 Announce Type: replace Abstract: Selecting the top-$k$ elements is a fundamental operation for inducing sparsity in large-scale models and optimization problems, enabling robust ex...