FastManly is a new implementation of mixtures of Manly transformations that replaces the Nelder–Mead optimization used in traditional EM algorithms with Newton’s method. The authors derive both the gradient and full Hessian for the EM–gradient algorithm. Simulation studies demonstrate that FastManly achieves improved performance and noticeable speedups compared to the conventional approach.
arXiv:2509.02109v3 Announce Type: replace-cross Abstract: The Expectation-Maximisation (EM) algorithm is a central tool in statistics and machine learning, widely used for latent-variable models such...
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:2606. 14971v1 Announce Type: cross Abstract: While large and diverse datasets have driven recent advances in large models, identifying the optimal data mixture for pre-training and post-training remains a significant open problem.
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).
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:2608. 15105v1 Announce Type: new Abstract: Recent progress in optimization research has highlighted the sharpness of the loss landscape as a key factor in narrowing the generalization gap.
arXiv:2605.11585v2 Announce Type: replace Abstract: This paper addresses the problem of image denoising for grayscale images. We propose a probabilistic image generative model that combines a quadtre...
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.
arXiv:2405. 18220v4 Announce Type: replace-cross Abstract: Tensor-based discrete density estimation requires flexible modeling and proper divergence criteria to enable effective learning; however, traditional approaches using $\alpha$-divergence face analytical challenges due to the $\alpha$-power terms in the objective function, which hinder the derivation of closed-form update rules.
arXiv:2608.29172v1 Announce Type: new Abstract: We present a novel variational approach to a tensor-based total variation formulation which is called gradient energy total variation, GETV. We introdu...
arXiv:2601. 16510v3 Announce Type: replace-cross Abstract: Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost.