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PixelCNN++: Improving the PixelCNN with discretized logistic mixture likelihood and other modifications

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arXiv Statistics ML
Sep 25

Riemannian Gradient Descent for Gaussian Mixture Models with unknown diagonal covariances

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
Hugging Face Trending Papers
Jun 29

Simplifying Flow Matching Transformations with Low-Rank Mixture Models

Normalizing flows are powerful generative models that learn an invertible mapping between complex data distributions and simple latent distributions, typically a standard normal density. However, this choice of latent density can impose unnecessary complexity on the learned flow transformation due to the topological mismatch between the latent and data densities, leading to slower training and suboptimal performance.

arXiv Machine Learning
Sep 11

Sublinear Variational Optimization of Gaussian Mixture Models with Millions to Billions of Parameters

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.

By Sebastian Salwig, Till Kahlke, Florian Hirschberger, Dennis Forster, J\"org L\"ucke