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

arXiv:2501.12299 · stat.ML, cs.CV, cs.LG · Submitted 2025-01-21 · Read on arXiv

stat.ML, cs.CV, cs.LG

Submitted: 2025-01-21

Updated: 2026-09-10

Comments: Published in Journal of Machine Learning Research, see https://jmlr.org/papers/v27/25-0639.html

Journal ref: S. Salwig, T. Kahlke, F. Hirschberger, D. Forster, J. Lücke, Journal of Machine Learning Research, 27(167):1-70, 2026

Code: https://github.com/variational-sublinear-clustering/vamm

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Benchmark — 26× in this paper · explained in 2 episodes
• Clustering — 22× in this paper · explained in 2 episodes
• Generative Model — 19× in this paper · explained in 2 episodes
• Analyzer — 14× in this paper · explained in 1 episode
• Generative Models — 12× in this paper · explained in 2 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Core — 7× in this paper · explained in 2 episodes
• Ablation — 5× in this paper · explained in 1 episode
• Convergence Guarantees — 5× in this paper · explained in 3 episodes
• Expectation Maximization — 5× in this paper
• Benchmarking — 4× in this paper · explained in 3 episodes
• Ablation study — 3× in this paper · explained in 1 episode
• Inverse Problem — 3× in this paper · explained in 2 episodes
• Quantization — 3× in this paper · explained in 12 episodes
• Robustness — 3× in this paper · explained in 5 episodes
• Expectation Conditional Maximization — 2× in this paper
• Representation Learning — 2× in this paper · explained in 2 episodes
• Scaling Laws — 2× in this paper · explained in 4 episodes
• Stochastic Gradient Descent — 2× in this paper
• Stochastic Gradient Descent (SGD) — 2× in this paper · explained in 5 episodes
• Alternating Expectation Conditional Maximization — 1× in this paper
• Computational Biology — 1× in this paper · explained in 2 episodes
• Computational overhead — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Downstream Tasks — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• In the Mixture of Factor Analyzers — 1× in this paper
• Interpretability — 1× in this paper · explained in 15 episodes
• Kullback-Leibler (KL) Divergence — 1× in this paper · explained in 3 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Transferability — 1× in this paper · explained in 4 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Variational Autoencoder (VAE) — 1× in this paper · explained in 3 episodes

Sources

• The Information Bottleneck EM Algorithm
• Scaling Laws for Autoregressive Generative Modeling
• Scaling Laws for Neural Language Models
• Truncated Variational Expectation Maximization

Related papers

• Behavior of prediction performance metrics with rare events
• Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
• A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
• One Permutation Is All You Need: Fast, Deterministic Feature Importance and Model Stress-Testing
• Online Conformal Prediction for Non-Exchangeable Panel Data
• Deep Time-Series Forecasting in 10 Years: A Survey