Generalized infinite dimensional Alpha-Procrustes based geometries

arXiv:2511.09801 · stat.ML, cs.LG, math.FA, math.OC · Submitted 2025-11-12 · Read on arXiv

stat.ML, cs.LG, math.FA, math.OC

Submitted: 2025-11-12

Updated: 2026-09-04

Comments: 42 pages

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

Terminology

• alpha — 34× in this paper · explained in 1 episode
• Wasserstein Distance — 28× in this paper · explained in 4 episodes
• Trace — 15× in this paper · explained in 2 episodes
• Generalization — 12× in this paper · explained in 13 episodes
• Embeddings — 11× in this paper · explained in 2 episodes
• Hilbert Space — 11× in this paper · explained in 2 episodes
• Optimal Transport — 10× in this paper · explained in 5 episodes
• Regularization — 9× in this paper · explained in 3 episodes
• 2-Wasserstein Distance — 6× in this paper · explained in 1 episode
• Benchmark — 4× in this paper · explained in 2 episodes
• Anisotropy — 3× in this paper · explained in 3 episodes
• Core — 3× in this paper · explained in 2 episodes
• GNNs — 3× in this paper · explained in 2 episodes
• Alignment — 2× in this paper · explained in 1 episode
• Log-Euclidean Signatures — 2× in this paper
• Point Clouds — 2× in this paper · explained in 2 episodes
• Riemannian optimization — 2× in this paper · explained in 2 episodes
• Unified Framework — 2× in this paper · explained in 5 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Computational Tractability — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Domain Adaptation — 1× in this paper · explained in 5 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Optimal Transport (OT) — 1× in this paper · explained in 4 episodes
• Point Cloud Data — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Stiefel manifold — 1× in this paper · explained in 2 episodes

Sources

• Estimation of Riemannian distances between covariance operators and Gaussian processes
• Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry
• Randomized algorithms for low-rank matrix approximation: Design, analysis, and applications

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