Another Look at Log-PCA for Probability Measures: A Dynamical Formulation and Statistical Convergence

arXiv:2606.17196 · stat.ML, cs.LG, stat.ME · Submitted 2026-06-15 · Read on arXiv

Peng Xu, Changbo Zhu, Young-Heon Kim, Xiaohui Chen

stat.ML, cs.LG, stat.ME

Submitted: 2026-06-15

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

Terminology

• Optimal Transport — 17× in this paper · explained in 5 episodes
• Wasserstein Distance — 10× in this paper · explained in 6 episodes
• Objective Function — 6× in this paper · explained in 2 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• 2-Wasserstein Distance — 2× in this paper · explained in 1 episode
• Generalization — 2× in this paper · explained in 14 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Orthogonal Projection — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Principal Component Analysis (PCA) — 1× in this paper · explained in 8 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 3 episodes

Sources

• A Unified Approach for Computing Wasserstein Barycenters of Discrete and Continuous Measures
• Statistical Inference for Bures-Wasserstein Flows

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