W-Kernel and Its Principal Space for Frequentist Evaluation of Bayesian Estimators

arXiv:2311.13017 · stat.ME, cond-mat.stat-mech, stat.ML · Submitted 2023-11-21 · Read on arXiv

stat.ME, cond-mat.stat-mech, stat.ML

Submitted: 2023-11-21

Updated: 2026-09-06

Comments: Minor revisions to figures and text, with additions including a Note Added in Proof. Essentially identical in content to the published version, except for editorial changes, notably equation numbering. Supplementary Material appended; references merged

Journal ref: Neural Computation (2026) 38(8) 1408-1468

DOI: 10.1162/NECO.a.1547

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

Terminology

• Accuracy — 10× in this paper · explained in 1 episode
• Influence Functions — 10× in this paper · explained in 2 episodes
• Generalization — 5× in this paper · explained in 13 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Reproducing Kernel Hilbert Space — 3× in this paper
• Score Function — 3× in this paper · explained in 4 episodes
• Bayesian Inference — 2× in this paper · explained in 5 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Bayesian Framework — 1× in this paper · explained in 3 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Reproducing Kernel Hilbert Space (RKHS) — 1× in this paper · explained in 3 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Variational Bayes — 1× in this paper · explained in 2 episodes

Sources

• The Bayesian Infinitesimal Jackknife for Variance
• A Higher-Order Swiss Army Infinitesimal Jackknife
• Posterior covariance information criterion for general loss functions
• The Memory Perturbation Equation: Understanding Model's Sensitivity to Data
• Learning Representation from Neural Fisher Kernel with Low-rank Approximation
• Prior Intensified Information Criterion

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