Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model

arXiv:2607.01895 · cs.LG, math.OC, math.ST, stat.ML · Submitted 2026-07-02 · Read on arXiv

Francis Bach

SIERRA

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

Submitted: 2026-07-02

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

Terminology

• Trace — 29× in this paper · explained in 2 episodes
• Regularization — 20× in this paper · explained in 3 episodes
• Mutual Information — 4× in this paper · explained in 2 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Phase Transition — 3× in this paper · explained in 3 episodes
• Generalization — 2× in this paper · explained in 14 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Nuclear Norm — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Augmentation — 1× in this paper · explained in 2 episodes
• Covariate Shift — 1× in this paper · explained in 3 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Fixed Point — 1× in this paper · explained in 2 episodes
• KKT conditions — 1× in this paper · explained in 2 episodes
• Localization — 1× in this paper · explained in 2 episodes
• Memorization — 1× in this paper · explained in 4 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Reduction Theorem — 1× in this paper · explained in 2 episodes
• Selection Bias — 1× in this paper · explained in 5 episodes
• Sparsity — 1× in this paper · explained in 5 episodes
• Universality — 1× in this paper · explained in 2 episodes
• Variance Reduction — 1× in this paper · explained in 2 episodes

Sources

• A Spectral Framework for Closed-Form Relative Density Estimation
• Finite-sample performance of the maximum likelihood estimator in logistic regression
• Existence of Direct Density Ratio Estimators
• The Gaussian min-max theorem in the Presence of Convexity

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