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This is a Quantitative Study study.

October 1, 2025Open Access

Dynamical mean-field analysis of adaptive Langevin diffusions: Replica-symmetric fixed point and empirical Bayes

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Authors

FZFan ZhouCentre National de la Recherche Scientifique JKJustin KoÉcole Normale Supérieure de Lyon BLBruno LoureiroCentre National de la Recherche Scientifique

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Implication

Dynamical mean-field theory reveals convergence of adaptive Langevin trajectories in Bayesian models, suggesting implications for statistical estimation.

Key Points

Adaptive Langevin trajectories converge to an equilibrium state characterized by fixed-point equations.
Analysis shows that prior parameter converges to a critical point of a replica-symmetric limit for model free energy.
Dynamical mean-field theory establishes a high-dimensional asymptotic limit for prior parameter evolution.
Settings satisfying log-Sobolev inequalities enhance the study of posterior laws in Bayesian linear regression.

Cite This Study

Zhou et al. (2025) studied this question.

synapsesocial.com/papers/68dd91c7fe798ba2fc498572 https://doi.org/10.48550/arxiv.2504.15558

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Implication

Dynamical mean-field theory reveals convergence of adaptive Langevin trajectories in Bayesian models, suggesting implications for statistical estimation.

Dynamical mean-field analysis of adaptive Langevin diffusions: Replica-symmetric fixed point and empirical Bayes

Discussion

Member takes

Implication

Key Points

Cite This Study

Dynamical mean-field analysis of adaptive Langevin diffusions: Replica-symmetric fixed point and empirical Bayes

Discussion

Member takes

Implication

Key Points

Cite This Study

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