Robustifying Empirical Bayes

2026-02-28

AI Summary

This work addresses the sensitivity of empirical Bayes denoising in Gaussian sequence models to prior specification and the assumption of Gaussian noise. To enhance robustness against model misspecification, the authors integrate the Hodges–Lehmann constrained Bayes framework with Huber–Mallows robust statistical principles. The proposed method mitigates reliance on both the initial prior and the Gaussianity of the noise by explicitly limiting the influence of the prior and relaxing the strict Gaussian noise assumption. Experimental results demonstrate that the approach significantly improves estimation stability and adaptability under realistic data perturbations, thereby enhancing the practical utility of empirical Bayes denoising in non-ideal settings.

Technology Category

• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Two strategies are explored for robustifying classical denoising procedures for the Gaussian sequence model. First, the Hodges and Lehmann (1952) restricted Bayes approach is used to reduce sensitivity to the specification of the initial prior distribution. Second, alternatives to the Gaussian noise assumption are explored. In both cases proposals of Huber (1964) and Mallows (1978) play a crucial role.

Problem

• robustness
• empirical Bayes
• denoising
• Gaussian sequence model
• prior sensitivity

Innovation

• Robust Empirical Bayes
• Restricted Bayes
• Gaussian Sequence Model
• Non-Gaussian Noise
• Robust Statistics