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[2602.12605] Block-Sample MAC-Bayes Generalization Bounds
Summary
The paper introduces Block-Sample MAC-Bayes bounds, a new approach to generalization error estimation in machine learning, enhancing traditional PAC-Bayes bounds by focusing on subsets of training data.
Why It Matters
This research is significant as it addresses limitations in existing PAC-Bayes bounds, offering a potentially tighter and more applicable framework for assessing model generalization. The findings could influence future machine learning methodologies and improve model performance in various applications.
Key Takeaways
- Block-Sample MAC-Bayes bounds provide a new framework for estimating generalization error.
- These bounds focus on subsets of training data, improving upon traditional PAC-Bayes bounds.
- The proposed method promises tighter bounds, enhancing model performance evaluation.
- The research demonstrates limitations of high-probability PAC-Bayes bounds in certain scenarios.
- Numerical examples illustrate the practical implications of the new bounds.
Computer Science > Machine Learning arXiv:2602.12605 (cs) [Submitted on 13 Feb 2026] Title:Block-Sample MAC-Bayes Generalization Bounds Authors:Matthias Frey, Jingge Zhu, Michael C. Gastpar View a PDF of the paper titled Block-Sample MAC-Bayes Generalization Bounds, by Matthias Frey and Jingge Zhu and Michael C. Gastpar View PDF HTML (experimental) Abstract:We present a family of novel block-sample MAC-Bayes bounds (mean approximately correct). While PAC-Bayes bounds (probably approximately correct) typically give bounds for the generalization error that hold with high probability, MAC-Bayes bounds have a similar form but bound the expected generalization error instead. The family of bounds we propose can be understood as a generalization of an expectation version of known PAC-Bayes bounds. Compared to standard PAC-Bayes bounds, the new bounds contain divergence terms that only depend on subsets (or \emph{blocks}) of the training data. The proposed MAC-Bayes bounds hold the promise of significantly improving upon the tightness of traditional PAC-Bayes and MAC-Bayes bounds. This is illustrated with a simple numerical example in which the original PAC-Bayes bound is vacuous regardless of the choice of prior, while the proposed family of bounds are finite for appropriate choices of the block size. We also explore the question whether high-probability versions of our MAC-Bayes bounds (i.e., PAC-Bayes bounds of a similar form) are possible. We answer this question in the negati...
