Characterizing the Generalization Error of Gibbs Algorithm with Symmetrized KL information

Abstract

Bounding the generalization error of a supervised learning algorithm is one of the most important problems in learning theory, and various approaches have been developed. However, existing bounds are often loose and lack of guarantees. As a result, they may fail to characterize the exact generalization ability of a learning algorithm. Our main contribution is an exact characterization of the expected generalization error of the well-known Gibbs algorithm in terms of symmetrized KL information between the input training samples and the output hypothesis. Such a result can be applied to tighten existing expected generalization error bound. Our analysis provides more insight on the fundamental role the symmetrized KL information plays in controlling the generalization error of the Gibbs algorithm.

arXiv commentThe first and second author have contributed equally to the paper. This paper is accepted in the ICML-21 Workshop on Information-Theoretic Methods for Rigorous, Responsible, and Reliable Machine Learning: https://sites.google.com/view/itr3/schedule

References in corpus (5)

• Understanding deep learning requires rethinking generalization
• From $\epsilon$-entropy to KL-entropy: Analysis of minimum information complexity density estimation
• Tighter expected generalization error bounds via Wasserstein distance
• Reasoning About Generalization via Conditional Mutual Information
• Generalization Error Bounds Via Rényi-, $f$-Divergences and Maximal Leakage

Cited by in corpus (2)

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