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Communication Dans Un Congrès Année : 2024

Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure

Résumé

In this paper, the worst-case probability measure over the data is introduced as a tool for characterizing the generalization capabilities of machine learning algorithms. More specifically, the worst-case probability measure is a Gibbs probability measure and the unique solution to the maximization of the expected loss under a relative entropy constraint with respect to a reference probability measure. Fundamental generalization metrics, such as the sensitivity of the expected loss, the sensitivity of the empirical risk, and the generalization gap are shown to have closed-form expressions involving the worst-case data-generating probability measure. Existing results for the Gibbs algorithm, such as characterizing the generalization gap as a sum of mutual information and lautum information, up to a constant factor, are recovered. A novel parallel is established between the worst-case data-generating probability measure and the Gibbs algorithm. Specifically, the Gibbs probability measure is identified as a fundamental commonality of the model space and the data space for machine learning algorithms.
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hal-04353957 , version 1 (19-12-2023)

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  • HAL Id : hal-04353957 , version 1

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Xinying Zou, Samir M. Perlaza, Iñaki Esnaola, Eitan Altman. Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure. AAAI 2024 - Conference on Artificial Intelligence, Feb 2024, Vancouver, Canada. ⟨hal-04353957⟩
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