Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure
DOI:
https://doi.org/10.1609/aaai.v38i15.29674Keywords:
ML: Learning Theory, ML: Information TheoryAbstract
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.Downloads
Published
2024-03-24
How to Cite
Zou, X., Perlaza, S. M., Esnaola, I., & Altman, E. (2024). Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure. Proceedings of the AAAI Conference on Artificial Intelligence, 38(15), 17271-17279. https://doi.org/10.1609/aaai.v38i15.29674
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Section
AAAI Technical Track on Machine Learning VI