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Statistical machine learning theory often tries to give generalizationguarantees of machine learning models. Those models naturally underlie somefluctuation, as they are based on a data sample. If we were unlucky, andgathered a sample that is not representative of the underlying distribution,one cannot expect to construct a reliable machine learning model. Followingthat, statements made about the performance of machine learning models have totake the sampling process into account. The two common approaches for that areto generate statements that hold either in high-probability, or in-expectation,over the random sampling process. In this short note we show how one maytransform one statement to another. As a technical novelty we address the caseof unbounded loss function, where we use a fairly new assumption, called thewitness condition.

A Note on High-Probability versus In-Expectation Guarantees of Generalization Bounds in Machine Learning