A Note on High-Probability versus In-Expectation Guarantees of Generalization Bounds in Machine Learning
This is an incremental theoretical contribution for researchers in statistical learning theory, focusing on technical transformations without broad practical impact.
The paper addresses the problem of converting between high-probability and in-expectation generalization guarantees in machine learning, particularly for unbounded loss functions using the witness condition, but does not report concrete numerical results.
Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample that is not representative of the underlying distribution, one cannot expect to construct a reliable machine learning model. Following that, statements made about the performance of machine learning models have to take the sampling process into account. The two common approaches for that are to generate statements that hold either in high-probability, or in-expectation, over the random sampling process. In this short note we show how one may transform one statement to another. As a technical novelty we address the case of unbounded loss function, where we use a fairly new assumption, called the witness condition.