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

TL;DR

This paper explores the relationship between high-probability and in-expectation generalization guarantees in machine learning, introducing a method to convert between them and addressing unbounded loss functions with the witness condition.

Contribution

It provides a novel approach to transform generalization bounds from high-probability to in-expectation and introduces the witness condition for unbounded loss functions.

Findings

Transformation method between high-probability and in-expectation guarantees

Application of witness condition to unbounded loss functions

Enhanced understanding of generalization bounds in statistical learning

Abstract

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.