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

arXiv: https://arxiv.org/abs/2010.02576 · HTML: https://mlsanity.com/paper/2010.02576/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2020.

## Built on by (most cited first, 3 of 3)

- [The Shape of Learning Curves: a Review](https://mlsanity.com/paper/2103.10948/) (2021)
- [DoubleGen: Debiased Generative Modeling of Counterfactuals](https://mlsanity.com/paper/2509.16842/) (2025)
- [FSL-SAGE: Accelerating Federated Split Learning via Smashed Activation Gradient Estimation](https://mlsanity.com/paper/2505.23182/) (2025)

## Abstract (arXiv)

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.