Ensuring reliability in machine learning algorithms. This paper introduces sanity-check bounds for the error of leave-one-out cross-validation. This cross-validation method provides an estimate of the generalization error, a crucial metric of algorithm performance. It demonstrates that the worst-case error of the leave-one-out estimate is not significantly worse than the training error estimate. Introducing a new notion of error stability, the authors expand the applicability of sanity-check bounds to a wider array of learning algorithms. The research also highlights the necessity of error stability for proving bounds and the dependence of these bounds on the Vapnik-Chervonenkis dimension of the hypothesis class. This research has a key function for *mathematics*.
Published in Neural Computation, this article is aligned with the journal's emphasis on theoretical aspects of neural networks and machine learning. By establishing sanity-check bounds for leave-one-out cross-validation, the paper addresses a theoretical challenge related to algorithm evaluation. The study's focus on algorithmic stability and error bounds contributes to the journal’s core theme of advancing the mathematical foundations of neural computation.