Corrections to ``The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithms''

Samir M. Perlaza

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arXiv · 2610.26245

Corrections to ``The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithms''

Samir M. Perlaza

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Abstract

In this paper, a counterexample to Lemma 5 of the paper referenced in the title is provided. Consequently, the formulation of the method of data-driven gaps presented in the referenced paper relies on an additional assumption, namely, that the conditional distribution of the training dataset given the learned model has identical data-point-specific marginals. To overcome this limitation, a generalized formulation of the method of data-driven gaps that does not rely on Lemma 5 and does not require the training samples to be independent or identically distributed is presented. Through this formulation, the applicability of the method of data-driven gaps is extended to a broader class of data distributions and randomized learning algorithms.

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Samir M. Perlaza. 2026-10-19. Corrections to ``The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithms''. https://arxiv.org/abs/2610.26245

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