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PreprintCC BY 4.0HAL

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

  • Samir M. Perlaza
Open at sourcePDFDOICite

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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Cite

BibTeXRIS
BibTeX
@misc{perlaza2026corrections,
  title = {{Corrections to ``The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithms}},
  author = {Samir M. Perlaza},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26245},
  eprint = {2610.26245},
  archivePrefix = {arXiv},
  url = {https://inria.hal.science/hal-05804381v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Corrections to ``The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithms
AU  - Samir M. Perlaza
PY  - 2026
DA  - 2026/10/17
PB  - HAL
DO  - 10.48550/arxiv.2610.26245
UR  - https://inria.hal.science/hal-05804381v1
AB  - 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.
ER  -