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Each is checked against this paper’s own text: does it say what the citing paper says it does?
The Blumer bound states that given two hypothesis spaces, searching the smaller space will result in fewer errors compared to the larger space, assuming that the target hypothesis is in both spaces.
“The Blumer bound (Blumer et al., 1987) (the bound is a reformulation of Lemma 2.1) helps explain this trade-off. This bound states that given two hypothesis spaces, searching the smaller space will result in fewer errors compared to the larger space, assuming that the target hypothesis is in both spaces.”
From Inductive Logic Programming At 30: A New Introduction (2022) · cites this paper as Blumer et al., 1987
The Blumer bound states that given two hypothesis spaces of different sizes, searching the smaller space will result in less error compared to the larger space, assuming that the target hypothesis is in both spaces.
“The Blumer bound (Blumer et al. 1987) says that given two hypothesis spaces of different sizes, then searching the smaller space will result in less error compared to the larger space, assuming that the target hypothesis is in both spaces.”
From Learning higher-order logic programs (2020) · cites this paper as Blumer et al. 1987
Cites
Valiant, L. G. (1984) · Communications of the ACM · doi:10.1145/1968.1972 · Cited by 3,279 · see citing works
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“…in , and a maximum program size n u , unabstracted MIL has sample complexity: Proof According to the Blumer bound, which appears as a reformulation of Lemma 2.1 in [ 2 ] , the error of consistent hypotheses is bounded by ε with probability at least , where | H | is the size of the hypothesis space.”
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Courtis, D., Li, W., & Sanner, S. (2026) · arXiv · doi:10.48550/arxiv.2607.01531
- Authors
- Blumer, A., Ehrenfeucht, A., Haussler, D., & Warmuth, M. K.
- Affiliations
- University of Denver (US)
- University of Colorado Boulder (US)
- University of California, Santa Cruz (US)
- Venue
- Information Processing Letters
- Publisher
- Elsevier BV
- Published
- 1987-04
- Volume
- 24
- Issue
- 6
- Pages
- 377-380
- ISSN
- 0020-0190 (ISSN-L)
- OpenAlex
- W2070902649
- Cited by
- 1,054
- References
- 1
- Citations by year
- 2026: 19 · 2025: 33 · 2024: 38 · 2023: 32 · 2022: 45 · 2021: 48 · 2020: 63 · 2019: 42 · 2018: 32 · 2017: 26 · 2016: 22 · 2015: 31 · 2014: 30 · 2013: 20 · 2012: 18
- FWCI
- 27.70
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Information Processing Letters (publishedVersion)
- Funders
- University of Denver
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computability, Logic, AI Algorithms
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Keywords
- Occam's razor, polynomial-time learning algorithm, PAC learning, consistency, computational learning theory
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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