Concentration Inequalities and Model Selection
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
By the Gilbert-Varshamov bound, for radius ∆ > 0 there exists a packing {y_1,...,y_M} ⊂ R^d with pairwise distance ≥ ∆ and M ≥ 2^{d/8}.
“by the Gilbert-Varshamov bound (Massart, 2007, Lem. 4.7) there exists a packing {y 1 , . . ., y M } ⊂ R d with ∥y m -y m ′ ∥ 2 ≥ ∆ for all m ̸ = m ′ , M ≥ 2 d/8 .(60)”
From RoPoLL: Robust Panel of LLM Judges (2026) · cites this paper as Massart, 2007
Cited by
Sorted by citations
Machine Learning Testing: Survey, Landscapes and Horizons
Zhang, J. M., Harman, M., Ma, L., & Liu, Y. (2022) · IEEE Transactions on Software Engineering · doi:10.1109/tse.2019.2962027 · Cited by 897 · see citing works
Xu (2022) · doi:10.1145/3546869 · Cited by 76 · see citing works
Subspace Estimation from Unbalanced and Incomplete Data Matrices: 𝓁2, ∞ Statistical Guarantees
Cai, C., Li, G., Chi, Y., Poor, H. V., & Chen, Y. (2021) · The Annals of Statistics · doi:10.1214/20-aos1986 · Cited by 37 · see citing works
RoPoLL: Robust Panel of LLM Judges
Acharya, A., Pan, K. W., & Verkhovsky, B. (2026) · arXiv · doi:10.48550/arxiv.2606.30931
- Authors
- Massart, P., & Picard, J.
- Affiliations
- Université Paris-Sud (FR)
- Université Blaise Pascal (FR)
- Venue
- Lecture Notes in Mathematics
- Publisher
- Springer Berlin Heidelberg
- Published
- 2007
- OpenAlex
- W156419107
- Cited by
- 744
- References
- 0
- Citations by year
- 2026: 2 · 2025: 9 · 2024: 11 · 2023: 21 · 2022: 39 · 2021: 49 · 2020: 45 · 2019: 49 · 2018: 33 · 2017: 50 · 2016: 34 · 2015: 86 · 2014: 50 · 2013: 56 · 2012: 59
- FWCI
- 8.53
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Springer eBooks (publishedVersion)
- International Linear Collider (submittedVersion)
- Digital Access to Libraries (Université catholique de Louvain (UCL), l'Université de Namur (UNamur) and the Université Saint-Louis (USL-B)) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- concentration inequalities, model selection, Talagrand inequality, Banach space geometry, feature selection, statistical learning, large deviations
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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