Concentration Inequalities on the Multislice and for Sampling Without Replacement
Sambale H, Sinulis A (2022)
Journal of Theoretical Probability 35: 2712–2737.
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| Veröffentlicht | Englisch
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Abstract / Bemerkung
We present concentration inequalities on the multislice which are based on (modified) log-Sobolev inequalities. This includes bounds for convex functions and multilinear polynomials. As an application, we show concentration results for the triangle count in the G(n, M) Erdos-Renyi model resembling known bounds in the G(n, p) case. Moreover, we give a proof of Talagrand's convex distance inequality for the multislice. Interpreting the multislice in a sampling without replacement context, we furthermore present concentration results for n out of N sampling without replacement. Based on a bounded difference inequality involving the finite-sampling correction factor 1 - (n/ N), we present an easy proof of Serfling's inequality with a slightly worse factor in the exponent, as well as a sub-Gaussian right tail for theKolmogorov distance between the empirical measure and the true distribution of the sample.
Stichworte
Concentration of measure;
Convex distance inequality;
Erdos-Renyi;
graphs;
Multislice;
Sampling without replacement
Erscheinungsjahr
2022
Zeitschriftentitel
Journal of Theoretical Probability
Band
35
Seite(n)
2712–2737
Urheberrecht / Lizenzen
ISSN
0894-9840
eISSN
1572-9230
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
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https://pub.uni-bielefeld.de/record/2958892
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Sambale H, Sinulis A. Concentration Inequalities on the Multislice and for Sampling Without Replacement. Journal of Theoretical Probability . 2022;35:2712–2737.
Sambale, H., & Sinulis, A. (2022). Concentration Inequalities on the Multislice and for Sampling Without Replacement. Journal of Theoretical Probability , 35, 2712–2737. https://doi.org/10.1007/s10959-021-01139-9
Sambale, Holger, and Sinulis, Arthur. 2022. “Concentration Inequalities on the Multislice and for Sampling Without Replacement”. Journal of Theoretical Probability 35: 2712–2737.
Sambale, H., and Sinulis, A. (2022). Concentration Inequalities on the Multislice and for Sampling Without Replacement. Journal of Theoretical Probability 35, 2712–2737.
Sambale, H., & Sinulis, A., 2022. Concentration Inequalities on the Multislice and for Sampling Without Replacement. Journal of Theoretical Probability , 35, p 2712–2737.
H. Sambale and A. Sinulis, “Concentration Inequalities on the Multislice and for Sampling Without Replacement”, Journal of Theoretical Probability , vol. 35, 2022, pp. 2712–2737.
Sambale, H., Sinulis, A.: Concentration Inequalities on the Multislice and for Sampling Without Replacement. Journal of Theoretical Probability . 35, 2712–2737 (2022).
Sambale, Holger, and Sinulis, Arthur. “Concentration Inequalities on the Multislice and for Sampling Without Replacement”. Journal of Theoretical Probability 35 (2022): 2712–2737.
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