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Journal of the Belarusian State University. Mathematics and Informatics, 2020, Volume 3, Pages 28–35
DOI: https://doi.org/10.33581/2520-6508-2020-3-28-35
(Mi bgumi74)
 

This article is cited in 1 scientific paper (total in 1 paper)

Theory of probability and Mathematical statistics

On outlier detection with the chebyshev type inequalities

M. A. Chepulis, G. L. Shevlyakov

Peter the Great St. Petersburg Polytechnic University, 29 Polytechnicheskaya Street, Saint Petersburg 195251, Russia
Full-text PDF (878 kB) Citations (1)
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Abstract: This work considers algorithms of outlier detection based on the Chebyshev inequality. It compares these algorithms with such classical methods as Tukey’s boxplot, the $N$-sigma rule and its robust modifications based on $MAD$ and $FQ$ scale estimates. To adjust the parameters of the algorithms, a selection procedure is proposed based on the complete knowledge of the data distribution model. Areas of suboptimal parameters are also determined in case of incomplete knowledge of the distribution model. It is concluded that the direct use of the Chebyshev inequality implies the classical $N$-sigma rule. With the non-classical Chebyshev inequality, a robust outlier detection method is obtained, which slightly outperforms other considered algorithms.
Keywords: anomaly; outlier detection; Chebyshev inequality; robustness.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-03250
This research is partially supported by the Russian Foundation for Basic Research (number of grant 18-29-03250).
Received: 28.09.2020
Document Type: Article
UDC: 519.254
Language: English
Citation: M. A. Chepulis, G. L. Shevlyakov, “On outlier detection with the chebyshev type inequalities”, Journal of the Belarusian State University. Mathematics and Informatics, 3 (2020), 28–35
Citation in format AMSBIB
\Bibitem{CheShe20}
\by M.~A.~Chepulis, G.~L.~Shevlyakov
\paper On outlier detection with the chebyshev type inequalities
\jour Journal of the Belarusian State University. Mathematics and Informatics
\yr 2020
\vol 3
\pages 28--35
\mathnet{http://mi.mathnet.ru/bgumi74}
\crossref{https://doi.org/10.33581/2520-6508-2020-3-28-35}
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  • This publication is cited in the following 1 articles:
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    Journal of the Belarusian State University. Mathematics and Informatics
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