Novel Bounds on the Probability of Misclassification in Majority Voting: Leveraging the Majority Size

A.T.J.R. Cobbenhagen; A. Carè; M.C. Campi; F.A. Ramponi; D.J. Antunes; W.P.M.H. Heemels

doi:10.1109/LCSYS.2020.3040961

Novel Bounds on the Probability of Misclassification in Majority Voting: Leveraging the Majority Size

A.T.J.R. Cobbenhagen (Corresponding author), A. Carè, M.C. Campi, F.A. Ramponi, D.J. Antunes, W.P.M.H. Heemels

Research output: Contribution to journal › Article › Academic › peer-review

1 Citation (Scopus)

Abstract

Majority voting is often employed as a tool to increase the robustness of data-driven decisions and control policies, a fact which calls for rigorous, quantitative evaluations of the limits and the potentials of majority voting schemes. This letter focuses on the case where the voting agents are binary classifiers and introduces novel bounds on the probability of misclassification conditioned on the size of the majority. We show that these bounds can be much smaller than the traditional upper bounds on the probability of misclassification. These bounds can be used in a 'Probably Approximately Correct' (PAC) setting, which allows for a practical implementation.

Original language	English
Article number	9272617
Pages (from-to)	1513-1518
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	5
Issue number	5
DOIs	https://doi.org/10.1109/LCSYS.2020.3040961
Publication status	Published - Nov 2021

Funding

Manuscript received September 14, 2020; revised November 14, 2020; accepted November 18, 2020. Date of publication November 26, 2020; date of current version December 22, 2020. The work of A. T. J. R. Cobbenhagen, D. J. Antunes, and W. P. M. H. Heemels were supported by “Toeslag voor Topconsortia voor Kennis en Innovatie” (TKI HTSM) from the Ministry of Economic Affairs, the Netherlands. The work of A. Carè, M. C. Campi, and F. A. Ramponi were supported by the H&W Program of the University of Brescia under Project CLAFITE. Recommended by Senior Editor G. Cherubini. (Corresponding author: A. T. J. R. Cobbenhagen.) A. T. J. R. Cobbenhagen, D. J. Antunes, and W. P. M. H. Heemels are with the Department of Mechanical Engineering, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands (e-mail: [email protected]; [email protected]; [email protected]). The work of A. T. J. R. Cobbenhagen, D. J. Antunes, and W. P. M. H. Heemels were supported by ?Toeslag voor Topconsortia voor Kennis en Innovatie? (TKI HTSM) from the Ministry of Economic Affairs, the Netherlands. The work of A. Car?, M. C. Campi, and F. A. Ramponi were supported by the H&W Program of the University of Brescia under Project CLAFITE.

Funders	Funder number
Ministerie van Economische Zaken en Klimaat
University of Brescia

Keywords

agents-based systems
Machine learning
statistical learning

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10.1109/LCSYS.2020.3040961

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Novel Bounds on the Probability of Misclassification in Majority Voting: Leveraging the Majority Size

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