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New insights on concentrations inequalities for martingales applications to statistics and machine learning

Abstract : The field of concentration inequalities has gained a significant traction over the last two decades, from contributing to the resolution of complex applied problems to enhancing the theoretical framework of probability.The thesis provides a thorough and exhaustive overview of the relevant scientific literature. The two main components of this scientific contribution are focused on developing new concentration inequalities for self-normalised martingales with applications to statistics, as well as a drastic improvement to the risk tail bounds of online machine learning algorithms.This work succeeded to connect two fields that have been relatively distinct. The findings bridge the gap between the field of online machine learning and the new concentration inequalities for both martingales and the improvements of the Bernstein type inequalities for random variables.
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Submitted on : Thursday, May 12, 2022 - 9:53:27 AM
Last modification on : Friday, August 5, 2022 - 3:00:08 PM

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  • HAL Id : tel-03665790, version 1

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Taieb Touati. New insights on concentrations inequalities for martingales applications to statistics and machine learning. Probability [math.PR]. Sorbonne Université, 2021. English. ⟨NNT : 2021SORUS411⟩. ⟨tel-03665790⟩

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