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Contributions to the theoretical analysis of the algorithms with adversarial and dependent data

Abstract : In this thesis firstly, I present concentration inequalities of Bernstein's type for the norms of Banach-valued random sums under functional weak-dependency assumption (the so-called functional $\mathcal{C}-$mixing). The latter is then used to prove, in the asymptotic framework, excess risk upper bounds of the regularised Hilbert-valued statistical learning rules under $\tau$-mixing assumption on the underlying training sample. These results (of the batch statistical setting) are then supplemented with the regret analysis over the classes of Sobolev balls of the type of kernel ridge regression algorithm in the setting of online nonparametric regression with arbitrary bounded data sequences. Here, in particular, a question of robustness of the kernel-based forecaster is investigated. in the framework of sequential learning, the multi-armed bandit problem under $\mathcal{C}-$mixing assumption on the arm's outputs is considered and the pseudo-regret analysis of a version of Improved UCB algorithm is given. Frinally probabilistic inequalities under the type of projective dependence condition are established for the case of deviations (both of Azuma-Hoeffding's and of Burkholder's type) to the partial sums of real-valued weakly dependent random fields.
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https://hal.archives-ouvertes.fr/tel-03711863
Contributor : Oleksandr Zadorozhnyi Connect in order to contact the contributor
Submitted on : Monday, September 19, 2022 - 10:35:22 AM
Last modification on : Saturday, September 24, 2022 - 3:17:20 AM

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Oleksandr Zadorozhnyi. Contributions to the theoretical analysis of the algorithms with adversarial and dependent data. Statistics [math.ST]. Universität Potsdam (Allemagne), 2021. English. ⟨tel-03711863v3⟩

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