Constructive approaches to concentration inequalities with independent random variables - PaRis AI Research InstitutE
Pré-Publication, Document De Travail Année : 2024

Constructive approaches to concentration inequalities with independent random variables

Résumé

Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration inequalities with independent random variables. Specifically, we extend the generalized problem of moments to independent random variables. We first introduce a variational approach that extends classical moment-generating functions, focusing particularly on first-order moment conditions. Second, we develop a polynomial approach, based on a hierarchy of sum-of-square approximations, to extend these techniques to higher-moment conditions. Building on these advancements, we refine Hoeffding's, Bennett's and Bernstein's inequalities, providing improved worst-case guarantees compared to existing results.
Fichier principal
Vignette du fichier
paper_public.pdf (648.11 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04681920 , version 1 (30-08-2024)

Identifiants

Citer

Céline Moucer, Adrien Taylor, Francis Bach. Constructive approaches to concentration inequalities with independent random variables. 2024. ⟨hal-04681920⟩
0 Consultations
0 Téléchargements

Altmetric

Partager

More