Constructive approaches to concentration inequalities with independent random variables
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909300390100992 |
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| author | Moucer, Celine Taylor, Adrien Bach, Francis |
| author_facet | Moucer, Celine Taylor, Adrien Bach, Francis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16480 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constructive approaches to concentration inequalities with independent random variables Moucer, Celine Taylor, Adrien Bach, Francis Probability Optimization and Control 60E15, 90C22, 90C25, 60F10 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. |
| title | Constructive approaches to concentration inequalities with independent random variables |
| topic | Probability Optimization and Control 60E15, 90C22, 90C25, 60F10 |
| url | https://arxiv.org/abs/2408.16480 |