Resilience of Rademacher chaos of low degree
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911326781046784 |
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| author | Aigner-Horev, Elad Rosenberg, Daniel Weiss, Roi |
| author_facet | Aigner-Horev, Elad Rosenberg, Daniel Weiss, Roi |
| contents | The {\em resilience} of a Rademacher chaos is the maximum number of adversarial sign-flips that the chaos can sustain without having its largest atom probability significantly altered. Inspired by probabilistic lower-bound guarantees for the resilience of linear Rademacher chaos (aka. resilience of the Littlewood-Offord problem), obtained by Bandeira, Ferber, and Kwan (Advances in Mathematics, Vol. $319$, $2017$), we provide probabilistic lower-bound guarantees for the resilience of Rademacher chaos of arbitrary degree; these being most meaningful provided that the degree is constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10504 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Resilience of Rademacher chaos of low degree Aigner-Horev, Elad Rosenberg, Daniel Weiss, Roi Probability Information Theory Machine Learning Combinatorics The {\em resilience} of a Rademacher chaos is the maximum number of adversarial sign-flips that the chaos can sustain without having its largest atom probability significantly altered. Inspired by probabilistic lower-bound guarantees for the resilience of linear Rademacher chaos (aka. resilience of the Littlewood-Offord problem), obtained by Bandeira, Ferber, and Kwan (Advances in Mathematics, Vol. $319$, $2017$), we provide probabilistic lower-bound guarantees for the resilience of Rademacher chaos of arbitrary degree; these being most meaningful provided that the degree is constant. |
| title | Resilience of Rademacher chaos of low degree |
| topic | Probability Information Theory Machine Learning Combinatorics |
| url | https://arxiv.org/abs/2402.10504 |