Abstract
We present new scalar and matrix Chernoff-style concentration bounds for a broad class of probability distributions over the binary hypercube {0, 1}n. Motivated by recent tools developed for the study of mixing times of Markov chains on discrete distributions, we say that a distribution is ℓ∞-independent when the infinity norm of its influence matrix is bounded by a constant. We show that any distribution which is ℓ∞-infinity independent satisfies a matrix Chernoff bound that matches the matrix Chernoff bound for independent random variables due to Tropp. Our matrix Chernoff bound is a broad generalization and strengthening of the matrix Chernoff bound of Kyng and Song (FOCS'18).
| Original language | English |
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| Title of host publication | ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 |
| Publisher | Association for Computing Machinery |
| Pages | 3732-3753 |
| Number of pages | 22 |
| ISBN (Electronic) | 9781611977073 |
| DOIs | |
| State | Published - 2022 |
| Event | 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 - Alexander, United States Duration: 9 Jan 2022 → 12 Jan 2022 |
Publication series
| Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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| Volume | 2022-January |
| ISSN (Print) | 1071-9040 |
| ISSN (Electronic) | 1557-9468 |
Conference
| Conference | 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 |
|---|---|
| Country/Territory | United States |
| City | Alexander |
| Period | 9/01/22 → 12/01/22 |
Bibliographical note
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