Optimized Tail Bounds for Random Matrix Series

Autor:	Xianjie Gao, Mingliang Zhang, Jinming Luo
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	tail bound intrinsic dimension random matrix series expectation bound Science Astrophysics QB460-466 Physics QC1-999
Zdroj:	Entropy, Vol 26, Iss 8, p 633 (2024)
Druh dokumentu:	article
ISSN:	1099-4300
DOI:	10.3390/e26080633
Popis:	Random matrix series are a significant component of random matrix theory, offering rich theoretical content and broad application prospects. In this paper, we propose modified versions of tail bounds for random matrix series, including matrix Gaussian (or Rademacher) and sub-Gaussian and infinitely divisible (i.d.) series. Unlike present studies, our results depend on the intrinsic dimension instead of ambient dimension. In some cases, the intrinsic dimension is much smaller than ambient dimension, which makes the modified versions suitable for high-dimensional or infinite-dimensional setting possible. In addition, we obtain the expectation bounds for random matrix series based on the intrinsic dimension.
Databáze:	Directory of Open Access Journals
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