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Positive Semidefinite Supermartingales and Randomized Matrix Concentration Inequalities
Feb. 22, 2024, 5:44 a.m. | Hongjian Wang, Aaditya Ramdas
stat.ML updates on arXiv.org arxiv.org
Abstract: We present new concentration inequalities for either martingale dependent or exchangeable random symmetric matrices under a variety of tail conditions, encompassing now-standard Chernoff bounds to self-normalized heavy-tailed settings. These inequalities are often randomized in a way that renders them strictly tighter than existing deterministic results in the literature, are typically expressed in the Loewner order, and are sometimes valid at arbitrary data-dependent stopping times. Along the way, we explore the theory of positive semidefinite supermartingales …
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