Positive Semidefinite Supermartingales and Randomized Matrix
Concentration Inequalities
- URL: http://arxiv.org/abs/2401.15567v3
- Date: Mon, 26 Feb 2024 05:12:46 GMT
- Title: Positive Semidefinite Supermartingales and Randomized Matrix
Concentration Inequalities
- Authors: Hongjian Wang, Aaditya Ramdas
- Abstract summary: We present new concentration inequalities for either martingale dependent or exchangeable random symmetric matrices under a variety of tail conditions.
These inequalities are often randomized in a way that renders them strictly tighter than existing deterministic results in the literature.
- Score: 35.61651875507142
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 and maximal inequalities, a natural matrix analog
of scalar nonnegative supermartingales that is potentially of independent
interest.
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