Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.02150 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912454735298560 |
|---|---|
| author | Neeman, Joe Shi, Bobby Ward, Rachel |
| author_facet | Neeman, Joe Shi, Bobby Ward, Rachel |
| contents | We give Hoeffding and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain. We consider time-dependent matrix-valued functions on a general state space, generalizing previous results that had only considered Hoeffding-type inequalities, and only for time-independent functions on a finite state space. In particular, we study a kind of noncommutative moment generating function, provide tight bounds on this object, and use a method of Garg et al. to turn this into tail bounds. Our proof proceeds spectrally, bounding the norm of a certain perturbed operator. In the process we make an interesting connection to dynamical systems and Banach space theory to prove a crucial result on the limiting behavior of our moment generating function that may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02150 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Concentration Inequalities for Sums of Markov Dependent Random Matrices Neeman, Joe Shi, Bobby Ward, Rachel Probability We give Hoeffding and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain. We consider time-dependent matrix-valued functions on a general state space, generalizing previous results that had only considered Hoeffding-type inequalities, and only for time-independent functions on a finite state space. In particular, we study a kind of noncommutative moment generating function, provide tight bounds on this object, and use a method of Garg et al. to turn this into tail bounds. Our proof proceeds spectrally, bounding the norm of a certain perturbed operator. In the process we make an interesting connection to dynamical systems and Banach space theory to prove a crucial result on the limiting behavior of our moment generating function that may be of independent interest. |
| title | Concentration Inequalities for Sums of Markov Dependent Random Matrices |
| topic | Probability |
| url | https://arxiv.org/abs/2303.02150 |