User-friendly tail bounds for sums of random matrices
Abstract
New probability bounds for sums of independent self-adjoint random matrices extend classical scalar concentration inequalities to the noncommutative setting, controlling maximum eigenvalues and matrix norms.
This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.
Get this paper in your agent:
hf papers read 1004.4389 Don't have the latest CLI?
curl -LsSf https://hf.co/cli/install.sh | bash Models citing this paper 0
No model linking this paper
Datasets citing this paper 1
Spaces citing this paper 0
No Space linking this paper
Collections including this paper 0
No Collection including this paper