Algorithms achieve almost-linear time for ℓ_p-norm flow and dual regression problems on unit-weighted graphs for a range of p, plus applications to max-flow and total variation.
User-friendly tail bounds for sums of random matrices
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abstract
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.
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cs.DS 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Flows in Almost Linear Time via Adaptive Preconditioning
Algorithms achieve almost-linear time for ℓ_p-norm flow and dual regression problems on unit-weighted graphs for a range of p, plus applications to max-flow and total variation.