A matrix hyperbolic cosine algorithm and applications
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Loose laplacian spectra of random hypergraphs
Random Structures & Algorithms
Aggregating crowdsourced binary ratings
Proceedings of the 22nd international conference on World Wide Web
Greedy sparsity-constrained optimization
The Journal of Machine Learning Research
An efficient algorithm for finding the ground state of 1D gapped local hamiltonians
Proceedings of the 5th conference on Innovations in theoretical computer science
Identification via quantum channels
Information Theory, Combinatorics, and Search Theory
Hi-index | 0.00 |
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.