This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for concentration of measure, as introduced by Chatterjee. Recent work of Mackey et al. uses these techniques to analyze… (More)
This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron–Stein inequalities developed by Boucheron et al. The proofs rely on the method of exchangeable pairs.
The construction and formal verification of dynamical models is important in engineering, biology and other disciplines. We focus on non-linear models containing a set of parameters governing their dynamics. The value of these parameters is often unknown and not directly observable through measurements, which are themselves noisy. When treating parameters… (More)
J o u r n a l o f P r o b a b i l i t y Electron. Abstract We prove concentration inequalities for general functions of weakly dependent random variables satisfying the Dobrushin condition. In particular, we show Talagrand's convex distance inequality for this type of dependence. We apply our bounds to a version of the stochastic salesman problem, the… (More)
Randomized single-view algorithms for low-rank matrix approximation. " Sep. 2016. 2 S. Oymak and J. A. Tropp, " Universality laws for randomized dimension reduction, with applications. " Nov. 2015. A foundation for analytical developments in the logarithmic region of turbulent channels. " Sep. 2014. BOOK CHAPTERS 8 J. A. Tropp, " The expected spectral norm… (More)
SUBMITTED FOR PUBLICATION 1 J. A. Tropp, " The expected spectral norm of a sum of independent random matrices: An elementary approach. " June 2015. 2 J. A. Tropp, " Integer factorization of a positive-definite matrix. " May 2015. 3 J. A. Tropp, " Second-order matrix concentration inequalities. " Apr. 2015. A foundation for analytical developments in the… (More)