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The Masked Sample Covariance Estimator: An Analysis via Matrix Concentration Inequalities
Richard Y. Chen, Alex Gittens, Joel A. Tropp
Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent…
The restricted isometry property for time-frequency structured random matrices
Götz E. Pfander, Holger Rauhut, Joel A. Tropp
We establish the restricted isometry property for finite dimensional Gabor systems, that is, for families of time--frequency shifts of a randomly chosen window function. We show th…
Tail bounds for all eigenvalues of a sum of random matrices
Alex Gittens, Joel A. Tropp
This work introduces the minimax Laplace transform method, a modification of the cumulant-based matrix Laplace transform method developed in "User-friendly tail bounds for sums of…
A comparison principle for functions of a uniformly random subspace
Joel A. Tropp
This note demonstrates that it is possible to bound the expectation of an arbitrary norm of a random matrix drawn from the Stiefel manifold in terms of the expected norm of a stand…
Freedman's inequality for matrix martingales
Joel A. Tropp
Freedman's inequality is a martingale counterpart to Bernstein's inequality. This result shows that the large-deviation behavior of a martingale is controlled by the predictable qu…
From joint convexity of quantum relative entropy to a concavity theorem of Lieb
Joel A. Tropp
This note provides a succinct proof of a 1973 theorem of Lieb that establishes the concavity of a certain trace function. The development relies on a deep result from quantum infor…