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Let A be a d by n matrix, d < n. Let T = T n−1 be the standard regular simplex in R n . We count the faces of the projected simplex AT in the case where the projection is random, the dimens...
Some standard numerical problems become intractable in high dimensions. Yet successes are often achieved in practice. This may be explained in terms of the underlying target function being somehow s...
We develop and analyze stochastic optimization algorithms for problems in which the ex-pected loss is strongly convex, and the optimum is (approximately)sparse. Previous approaches are able to exploit...
The performance of known and new parametric estimators for Archimedean copulas is investigated, with special focus on large dimensions. In particular,method-of-moments-like estimators based on pairwis...
The global existence of solutions in $H^{2}$ is well known for $H^{2}$ critical nonlinear Schr\"{o}dinger equations with small initial data in high dimensions $d\geq8$. However, even though the soluti...
This paper presents results pertaining to sequential methods for support recovery of sparse signals in noise. Specifically, we show that any sequential measurement procedure fails provided the aver...
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are the noisy realizations of the sum of an (appproximately) lo...
This article considers the problem of multiple hypothesis testing using $t$-tests. The observed data are assumed to be independently generated conditional on an underlying and unknown two-state hidden...
In this paper we introduce an influence measure based on second order expansion of the RV and GCD measures for the comparison between unperturbed and perturbed eigenvectors of a symmetric matrix estim...
In this paper we propose a new regression interpretation of the Cholesky factor of the covariance matrix, as opposed to the well known regression interpretation of the Cholesky factor of the inverse c...

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