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Neighborliness of Randomly-Projected Simplices in High Dimensions
Neighborly Polytopes Convex Hull of Gaussian Sample
2015/8/21
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...
Stochastic optimization and sparse statistical recovery: An optimal algorithm for high dimensions
Stochastic optimization sparse statistical recovery optimal algorithm high dimensions
2012/9/19
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...
Estimators for Archimedean copulas in high dimensions: A comparison
Archimedean copulas parameter estimation Kendall’s tau Blomqvist’s beta minimum distance estimators (diagonal/simulated) maximum-likelihood estimation.
2012/9/19
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...
Continuous dependence for $H^{2}$ critical nonlinear Schr鰀inger equations in high dimensions
Nonlinear Schrodinger equation Continuous dependence Cauchy problem Strichartz抯 estimates
2012/4/17
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...
On the Limits of Sequential Testing in High Dimensions
On the Limits of Sequential Testing High Dimensions
2011/6/21
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...
Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions
Noisy matrix decomposition via convex relaxation high dimensions
2011/3/24
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...
Simultaneous critical values for $t$-tests in very high dimensions
empirical processes FDR high dimension microarrays multiple hypothesis testing one-sample t-statistics self-normalized moderate deviation two-sample t-statistics
2011/3/21
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...
A note on sensitivity of principal component subspaces and the efficient detection of influential observations in high dimensions
distance between subspaces influential observations perturbation principal component analysis
2009/9/16
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...
A new approach to Cholesky-based covariance regularization in high dimensions
new approach Cholesky-based covariance regularization high dimensions
2010/3/18
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...