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For linear systems that contain unspecified parameters that lie in given intervals, we present a branch and bound algorithm for computing the maximum H_infinity-norm over the set of uncertain paramete...
In this note we give a proof showing that even though the number of false discoveries and the total number of discoveries are not continuous functions of the parameters, the formulas we obtain for the...
Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-c...
We discuss structured Schatten norms for tensor decomposition that includes two recently proposed norms ("overlapped" and "latent") for convex-optimization-based tensor decomposition, and connect tens...
Recently, $l_{2,1}$ matrix norm has been widely applied to many areas such as computer vision, pattern recognition, biological study and etc. As an extension of $l_1$ vector norm, the mixed $l_{2,1}$ ...
Aulbach et al. (2012) introduced some mathematical framework for extreme value theory in the space of continuous functions on compact intervals. Continuous max-stable processes on [0,1] were character...
This paper studies matrix completion under a general sampling model using the max-norm as a convex relaxation for the rank of the matrix. The optimal rate of convergence is established for the Frobeni...
To recover a sparse signal from an underdetermined system, we often solve a constrained`1-norm minimization problem. In many cases, the signal sparsity and the recovery performance can be further impr...
We provide rigorous guarantees on learning with the weighted trace-norm under arbitrary sampling distributions.
On the extension of trace norm to tensors     On the extension.trace norm .tensors       font style='font-size:12px;'> 2010/10/14
In this paper, we propose three extensions of trace norm for the minimization of tensor rank via convex optimization. The alternating direction method of multipliers is used to efficiently solve the o...
Maxiset in sup-norm for kernel estimators      Maxiset  sup-norm for kernel estimators       font style='font-size:12px;'> 2010/4/26
Maxiset in sup-norm for kernel estimators。
Following Hartigan [1975], a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering a...
A new approximation of the unifonn empirical and quantile processes results in a weak invariance principle indexed by functions for the general empirical process. Consequences of this result are we...
A roumula for the density of the norm of stable random vectors in Hilbert spaces。
On density of a stable uniformly convex norm      density  a stable uniformly convex norm        font style='font-size:12px;'> 2009/9/23
On density of a stable uniformly convex norm

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