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Supplementary materials for Statistical Estimation and Testing via the Sorted 1 Norm
Supplementary materials Statistical Estimation Sorted 1 Norm
2015/6/17
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...
Stable Estimation of a Covariance Matrix Guided by Nuclear Norm Penalties
Covariance estimation Regularization Condition number Canonical correlation analysis Discriminant analysis Clustering
2013/6/14
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...
Convex Tensor Decomposition via Structured Schatten Norm Regularization
Convex Tensor Decomposition Structured Schatten Norm Regularization
2013/4/28
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...
$l_{2,p}$ Matrix Norm and Its Application in Feature Selection
$l_{2,p}$ Matrix Norm Its Application Feature Selection
2013/5/2
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 $l_{2,1}$ ...
Max-stable processes and the functional D-norm revisited
Max-stable process D-norm functional max-domain of attraction copula process generalized Pareto process δ-neighborhood of generalized Pareto process t-test for max-stable and for generalized Pareto process
2013/5/2
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...
Matrix completion via max-norm constrained optimization
Compressed sensing low-rank matrix matrix completion max-norm con-strained minimization optimal rate of convergence sparsity
2013/4/28
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...
Learning with the Weighted Trace-norm under Arbitrary Sampling Distributions
Learning Weighted Trace-norm Arbitrary Sampling Distributions
2011/7/7
We provide rigorous guarantees on learning with the weighted trace-norm under arbitrary sampling distributions.
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。
Operator norm convergence of spectral clustering on level sets
Spectral clustering graph unsupervised classification levelsets connected components
2010/3/10
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...
Sup-norm convergence of the empirical process indexed by functions and applications
Sup-norm convergence the empirical process functions and applications
2009/9/23
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
the density of the norm stable random vectors Hilbert spaces
2009/9/23
A roumula for the density of the norm of stable random vectors in Hilbert spaces。
On density of a stable uniformly convex norm。
SHARP NORM INEQUALITIES FOR STOCHASTIC INTEGRALS IN WHICH THE INTEGRATOR IS A NONNEGATIVE SUPERMARTINGALE
Stochastic integral martingale norm inequality differential subordination
2009/9/18
The paper is devoted to sharp inequalities between moments
of nonnegative supermartingales and their strong subordinates. Analogous
estimates hold true for stochastic integrals with respect to a non...
L1-Norm of Infinitely Divisible Random Vectors and Certain Stochastic Integrals
Infinitely divisible random variables stochastic integrals
2009/5/4
Equivalent upper and lower bounds for the L1 norm of Hilbert space valued infinitely divisible random variables are obtained and used to find bounds for different types of stochastic integrals.