1,635 research outputs found
The Masked Sample Covariance Estimator: An Analysis via Matrix Concentration Inequalities
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 this problem is to assume that the covariance
matrix is nearly sparse and to focus on estimating only the significant
entries. To analyze this approach, Levina and Vershynin (2011) introduce a
formalism called masked covariance estimation, where each entry of the sample
covariance estimator is reweighted to reflect an a priori assessment of its
importance. This paper provides a short analysis of the masked sample
covariance estimator by means of a matrix concentration inequality. The main
result applies to general distributions with at least four moments. Specialized
to the case of a Gaussian distribution, the theory offers qualitative
improvements over earlier work. For example, the new results show that n = O(B
log^2 p) samples suffice to estimate a banded covariance matrix with bandwidth
B up to a relative spectral-norm error, in contrast to the sample complexity n
= O(B log^5 p) obtained by Levina and Vershynin
High-dimensional semi-supervised learning: in search for optimal inference of the mean
We provide a high-dimensional semi-supervised inference framework focused on
the mean and variance of the response. Our data are comprised of an extensive
set of observations regarding the covariate vectors and a much smaller set of
labeled observations where we observe both the response as well as the
covariates. We allow the size of the covariates to be much larger than the
sample size and impose weak conditions on a statistical form of the data. We
provide new estimators of the mean and variance of the response that extend
some of the recent results presented in low-dimensional models. In particular,
at times we will not necessitate consistent estimation of the functional form
of the data. Together with estimation of the population mean and variance, we
provide their asymptotic distribution and confidence intervals where we
showcase gains in efficiency compared to the sample mean and variance. Our
procedure, with minor modifications, is then presented to make important
contributions regarding inference about average treatment effects. We also
investigate the robustness of estimation and coverage and showcase widespread
applicability and generality of the proposed method
Strong Coupling Lattice Schwinger Model on Large Spherelike Lattices
The lattice regularized Schwinger model for one fermion flavor and in the
strong coupling limit is studied through its equivalent representation as a
restricted 8-vertex model. The Monte Carlo simulation on lattices with
torus-topology is handicapped by a severe non-ergodicity of the updating
algorithm; introducing lattices with spherelike topology avoids this problem.
We present a large scale study leading to the identification of a critical
point with critical exponent , in the universality class of the Ising
model or, equivalently, the lattice model of free fermions.Comment: 16 pages + 7 figures, gzipped POSTSCRIPT fil
- …