The estimation of large covariance and precision matrices is fundamental in modern
multivariate analysis. However, problems arise from the statistical analysis of large panel …

Regularization is a widely used technique throughout statistics, machine learning, and
applied mathematics. Modern applications in science and engineering lead to massive and …

Statistical Foundations of Data Science gives a thorough introduction to commonly used
statistical models, contemporary statistical machine learning techniques and algorithms …

This article proposes a constrained ℓ 1 minimization method for estimating a sparse inverse
covariance matrix based on a sample of n iid p-variate random variables. The resulting …

Although the standard formulations of prediction problems involve fully-observed and
noiseless data drawn in an iid manner, many applications involve noisy and/or missing data …

We propose a semiparametric approach called the nonparanormal SKEPTIC for efficiently
and robustly estimating high-dimensional undirected graphical models. To achieve …

We study a decomposition-based scalable approach to kernel ridge regression, and show
that it achieves minimax optimal convergence rates under relatively mild conditions. The …

Sparse estimation methods are aimed at using or obtaining parsimonious representations of
data or models. While naturally cast as a combinatorial optimization problem, variable or …

The paper considers in the high dimensional setting a canonical testing problem in
multivariate analysis, namely testing the equality of two mean vectors. We introduce a new …

This is an expository paper that reviews recent developments on optimal estimation of
structured high-dimensional covariance and precision matrices. Minimax rates of …