High dimensional statistical problems arise from diverse fields of scientific research and
technological development. Variable selection plays a pivotal role in contemporary statistical …

This article reviews the literature on sparse high-dimensional models and discusses some
applications in economics and finance. Recent developments in theory, methods, and …

Best subset selection via a modern optimization lens Page 1 The Annals of Statistics 2016, Vol.
44, No. 2, 813–852 DOI: 10.1214/15-AOS1388 © Institute of Mathematical Statistics, 2016 …

Despite the wide adoption of spike-and-slab methodology for Bayesian variable selection,
its potential for penalized likelihood estimation has largely been overlooked. In this article …

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

We study minimization of the difference of \ell_1 and \ell_2 norms as a nonconvex and
Lipschitz continuous metric for solving constrained and unconstrained compressed sensing …

We consider the problem of clustering observations using a potentially large set of features.
One might expect that the true underlying clusters present in the data differ only with respect …

Determining how to select the tuning parameter appropriately is essential in penalized
likelihood methods for high dimensional data analysis. We examine this problem in the …

Penalized likelihood methods are fundamental to ultrahigh dimensional variable selection.
How high dimensionality such methods can handle remains largely unknown. In this paper …

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 …