The growing energy and performance costs of deep learning have driven the community to
reduce the size of neural networks by selectively pruning components. Similarly to their …

We show that gradient descent on full-width linear convolutional networks of depth $ L $
converges to a linear predictor related to the $\ell_ {2/L} $ bridge penalty in the frequency …

This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

We present an accelerated gradient method for nonconvex optimization problems with
Lipschitz continuous first and second derivatives. In a time O(ϵ^-7/4\log(1/ϵ)), the method …

Time series data occurs widely, and outlier detection is a fundamental problem in data
mining, which has numerous applications. Existing autoencoder-based approaches deliver …

In the past decade, sparse and low-rank recovery has drawn much attention in many areas
such as signal/image processing, statistics, bioinformatics, and machine learning. To …

In this paper, we first study \ell_q minimization and its associated iterative reweighted
algorithm for recovering sparse vectors. Unlike most existing work, we focus on …

We consider a class of smoothing methods for minimization problems where the feasible set
is convex but the objective function is not convex, not differentiable and perhaps not even …

Mathematical programming problems with semi-continuous variables and cardinality
constraint have many applications, including production planning, portfolio selection …

We consider linear, high-dimensional sparse (HDS) regression models in econometrics. The
HDS regression model allows for a large number of regressors, p, which is possibly much …