Hashing embeddings of optimal dimension, with applications to linear least squares

The aim of this paper is two-fold: firstly, to present subspace embedding properties for s-hashing sketching matrices, with $s\geq 1$, that are optimal in the projection dimension $m$ of the sketch, namely, $m=O(d)$, where $d$ is the dimension of the subspace. A diverse set of results are presented that address the case when the input … Read more

A Coordinate Gradient Descent Method for L_1-regularized Convex Minimization

In applications such as signal processing and statistics, many problems involve finding sparse solutions to under-determined linear systems of equations. These problems can be formulated as a structured nonsmooth optimization problems, i.e., the problem of minimizing L_1-regularized linear least squares problems. In this paper, we propose a block coordinate gradient descent method (abbreviated as CGD) … Read more