This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …

In this monograph, we have attempted to summarize the actively develo** field of
statistical learning with sparsity. A sparse statistical model is one having only a small …

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 …

Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in
electrical engineering, applied mathematics, statistics and computer science. This book …

This article presents novel results concerning the recovery of signals from undersampled
data in the common situation where such signals are not sparse in an orthonormal basis or …

An oblivious subspace embedding (OSE) given some parameters ε, d is a distribution D over
matrices Π∈ R m× n such that for any linear subspace W⊆ R n with dim (W)= d, P Π~ D (∀ …

We give two different and simple constructions for dimensionality reduction in ℓ 2 via linear
map**s that are sparse: only an O (ε)-fraction of entries in each column of our embedding …

This paper presents an improved analysis of a structured dimension-reduction map called
the subsampled randomized Hadamard transform. This argument demonstrates that the …

Consider an instance of Euclidean k-means or k-medians clustering. We show that the cost
of the optimal solution is preserved up to a factor of (1+ ε) under a projection onto a random …

The nearest neighbor problem is defined as follows: Given a set P of n points in some metric
space (X, D), build a data structure that, given any point q, returns a point in P that is closest …