Low-rank matrix approximations, such as the truncated singular value decomposition and
the rank-revealing QR decomposition, play a central role in data analysis and scientific …

On the heels of compressed sensing, a new field has very recently emerged. This field
addresses a broad range of problems of significant practical interest, namely, the recovery of …

High-dimensional probability offers insight into the behavior of random vectors, random
matrices, random subspaces, and objects used to quantify uncertainty in high dimensions …

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 …

This article is about a curious phenomenon. Suppose we have a data matrix, which is the
superposition of a low-rank component and a sparse component. Can we recover each …

We propose a new method for estimation in linear models. The 'lasso'minimizes the residual
sum of squares subject to the sum of the absolute value of the coefficients being less than a …

Suppose that one observes an incomplete subset of entries selected from a low-rank matrix.
When is it possible to complete the matrix and recover the entries that have not been seen …

A key challenge in analyzing single cell RNA-sequencing data is the large number of false
zeros, where genes actually expressed in a given cell are incorrectly measured as …

In this article, we study methods for estimating causal effects in settings with panel data,
where some units are exposed to a treatment during some periods and the goal is …

In this paper, we propose an algorithm to estimate missing values in tensors of visual data.
The values can be missing due to problems in the acquisition process or because the user …