We consider the problem of recovering a complete (ie, square and invertible) matrix A 0,
from Y∈ R n× p with Y= A 0 X 0, provided X 0 is sufficiently sparse. This recovery problem is …

Signal processing, communications, and control have traditionally relied on classical
statistical modeling techniques. Such model-based methods utilize mathematical …

A vast majority of machine learning algorithms train their models and perform inference by
solving optimization problems. In order to capture the learning and prediction problems …

Can we recover a complex signal from its Fourier magnitudes? More generally, given a set
of m measurements, y_k=\left| a _k^* x\right| yk= ak∗ x for k= 1, ..., mk= 1,…, m, is it possible …

Despite the empirical success of using adversarial training to defend deep learning models
against adversarial perturbations, so far, it still remains rather unclear what the principles are …

Phase retrieval problems involve solving linear equations, but with missing sign (or phase,
for complex numbers) information. Over the last two decades, a popular generic empirical …

Principal components analysis (PCA) is a well-known technique for approximating a tabular
data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets …

One popular method for dealing with large-scale data sets is sampling. Using the empirical
statistical leverage scores as an importance sampling distribution, the method of algorithmic …

We propose a new provable method for robust PCA, where the task is to recover a low-rank
matrix, which is corrupted with sparse perturbations. Our method consists of simple …

In recent years, a large amount of multi-disciplinary research has been conducted on sparse
models and their applications. In statistics and machine learning, the sparsity principle is …