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 …

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 …

We consider the fundamental problem in non-convex optimization of efficiently reaching a
stationary point. In contrast to the convex case, in the long history of this basic problem, the …

A first line of attack in exploratory data analysis is\emph {data visualization}, ie, generating a
2-dimensional representation of data that makes\emph {clusters} of similar points visually …

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 give algorithms with provable guarantees that learn a class of deep nets in the
generative model view popularized by Hinton and others. Our generative model is an n …

Vast amount of data generated from networks of sensors, wearables, and the Internet of
Things (IoT) devices underscores the need for advanced modeling techniques that leverage …

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 …