Low-rank matrices play a fundamental role in modeling and computational methods for
signal processing and machine learning. In many applications where low-rank matrices …

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 …

Training neural networks is a challenging non-convex optimization problem, and
backpropagation or gradient descent can get stuck in spurious local optima. We propose a …

Understanding how a fictional relationship between two characters changes over time (eg,
from best friends to sworn enemies) is a key challenge in digital humanities scholarship. We …

This book revolves around the question of designing a matrix D∈ Rm× n called dictionary,
such that to obtain good sparse representations y≈ Dx for a class of signals y∈ Rm given …

We study robust distributed learning that involves minimizing a non-convex loss function
with saddle points. We consider the Byzantine setting where some worker machines have …

In recent years, sparse signal modeling, especially using the synthesis model has been
popular. Sparse coding in the synthesis model is however, NP-hard. Recently, interest has …

We survey optimization problems that involve the cardinality of variable vectors in
constraints or the objective function. We provide a unified viewpoint on the general problem …

This paper considers the fundamental problem of learning a complete (orthogonal)
dictionary from samples of sparsely generated signals. Most existing methods solve the …

We study robust PCA for the fully observed setting, which is about separating a low rank
matrix L and a sparse matrix S from their sum D= L+ S. In this paper, a new algorithm …