Substantial progress has been made recently on developing provably accurate and efficient
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …

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 …

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 …

The objective in extreme multi-label learning is to train a classifier that can automatically tag
a novel data point with the most relevant subset of labels from an extremely large label set …

We show that there are no spurious local minima in the non-convex factorized
parametrization of low-rank matrix recovery from incoherent linear measurements. With …

As a paradigm to recover unknown entries of a matrix from partial observations, low-rank
matrix completion (LRMC) has generated a great deal of interest. Over the years, there have …

Alternating minimization represents a widely applicable and empirically successful
approach for finding low-rank matrices that best fit the given data. For example, for the …

Recovering a large matrix from a small subset of its entries is a challenging problem arising
in many real applications, such as image inpainting and recommender systems. Many …

Optimization problems with rank constraints arise in many applications, including matrix
regression, structured PCA, matrix completion and matrix decomposition problems. An …

Let M be an n¿× n matrix of rank r, and assume that a uniformly random subset E of its
entries is observed. We describe an efficient algorithm, which we call OptSpace, that …