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 …

Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

We show that the gradient descent algorithm provides an implicit regularization effect in the
learning of over-parameterized matrix factorization models and one-hidden-layer neural …

We consider a family of algorithms that successively sample and minimize simple stochastic
models of the objective function. We show that under reasonable conditions on …

Recent years have seen a flurry of activities in designing provably efficient nonconvex
optimization procedures for solving statistical estimation problems. For various problems like …

This paper considers the problem of solving systems of quadratic equations, namely,
recovering an object of interest x^ ♮ ∈ R^ nx♮∈ R n from m quadratic equations/samples …

This paper is concerned with finding a solution x to a quadratic system of equations yi=|< ai,
x>|^ 2, i= 1, 2,..., m. We prove that it is possible to solve unstructured quadratic systems in n …

We consider the fundamental problem of solving quadratic systems of equations in, and is
unknown. We propose a novel method, which starts with an initial guess computed by …

This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal
x∈R^p from noisy quadratic measurements y_j=(a_j'x)^2+j, j=1,...,m, with independent sub …