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

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

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 …

We consider the recovery of a (real-or complex-valued) signal from magnitude-only
measurements, known as phase retrieval. We formulate phase retrieval as a convex …

This book presents a unified theory of random matrices for applications in machine learning,
offering a large-dimensional data vision that exploits concentration and universality …

Phase retrieval, ie the problem of recovering a function from the squared magnitude of its
Fourier transform, arises in many applications, such as X-ray crystallography, diffraction …

We consider the problem of signal estimation in generalized linear models defined via
rotationally invariant design matrices. Since these matrices can have an arbitrary spectral …

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising
in high-dimensional inference tasks. Here one produces an estimator of an unknown …

In phase retrieval we want to recover an unknown signal $\boldsymbol x\in\mathbb C^ d $
from $ n $ quadratic measurements of the form $ y_i=|⟨\boldsymbol a_i,\boldsymbol x⟩|^ 2+ …