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 …

Noisy matrix completion aims at estimating a low-rank matrix given only partial and
corrupted entries. Despite remarkable progress in designing efficient estimation algorithms …

We study a completion problem of broad practical interest: the reconstruction of a low-rank
symmetric tensor from highly incomplete and randomly corrupted observations of its entries …

This paper studies noisy low-rank matrix completion: given partial and noisy entries of a
large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently …

This paper is concerned with the problem of top-K ranking from pairwise comparisons. Given
a collection of n items and a few pairwise comparisons across them, one wishes to identify …

This paper is concerned with the problem of reconstructing an unknown rank-one matrix with
prior structural information from noisy observations. While computing the Bayes optimal …

The problem of estimating the phases (angles) of a complex unit-modulus vector z from their
noisy pairwise relative measurements C=zz^*+σW, where W is a complex-valued Gaussian …