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 …

In this paper, we study the problem of recovering a low-rank matrix from a number of random
linear measurements that are corrupted by outliers taking arbitrary values. We consider a …

Many problems in data science can be treated as estimating a low-rank matrix from highly
incomplete, sometimes even corrupted, observations. One popular approach is to resort to …

Tensors, which provide a powerful and flexible model for representing multi-attribute data
and multi-way interactions, play an indispensable role in modern data science across …

Many contemporary applications in signal processing and machine learning give rise to
structured nonconvex nonsmooth optimization problems that can often be tackled by simple …

Often in applications ranging from medical imaging and sensor networks to error correction
and data science (and beyond), one needs to solve large-scale linear systems in which a …

Low-rank matrix estimation plays a central role in various applications across science and
engineering. Recently, nonconvex formulations based on matrix factorization are provably …

We consider linear systems where consists of normalized rows,, and where up to entries of
have been corrupted (possibly by arbitrarily large numbers). Haddock, Needell, Rebrova & …

Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the
problem of learning an unknown filter by observing its circulant convolutions with multiple …