arXiv research

Flat minima lead to better generalization in low-rank matrix recovery models.

This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are arbitrarily corrupted. We provide a new unified performance guarantee on when the natura…

Sign-RIP improves robust low-rank matrix recovery by preserving norms even with corrupted measurements.

Study reveals efficient recovery of multi-modal signals via Bayesian methods and sequential learning.

HSNLD solves robust Hankel recovery efficiently and robustly.

Develops PRPCA for smooth image recovery combining low-rank and smoothness.

Improved stability for matrix recovery from rank-one measurements.

Low-rank matrix recovery has found many applications in science and engineering such as machine learning, signal processing, collaborative filtering, system identification, and Euclidean embedding. But the low-rank matrix recovery problem is an NP hard problem and thus challenging. A commonly used heuristic approach is…

Study robust recovery of low-rank matrices from corrupted measurements without rank prior.

New method recovers matrix column space with active sampling for better results.

Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.

Paper recovers multi-subspace matrices from permuted data.

New algorithm recovers matrices with unknown correspondences.

We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common measurements of the columns. In the second step, the subspace aware recovery of …

Study generalizes matrix completion with side info in low noise settings.

Gradient descent recovers low-rank matrices from corrupted measurements with double over-parameterization.

Simplifies solving noisy SDPs for low rank matrix recovery problems.

Improves sparse recovery with non-linear Fourier features.

New method recovers matrices with nonlinear structures using optimization on Grassmann manifold.

Paper tackles low-rank matrix recovery with column $\ell_{2,0}$-norm regularization.

We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix $X$. This setting arises naturally in applications from different domains. However, current algorithms developed for standard matrix rec…

Paper develops methods for non-quadratic loss low-rank matrix recovery.

We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We consider the usual matrix recovery formulation through maximum likelihood with pro…

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous theoretical analysis. We show that the proposed algorithms enjoy linear convergence a…

Nonnegative low-rank matrix recovery can have spurious local minima.

SDP approach recovers communities in multilayer hypergraphs from aggregated similarity matrices.

When the linear measurements of an instance of low-rank matrix recovery satisfy a restricted isometry property (RIP)---i.e. they are approximately norm-preserving---the problem is known to contain no spurious local minima, so exact recovery is guaranteed. In this paper, we show that moderate RIP is not enough to elimin…

Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by incorporating temporal information and allowing for the possibility of time-varying …

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of methods have been developed for this recovery problem. However, a principled meth…

Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with tra…

We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs projected gradient descent based on a novel semi-stochastic gradient specifically desi…

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery using a random subset of entries observed with additive noise under general non-unif…

Scaled gradient descent improves matrix recovery for ill-conditioned matrices with optimal sampling complexity.

For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation matrix completion in various fields such as the financial market and the low-ra…

New method avoids spurious critical points for low-rank matrix recovery.

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 noisy measurements we show all local minima are very close to a global optimum. Together with a curvature bound at saddle points, this yields a polynomial ti…

Active seriation recovers item order from noisy pairwise similarity measurements.

Nonconvex matrix recovery is known to contain no spurious local minima under a restricted isometry property (RIP) with a sufficiently small RIP constant $δ$. If $δ$ is too large, however, then counterexamples containing spurious local minima are known to exist. In this paper, we introduce a proof technique that is capa…

This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the dictionary being used, a diagonal weighted matrix is obtained and then the sensing ma…

Magnetic particle imaging (MPI) data is commonly reconstructed using a system matrix acquired in a time-consuming calibration measurement. The calibration approach has the important advantage over model-based reconstruction that it takes the complex particle physics as well as system imperfections into account. This be…

New nonconvex regularizer speeds up low-rank matrix completion.

In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we derive a relative upper bound for recovering the best low-rank approximation of t…

New method recovers signals from compressed measurements using generative networks with contractive layers.

The paper validates a method for recovering over-parameterized matrices and images from noisy measurements.

Study on signal recovery from low-rank matrix with sparse noise.

Paper tackles sparse recovery with shuffled labels, establishing statistical and computational limits.

Paper proposes fast, robust methods for low-rank matrix recovery.

The paper improves support recovery in high-dimensional precision matrix estimation using meta learning.