arXiv research

Rank-one measurements limit feasible sets for low-rank PSD matrices.

We develop an efficient alternating framework for learning a generalized version of Factorization Machine (gFM) on steaming data with provable guarantees. When the instances are sampled from $d$ dimensional random Gaussian vectors and the target second order coefficient matrix in gFM is of rank $k$, our algorithm conve…

We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We propose a hypothesis test on the presence of the signal by utilizing the linear spectral statistics of the data matrix. The test is data-driven and does no…

Estimates rank-one spikes from heavy-tailed noise using self-avoiding walks.

Improved stability for matrix recovery from rank-one measurements.

Gradient descent solves rank-one matrix estimation problem with detailed time evolution analysis.

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

Study shows how fast a specific matrix completion method works.

This paper sets fundamental limits for rank-one matrix estimation with varying noise levels.

Algorithm recovers factors of rank-1 matrices from noisy measurements.

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

Develops Hilbert geometries and characterizes their isometries.

Study quantifies performance gap between tensor and matrix-based approaches in nested matrix-tensor model.

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…

Novel algorithm for Markov decision processes using rank-one approximation.

New algorithms improve rank one signal estimation from noisy data.

Convex optimization method recovers low-rank matrices from rank-one projections efficiently.

We consider worker skill estimation for the single-coin Dawid-Skene crowdsourcing model. In practice, skill-estimation is challenging because worker assignments are sparse and irregular due to the arbitrary and uncontrolled availability of workers. We formulate skill estimation as a rank-one correlation-matrix completi…

New method unifies and formalizes data partitioning using a single vector.

Estimates the probability of a random symmetric tensor being close to rank-one.

Given a family of Dirac operators with vanishing spectral flow we construct a thin-invariant rank-one field theory in the sense of Turner and Willerton arXiv:math.AT/0201116. Our construction of the field theory generalizes the one of the index gerbe by Lott, arXiv:math.DG/0106177, and it also complements the relation …

Unrolled networks learn optimal Bayesian inference for unknown priors.

Researchers describe the metric structure of compact ECS manifolds.

Study on signal-plus-noise decomposition in nonlinear spiked random matrices.

We study an extreme scenario in multi-label learning where each training instance is endowed with a single one-bit label out of multiple labels. We formulate this problem as a non-trivial special case of one-bit rank-one matrix sensing and develop an efficient non-convex algorithm based on alternating power iteration. …

Paper proposes a tensor model for clustering noisy multi-view data.

Study on tensor signal estimation from incomplete data.

AMP method reconstructs rank-one matrices from noisy data efficiently.

New methods estimate covariance for matrix data without assuming fixed size or specific distributions.

Paper shows no spurious local minima in a specific matrix factorization problem.

New method solves matrix completion problems to certifiable optimality.

This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.

Study linear perturbations of Spin(7) metrics, finding only rank one nilpotent matrices.

Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is…

Study on rank-one ECS manifolds, focusing on dilational type.

New algorithms detect and estimate rank-one signals with prior directional information.

Unified approach for robust low rank matrix estimation with adversaries.

Weight normalization speeds up matrix sensing problems.

We propose a geometric assumption on nonnegative data matrices such that under this assumption, we are able to provide upper bounds (both deterministic and probabilistic) on the relative error of nonnegative matrix factorization (NMF). The algorithm we propose first uses the geometric assumption to obtain an exact clus…

In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this factorization one can derive notion of tensor rank, referred to as the tensor tubal…

This work presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations. GROUSE requires only basic linear algebraic manipulations at each iteration, and each subspace update can be performed in linear time in the dimension of…

In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time. This premise has recently guided the research to the innovative and meaningful …

New method proves asymptotic normality for matrix sensing problems.

SON-NMF estimates nonnegative rank on-the-fly for NMF.

New method tackles over-parameterized matrix sensing with FGD, improving statistical and computational complexity.

This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix $\Ab$ an…

In this paper, we study the adversarial robustness of subspace learning problems. Different from the assumptions made in existing work on robust subspace learning where data samples are contaminated by gross sparse outliers or small dense noises, we consider a more powerful adversary who can first observe the data matr…

We formulate and solve a tensor model using a latent-variable approach.