arXiv research

New method improves robust low-rank matrix completion for computer vision.

Riemannian gradient descent escapes some spurious critical points on low-rank matrix manifold.

New method reduces computational cost for nonnegative low rank matrix approximation.

Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank matrices, and proposes two algorithms (for two versions of retractions) based on ma…

Solves weakly supervised regression using low-rank approximations and manifold regularization.

Equivalent formulations for low-rank matrix optimization are proven.

New method finds efficient low-rank neural networks during training.

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over the Riemannian manifold of fixed-rank matrices. The algorithm is an adaptation of…

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the low-rank and the structural constraints onto separate factors. We formulate the optim…

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

New method proves asymptotic normality for matrix sensing problems.

Matrix completion works well for smooth non-linear structures, even without low-rank assumptions.

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model w…

New spectral methods improve matrix estimation in RL with low-rank structure.

New Bayesian matrix completion method using Stiefel manifolds.

Novel method for efficient low-rank matrix estimation and bandit algorithms.

New method for online low-rank matrix completion with improved regret.

New approach to convex hulls for low-rank problems.

New nonconvex regularizer speeds up low-rank matrix completion.

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a W…

SGD with mini-batches can solve convex low-rank matrix problems efficiently.

Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume that the input partially-observed matrix is low rank. The success of these methods…

Paper develops a new weighted low-rank matrix approximation technique.

This paper studies clustering for possibly high dimensional data (e.g. images, time series, gene expression data, and many other settings), and rephrase it as low rank matrix estimation in the PAC-Bayesian framework. Our approach leverages the well known Burer-Monteiro factorisation strategy from large scale optimisati…

ScaledGD improves gradient descent for ill-conditioned low-rank matrix estimation.

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

The paper examines how gradient descent stabilizes low-rank matrix factorization in noisy conditions.

Unified approach for robust low rank matrix estimation with adversaries.

Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict inductively on new users/movies. In this paper, we study the problem of inductive matr…

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general case with noisy observations, we show that our algorithm is guaranteed to linearl…

In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the underlying low-rank matrix to …

New framework explains why nonconvex methods work well in low-rank matrix estimation.

We present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty. Moreover, we rigorously show that under a certain condition on the magnitude of t…

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is distorted by a (typically unknown) nonlinear transformation. This paper addresses the…

Proposes a new model for image restoration combining deep learning and total variation.

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

New method solves nonsmooth low-rank matrix optimization problems efficiently.

Matrices of (approximate) low rank are pervasive in data science, appearing in recommender systems, movie preferences, topic models, medical records, and genomics. While there is a vast literature on how to exploit low rank structure in these datasets, there is less attention on explaining why the low rank structure ap…

Gradient descent solves asymmetric low-rank matrix sensing without balancing.

CoreFlow models matrix-valued distributions efficiently, preserving shared low-rank structure.

New algorithm improves deep learning models' robustness without sacrificing accuracy.

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern high-dimensional data and interactions thereof can be modeled as lying approximat…

This paper considers the problem of estimating a low-rank matrix from the observation of all or a subset of its entries in the presence of Poisson noise. When we observe all entries, this is a problem of matrix denoising; when we observe only a subset of the entries, this is a problem of matrix completion. In both case…

New algorithm for weighted low rank approximation with provable guarantees.

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

Paper finds a lower bound for estimating low-rank matrices in logistic regression.

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…

New method for robust matrix completion with mixed data types.