Related papers: Tensor Robust Principal Component Analysis: Better…

In this paper, we explore the theoretical properties of subspace recovery using Winsorized Principal Component Analysis (WPCA), utilizing a common data transformation technique that caps extreme values to mitigate the impact of outliers.…

Matrix learning is at the core of many machine learning problems. A number of real-world applications such as collaborative filtering and text mining can be formulated as a low-rank matrix completion problem, which recovers incomplete…

We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…

We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…

For the problem of reconstructing a low-rank matrix from a few linear measurements, two classes of algorithms have been widely studied in the literature: convex approaches based on nuclear norm minimization, and non-convex approaches that…

We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value…

The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…

We consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process A. We propose a variational formulation…

We consider the problem of recovering elements of a low-dimensional model from under-determined linear measurements. To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constraint. Given a model,…

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…

Modern empirical analysis often relies on high-dimensional panel datasets with non-negligible cross-sectional and time-series correlations. Factor models are natural for capturing such dependencies. A tensor factor model describes the…

Low-rank matrix recovery problems involving high-dimensional and heterogeneous data appear in applications throughout statistics and machine learning. The contribution of this paper is to establish the fundamental limits of recovery for a…

Low-rank matrix recovery can be solved to statistical optimality by convex matrix optimization under the classical assumption of restricted isometry property (RIP). However, for large problems, the convex formulation is commonly replaced by…

This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at $p$ locations and $n$ time points with the possibility that $p>n$. While principal component analysis…

To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the…

This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the…

In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…

In this paper we propose a novel optimization framework to systematically solve robust PCA problem with rigorous theoretical guarantee, based on which we investigate very computationally economic updating algorithms.

Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework…