Related papers: Sketching low-rank matrices with a shared column s…

We introduce a flexible framework for high-dimensional matrix estimation to incorporate side information for both rows and columns. Existing approaches, such as inductive matrix completion, often impose restrictive structure-for example, an…

Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…

The energy cost of a sensor network is dominated by the data acquisition and communication cost of individual sensors. At each sampling instant it is unnecessary to sample and communicate the data at all sensors since the data is highly…

A few matrix-vector multiplications with random vectors are often sufficient to obtain reasonably good estimates for the norm of a general matrix or the trace of a symmetric positive semi-definite matrix. Several such probabilistic…

Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have…

In this paper, we employ fixed point theory and semidefinite programming to compute the performance bounds on convex block-sparsity recovery algorithms. As a prerequisite for optimal sensing matrix design, a computable performance bound…

The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…

Nonconvex regularization has been popularly used in low-rank matrix learning. However, extending it for low-rank tensor learning is still computationally expensive. To address this problem, we develop an efficient solver for use with a…

This paper introduces a general multi-class approach to weakly supervised classification. Inferring the labels and learning the parameters of the model is usually done jointly through a block-coordinate descent algorithm such as…

Networked sensing, where the goal is to perform complex inference using a large number of inexpensive and decentralized sensors, has become an increasingly attractive research topic due to its applications in wireless sensor networks and…

In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and…

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…

This paper investigates recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples within the framework of spectral compressed sensing and super-resolution. We show that the existing…

Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the…

We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…

Matrix sensing is the problem of reconstructing a low-rank matrix from a few linear measurements. In many applications such as collaborative filtering, the famous Netflix prize problem, and seismic data interpolation, there exists some…

Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…

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.…

Low-rank matrix approximation (LRMA) has been arisen in many applications, such as dynamic MRI, recommendation system and so on. The alternating direction method of multipliers (ADMM) has been designed for the nuclear norm regularized least…

We consider the problem of multi-task learning in the high dimensional setting. In particular, we introduce an estimator and investigate its statistical and computational properties for the problem of multiple connected linear regressions…