Related papers: Reduced-Rank Matrix Autoregressive Models: A Mediu…
The problem of time series approximation by series of finite rank is considered from the viewpoint of signal extraction. For signal estimation, a weighted least-squares method is applied to the trajectory matrix of the considered time…
We introduce an adaptive structured low rank algorithm to recover MR images from their undersampled Fourier coefficients. The image is modeled as a combination of a piecewise constant component and a piecewise linear component. The Fourier…
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…
In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…
Matrix-valued time series are ubiquitous in modern economics and finance, yet modeling them requires navigating a trade-off between flexibility and parsimony. We propose the Matrix Autoregressive model with Common Factors (MARCF), a unified…
Nonconvex methods have emerged as a dominant approach for low-rank matrix estimation, a problem that arises widely in machine learning and AI for learning and representing high-dimensional data. Existing analyses for these methods often…
Linear regression is effective at identifying interpretable trends in a data set, but averages out potentially different effects on subgroups within data. We propose an iterative algorithm based on the randomized Kaczmarz (RK) method to…
This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…
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…
Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong…
In this paper, we consider multivariate response regression models with high dimensional predictor variables. One way to model the correlation among the response variables is through the low rank decomposition of the coefficient matrix,…
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…
New types of high-resolution animal movement data allow for increasingly comprehensive biological inference, but method development to meet the statistical challenges associated with such data is lagging behind. In this contribution, we…
Many applications of machine learning involve the analysis of large data frames-matrices collecting heterogeneous measurements (binary, numerical, counts, etc.) across samples-with missing values. Low-rank models, as studied by Udell et al.…
Interval-valued data receives much attention due to its wide applications in the fields of finance, econometrics, meteorology and medicine. However, most regression models developed for interval-valued data assume observations are mutually…
In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…
In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed ``sparse'' noise. In theory, we bound the tracking error. In…
Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…
In this paper, we present a compressed data structure for moving object trajectories in a road network, which are represented as sequences of road edges. Unlike existing compression methods for trajectories in a network, our method supports…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…