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We consider reduced-rank modeling of the white noise covariance matrix in a large dimensional vector autoregressive (VAR) model. We first propose the reduced-rank covariance estimator under the setting where independent observations are…

Applications · Statistics 2014-12-09 Richard A. Davis , Pengfei Zang , Tian Zheng

This paper considers joint learning of multiple sparse Granger graphical models to discover underlying common and differential Granger causality (GC) structures across multiple time series. This can be applied to drawing group-level brain…

Machine Learning · Computer Science 2021-05-25 Parinthorn Manomaisaowapak , Jitkomut Songsiri

Vector autoregression (VAR) models are widely used to analyze the interrelationship between multiple variables over time. Estimation and inference for the transition matrices of VAR models are crucial for practitioners to make decisions in…

Methodology · Statistics 2020-09-22 Ke Zhu , Hanzhong Liu

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…

Machine Learning · Statistics 2017-03-01 Pan Xu , Jian Ma , Quanquan Gu

We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…

Machine Learning · Computer Science 2023-11-14 Dimitris Bertsimas , Vassilis Digalakis , Michael Linghzi Li , Omar Skali Lami

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…

Methodology · Statistics 2016-03-18 Zhuang Ma , Zongming Ma , Tingni Sun

Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply…

Machine Learning · Computer Science 2019-12-04 Zhao Kang , Xiao Lu , Yiwei Lu , Chong Peng , Zenglin Xu

Recent technological advancements have led to the rapid generation of high-throughput biological data, which can be used to address novel scientific questions in broad areas of research. These data can be thought of as a large matrix with…

Computation · Statistics 2021-03-01 Jane W. Liang , Saunak Sen

This paper studies inference in linear models with a high-dimensional parameter matrix that can be well-approximated by a ``spiked low-rank matrix.'' A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero…

Statistics Theory · Mathematics 2023-01-04 Victor Chernozhukov , Christian Hansen , Yuan Liao , Yinchu Zhu

Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…

Machine Learning · Computer Science 2019-07-09 Frank Nussbaum , Joachim Giesen

For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained…

Numerical Analysis · Computer Science 2016-06-29 Yuji Nakatsukasa , Tasuku Soma , André Uschmajew

In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…

Machine Learning · Computer Science 2016-11-18 Ashkan Esmaeili , Arash Amini , Farokh Marvasti

Learning the latent network structure from large scale multivariate point process data is an important task in a wide range of scientific and business applications. For instance, we might wish to estimate the neuronal functional…

Methodology · Statistics 2021-01-21 Biao Cai , Jingfei Zhang , Yongtao Guan

We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…

Computer Vision and Pattern Recognition · Computer Science 2013-08-02 Qiang Qiu , Guillermo Sapiro

In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate…

Machine Learning · Statistics 2016-03-28 Yi Zhao , Xi Luo

Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming…

Multiagent Systems · Computer Science 2013-10-01 Morteza Mardani , Gonzalo Mateos , Georgios B. Giannakis

This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With…

Systems and Control · Computer Science 2016-10-03 J. Jin , Y. Yuan , W. Pan , D. L. T. Pham , C. J. Tomlin , A. Webb , J. Goncalves

Low-rank tensors are an established framework for high-dimensional least-squares problems. We propose to extend this framework by including the concept of block-sparsity. In the context of polynomial regression each sparsity pattern…

Numerical Analysis · Mathematics 2021-04-30 Michael Götte , Reinhold Schneider , Philipp Trunschke

We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…

Machine Learning · Statistics 2026-04-15 Angelo Giorgio Cavaliere , Riki Nagasawa , Shuta Yokoi , Tomoyuki Obuchi , Hajime Yoshino

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…

Optimization and Control · Mathematics 2011-08-09 Venkat Chandrasekaran , Sujay Sanghavi , Pablo A. Parrilo , Alan S. Willsky