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We study the dynamics of matrix-valued time series with observed network structures by proposing a matrix network autoregression model with row and column networks of the subjects. We incorporate covariate information and a low rank…

Methodology · Statistics 2023-02-07 Xuening Zhu , Feifei Wang , Zeng Li , Yanyuan Ma

Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…

Methodology · Statistics 2024-07-19 Yuefeng Han , Rong Chen , Dan Yang , Cun-Hui Zhang

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…

Machine Learning · Computer Science 2016-04-28 Animashree Anandkumar , Prateek Jain , Yang Shi , U. N. Niranjan

In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…

Econometrics · Economics 2025-08-25 Degui Li , Yayi Yan , Qiwei Yao

Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks, characterized by a lack of inherent ordering of features (variables). The brute force approach of learning a parameter for each interaction…

Machine Learning · Computer Science 2021-03-31 Alexandros Haliassos , Kriton Konstantinidis , Danilo P. Mandic

The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensor data that can…

Numerical Analysis · Computer Science 2018-06-22 Grey Ballard , Koby Hayashi , Ramakrishnan Kannan

We consider the tensor completion problem of predicting the missing entries of a tensor. The commonly used CP model has a triple product form, but an alternate family of quadratic models, which are the sum of pairwise products instead of a…

Machine Learning · Computer Science 2023-08-01 Hongyang R. Zhang , Vatsal Sharan , Moses Charikar , Yingyu Liang

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

Numerical Analysis · Mathematics 2016-07-06 Namgil Lee , Andrzej Cichocki

The CANDECOMP/PARAFAC (CP) decomposition is a leading method for the analysis of multiway data. The standard alternating least squares algorithm for the CP decomposition (CP-ALS) involves a series of highly overdetermined linear least…

Numerical Analysis · Computer Science 2018-08-23 Casey Battaglino , Grey Ballard , Tamara G. Kolda

The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought after since many high-dimensional tensors have low intrinsic rank relative to the…

Numerical Analysis · Computer Science 2020-03-16 N. Benjamin Erichson , Krithika Manohar , Steven L. Brunton , J. Nathan Kutz

This paper deals with the dimension reduction for high-dimensional time series based on common factors. In particular we allow the dimension of time series $p$ to be as large as, or even larger than, the sample size $n$. The estimation for…

Statistics Theory · Mathematics 2010-06-15 Clifford Lam , Qiwei Yao , Neil Bathia

Modeling matrix-valued time series is an interesting and important research topic. In this paper, we extend the method of Chang et al. (2017) to matrix-valued time series. For any given $p\times q$ matrix-valued time series, we look for…

Methodology · Statistics 2020-02-11 Zhaoxing Gao

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…

Methodology · Statistics 2023-09-28 Di Wang , Yao Zheng , Guodong Li

The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…

Machine Learning · Statistics 2022-09-20 Yuefeng Han , Cun-Hui Zhang

The canonical polyadic (CP) decomposition is one of the most widely used tensor decomposition techniques. The conventional CP decomposition algorithm combines alternating least squares (ALS) with the normal equation. However, the normal…

Numerical Analysis · Mathematics 2025-10-28 Wenchao Xie , Jiawei Xu , Zheng Peng , Qingsong Wang

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Statistics Theory · Mathematics 2021-02-08 Rungang Han , Rebecca Willett , Anru R. Zhang

The letter proposes an adaptive model reduction approach based on tensor decomposition to speed up time-domain power system simulation. Taylor series expansion of a power system dynamic model is calculated around multiple equilibria…

Systems and Control · Computer Science 2019-04-02 Denis Osipov , Kai Sun

We investigate a novel approach to approximate tensor-network contraction via the exact, matrix-free decomposition of full tensor-networks. We study this method as a means to eliminate the propagation of error in the approximation of…

Chemical Physics · Physics 2025-06-23 Karl Pierce

We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to…

Machine Learning · Computer Science 2019-04-29 Anish Agarwal , Muhammad Jehangir Amjad , Devavrat Shah , Dennis Shen

This paper explores a new version of the Levenberg-Marquardt algorithm used for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image compression and reconstruction. Tensor computation, especially CP decomposition, holds…

Numerical Analysis · Mathematics 2024-07-26 Ramin Goudarzi Karim , Dipak Dulal , Carmeliza Navasca