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Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…

Information Theory · Computer Science 2021-07-19 Marvin Geiselhart , Ahmed Elkelesh , Moustafa Ebada , Sebastian Cammerer , Stephan ten Brink

The existing tensor networks adopt conventional matrix product for connection. The classical matrix product requires strict dimensionality consistency between factors, which can result in redundancy in data representation. In this paper,…

Machine Learning · Computer Science 2021-10-01 Hengling Zhao , Yipeng Liu , Xiaolin Huang , Ce Zhu

Tensor decomposition is a fundamental method used in various areas to deal with high-dimensional data. \emph{Tensor power method} (TPM) is one of the widely-used techniques in the decomposition of tensors. This paper presents a novel tensor…

Machine Learning · Computer Science 2023-06-02 Yichuan Deng , Zhao Song , Junze Yin

Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…

Machine Learning · Computer Science 2021-05-21 Chenjian Pan , Chen Ling , Hongjin He , Liqun Qi , Yanwei Xu

Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A class of these codes was introduced by Roth, who also…

Information Theory · Computer Science 2026-05-14 Eimear Byrne , Alain Couvreur , Lucien François

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Machine Learning · Computer Science 2020-11-26 Talal Ahmed , Haroon Raja , Waheed U. Bajwa

Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-02-03 Hussam Al Daas , Grey Ballard , Laura Grigori , Suraj Kumar , Kathryn Rouse

In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive…

Statistics Theory · Mathematics 2020-01-09 Anru Zhang , Dong Xia

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

Numerical Analysis · Mathematics 2020-11-03 Lingjie Li , Wenjian Yu , Kim Batselier

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

Numerical Analysis · Computer Science 2018-07-03 Alp Ozdemir , Ali Zare , Mark A. Iwen , Selin Aviyente

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Numerical Analysis · Mathematics 2014-11-04 Holger Rauhut , Reinhold Schneider , Zeljka Stojanac

We consider the problem of downlink channel estimation for millimeter wave (mmWave) MIMO-OFDM systems, where both the base station (BS) and the mobile station (MS) employ large antenna arrays for directional precoding/beamforming. Hybrid…

Information Theory · Computer Science 2016-11-02 Zhou Zhou , Jun Fang , Linxiao Yang , Hongbin Li , Zhi Chen , Rick S. Blum

Tensor data are increasingly available in many application domains. We develop several tensor decomposition methods for binary tensor data. Different from classical tensor decompositions for continuous-valued data with squared error loss,…

Applications · Statistics 2021-06-30 Jianhao Zhang , Yoonkyung Lee

Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…

Machine Learning · Computer Science 2023-05-17 Yicong He , George K. Atia

Define the codewords of the Tensor Reed-Muller code $\mathsf{TRM}(r_1,m_1;r_2,m_2;\dots;r_t,m_t)$ to be the evaluation vectors of all multivariate polynomials in the variables $\left\{x_{ij}\right\}_{i=1,\dots,t}^{j=1,\dots m_i}$ with…

Information Theory · Computer Science 2026-01-23 Emmanuel Abbe , Colin Sandon , Oscar Sprumont

Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…

Information Theory · Computer Science 2021-07-28 Marvin Geiselhart , Ahmed Elkelesh , Moustafa Ebada , Sebastian Cammerer , Stephan ten Brink

We address the problem of tensor decomposition in application to direction-of-arrival (DOA) estimation for transmit beamspace (TB) multiple-input multiple-output (MIMO) radar. A general 4-order tensor model that enables computationally…

Information Theory · Computer Science 2022-06-29 Feng Xu , Matthew W. Morency , Sergiy A. Vorobyov

In the literature, tensors have been effectively used for capturing the context information in language models. However, the existing methods usually adopt relatively-low order tensors, which have limited expressive power in modeling…

Computation and Language · Computer Science 2019-02-01 Lipeng Zhang , Peng Zhang , Xindian Ma , Shuqin Gu , Zhan Su , Dawei Song

In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained…

Numerical Analysis · Mathematics 2014-12-12 Shmuel Friedland , Venu Tammali

We consider the problem of learning mixtures of generalized linear models (GLM) which arise in classification and regression problems. Typical learning approaches such as expectation maximization (EM) or variational Bayes can get stuck in…

Machine Learning · Computer Science 2016-01-14 Hanie Sedghi , Majid Janzamin , Anima Anandkumar