mlsanityData to 7 Oct 2026

Multilinear tensor regression for longitudinal relational data

arXiv 1412.0048 ↗First posted 28 Nov 2014stat.MEcited by 28

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Abstract (arXiv)

A fundamental aspect of relational data, such as from a social network, is the possibility of dependence among the relations. In particular, the relations between members of one pair of nodes may have an effect on the relations between members of another pair. This article develops a type of regression model to estimate such effects in the context of longitudinal and multivariate relational data, or other data that can be represented in the form of a tensor. The model is based on a general multilinear tensor regression model, a special case of which is a tensor autoregression model in which the tensor of relations at one time point are parsimoniously regressed on relations from previous time points. This is done via a separable, or Kronecker-structured, regression parameter along with a separable covariance model. In the context of an analysis of longitudinal multivariate relational data, it is shown how the multilinear tensor regression model can represent patterns that often appear in relational and network data, such as reciprocity and transitivity.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Nov 2014.

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Citing papers per year: 2021: 7; 2022: 4; 2023: 4; 2024: 9; 2025: 4.

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  1. 2022Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplaycited by 15
  2. 2025LLM/Agent-as-Data-Analyst: A Surveycited by 15
  3. 2021Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergencecited by 13
  4. 2021Tensor Principal Component Analysis in High Dimensional CP Modelscited by 7
  5. 2024Factor Augmented Tensor-on-Tensor Neural Networkscited by 7
  6. 2021Rank-R FNN: A Tensor-Based Learning Model for High-Order Data Classificationcited by 6
  7. 2021Covariate-assisted Sparse Tensor Completioncited by 4
  8. 2024Computational and Statistical Guarantees for Tensor-on-Tensor Regression with Tensor Train Decompositioncited by 4
  9. 2025A Scalable Factorization Approach for High-Order Structured Tensor Recoverycited by 4
  10. 2023Understanding MLP-Mixer as a Wide and Sparse MLPcited by 3
  11. 2024Bilinear Sequence Regression: A Model for Learning from Long Sequences of High-dimensional Tokenscited by 3
  12. 2025Interpretable Bayesian Tensor Network Kernel Machines with Automatic Rank and Feature Selectioncited by 3
16 more
  1. 2021A Latent Space Model for Multilayer Network Datacited by 2
  2. 2022Structured Optimal Variational Inference for Dynamic Latent Space Modelscited by 2
  3. 2024Robust Low-rank Tensor Train Recoverycited by 2
  4. 2021Inference for Network Regression Models with Community Structurecited by 1
  5. 2023Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Modelcited by 1
  6. 2024TEAFormers: TEnsor-Augmented Transformers for Multi-Dimensional Time Series Forecastingcited by 1
  7. 2021A Probit Tensor Factorization Model For Relational Learningcited by 0
  8. 2022Factorized Fusion Shrinkage for Dynamic Relational Datacited by 0
  9. 2022Elliptically-Contoured Tensor-variate Distributions with Application to Improved Image Learningcited by 0
  10. 2023Statistical and computational rates in high rank tensor estimationcited by 0
  11. 2023Alteration Detection of Tensor Dependence Structure via Sparsity-Exploited Reranking Algorithmcited by 0
  12. 2024The ALℓ0CORE Tensor Decomposition for Sparse Count Datacited by 0
  13. 2024Functional-Edged Network Modelingcited by 0
  14. 2024BAMITA: Bayesian Multiple Imputation for Tensor Arrayscited by 0
  15. 2024Bivariate Matrix-valued Linear Regression (BMLR): Finite-sample performance under Identifiability and Sparsity Assumptionscited by 0
  16. 2025Tensor State Space-based Dynamic Multilayer Network Modelingcited by 0