mlsanityData to 7 Oct 2026

Tensor-on-tensor regression

arXiv 1701.01037 ↗First posted 4 Jan 2017stat.ME stat.MLcited by 22

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Abstract (arXiv)

We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or a tensor from a scalar. We describe an approach that exploits the multiway structure of both the predictors and the outcomes by restricting the coefficients to have reduced CP-rank. We propose a general and efficient algorithm for penalized least-squares estimation, which allows for a ridge (L_2) penalty on the coefficients. The objective is shown to give the mode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for inference. We illustrate the approach with an application to facial image data. An R package is available at https://github.com/lockEF/MultiwayRegression .

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Jan 2017.

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Citing papers per year: 2021: 1; 2022: 4; 2023: 1; 2024: 6; 2025: 4; 2026: 6.

22 papers.

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  1. 2022Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplaycited by 15
  2. 2024Factor Augmented Tensor-on-Tensor Neural Networkscited by 7
  3. 2024Low-Rank Robust Subspace Tensor Clustering for Metro Passenger Flow Modelingcited by 5
  4. 2024Computational and Statistical Guarantees for Tensor-on-Tensor Regression with Tensor Train Decompositioncited by 4
  5. 2026Near-Universal Multiplicative Updates for Nonnegative Einsum Factorizationcited by 2
  6. 2021Multiway sparse distance weighted discriminationcited by 1
  7. 2024Efficient Decision Trees for Tensor Regressionscited by 1
  8. 2022Coupled Support Tensor Machine Classification for Multimodal Neuroimaging Datacited by 0
  9. 2022Elliptically-Contoured Tensor-variate Distributions with Application to Improved Image Learningcited by 0
  10. 2022Decomposable Sparse Tensor on Tensor Regressioncited by 0
  11. 2023Few-shot Personalized Saliency Prediction Based on Interpersonal Gaze Patternscited by 0
  12. 2024Tensor-based process control and monitoring for semiconductor manufacturing with unstable disturbancescited by 0
10 more
  1. 2024Integrative Variational Autoencoders for Generative Modeling of an Image Outcome with Multiple Input Imagescited by 0
  2. 2025Generalized Nonnegative Structured Kruskal Tensor Regressioncited by 0
  3. 2025Guaranteed Noisy CP Tensor Recovery via Riemannian Optimization on the Segre Manifoldcited by 0
  4. 2025Tensor-on-tensor Regression Neural Networks for Process Modeling with High-dimensional Datacited by 0
  5. 2025A Latent-Variable Formulation of the Poisson Canonical Polyadic Tensor Model: Maximum Likelihood Estimation and Fisher Informationcited by 0
  6. 2026Combinatorial Bandit Bayesian Optimization for Tensor Outputscited by 0
  7. 2026Cellwise Outlierscited by 0
  8. 2026Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selectioncited by 0
  9. 2026Beyond Additive Decompositions: Interpretability Through Separabilitycited by 0
  10. 2026Structured Adaptive Tensor Prediction for Streaming Datacited by 0