mlsanityData to 7 Oct 2026

Bayesian Tensor Regression

arXiv 1509.06490 ↗First posted 22 Sep 2015stat.MEcited by 21

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Abstract (arXiv)

This article proposes a Bayesian approach to regression with a scalar response against vector and tensor covariates. Tensor covariates are commonly vectorized prior to analysis, failing to exploit the structure of the tensor, and resulting in poor estimation and predictive performance. We develop a novel class of multiway shrinkage priors for the coefficients in tensor regression models. Properties are described, including posterior consistency under mild conditions, and an efficient Markov chain Monte Carlo algorithm is developed for posterior computation. Simulation studies illustrate substantial gains over vectorizing or using existing tensor regression methods in terms of estimation and parameter inference. The approach is further illustrated in a neuroimaging application. Keywords: Dimension reduction; multiway shrinkage prior; magnetic resonance imaging (MRI); parafac decomposition; posterior consistency; tensor regression

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Sep 2015.

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Citing papers per year: 2021: 4; 2022: 3; 2023: 3; 2024: 5; 2025: 3; 2026: 3.

21 papers.

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  1. 2022Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplaycited by 15
  2. 2021Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergencecited by 13
  3. 2023Low Rank Optimization for Efficient Deep Learning: Making A Balance between Compact Architecture and Fast Trainingcited by 5
  4. 2021Scalable Spatiotemporally Varying Coefficient Modelling with Bayesian Kernelized Tensor Regressioncited by 3
  5. 2025Interpretable Bayesian Tensor Network Kernel Machines with Automatic Rank and Feature Selectioncited by 3
  6. 2023Bayesian longitudinal tensor response regression for modeling neuroplasticitycited by 2
  7. 2021High-Dimensional Uncertainty Quantification via Tensor Regression with Rank Determination and Adaptive Samplingcited by 1
  8. 2022Targeted Advertising on Social Networks Using Online Variational Tensor Regressioncited by 1
  9. 2024An Adaptive Tensor-Train Decomposition Approach for Efficient Deep Neural Network Compressioncited by 1
  10. 2024Efficient Decision Trees for Tensor Regressionscited by 1
  11. 2021Efficient Tensor Contraction via Fast Count Sketchcited by 0
  12. 2022Bayesian predictive modeling of multi-source multi-way datacited by 0
9 more
  1. 2023Bayesian Additive Main Effects and Multiplicative Interaction Models using Tensor Regression for Multi-environmental Trialscited by 0
  2. 2024Heterogeneous Image-based Classification Using Distributional Data Analysiscited by 0
  3. 2024Maximum likelihood inference for high-dimensional problems with multiaffine variable relationscited by 0
  4. 2024BAMITA: Bayesian Multiple Imputation for Tensor Arrayscited by 0
  5. 2025Generalized Nonnegative Structured Kruskal Tensor Regressioncited by 0
  6. 2025Low-rank MMSE filters, Kronecker-product representation, and regularization: a new perspectivecited by 0
  7. 2026Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selectioncited by 0
  8. 2026Bayesian Poisson-Randomized Gamma Tensor Factorization with Application to International Trade Flowscited by 0
  9. 2026Additive Nonparametric Regression with Spatial and Network Objectscited by 0