# Tucker Tensor Regression and Neuroimaging Analysis

arXiv: https://arxiv.org/abs/1304.5637 · HTML: https://mlsanity.com/paper/1304.5637/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2013.

## Built on by (most cited first, 26 of 26)

- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence](https://mlsanity.com/paper/2104.12031/) (2021)
- [Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption](https://mlsanity.com/paper/2305.04080/) (2023)
- [Factor Augmented Tensor-on-Tensor Neural Networks](https://mlsanity.com/paper/2405.19610/) (2024)
- [Rank-R FNN: A Tensor-Based Learning Model for High-Order Data Classification](https://mlsanity.com/paper/2104.05048/) (2021)
- [On High-dimensional and Low-rank Tensor Bandits](https://mlsanity.com/paper/2305.03884/) (2023)
- [A Scalable Factorization Approach for High-Order Structured Tensor Recovery](https://mlsanity.com/paper/2506.16032/) (2025)
- [Robust Regularized Low-Rank Matrix Models for Regression and Classification](https://mlsanity.com/paper/2205.07106/) (2022)
- [Composing Linear Layers from Irreducibles](https://mlsanity.com/paper/2507.11688/) (2025)
- [Tensor-on-tensor Regression Neural Networks for Process Modeling with High-dimensional Data](https://mlsanity.com/paper/2510.05329/) (2025)
- [Structured Low-Rank Tensors for Generalized Linear Models](https://mlsanity.com/paper/2308.02922/) (2023)
- [Efficient Decision Trees for Tensor Regressions](https://mlsanity.com/paper/2408.01926/) (2024)
- [Coupled Support Tensor Machine Classification for Multimodal Neuroimaging Data](https://mlsanity.com/paper/2201.07683/) (2022)
- [Low-Rank Phase Retrieval with Structured Tensor Models](https://mlsanity.com/paper/2202.08260/) (2022)
- [Bayesian predictive modeling of multi-source multi-way data](https://mlsanity.com/paper/2208.03396/) (2022)
- [Enhancing Deep Learning Models through Tensorization: A Comprehensive Survey and Framework](https://mlsanity.com/paper/2309.02428/) (2023)
- [Oblivious subspace embeddings for compressed Tucker decompositions](https://mlsanity.com/paper/2406.09387/) (2024)
- [Time Series Generative Learning with Application to Brain Imaging Analysis](https://mlsanity.com/paper/2407.14003/) (2024)
- [Federated Low-Rank Tensor Estimation for Multimodal Image Reconstruction](https://mlsanity.com/paper/2502.02761/) (2025)
- [Tensorized Multi-Task Learning for Personalized Modeling of Heterogeneous Individuals with High-Dimensional Data](https://mlsanity.com/paper/2508.15676/) (2025)
- [Generalized Nonnegative Structured Kruskal Tensor Regression](https://mlsanity.com/paper/2509.19900/) (2025)
- [MELCOT: A Hybrid Learning Architecture with Marginal Preservation for Matrix-Valued Regression](https://mlsanity.com/paper/2509.23315/) (2025)
- [Low-rank MMSE filters, Kronecker-product representation, and regularization: a new perspective](https://mlsanity.com/paper/2512.14932/) (2025)
- [A Muon-Accelerated Algorithm for Low Separation Rank Tensor Generalized Linear Models](https://mlsanity.com/paper/2604.04726/) (2026)
- [Robust Tensor Regression with Nonconvexity: Algorithmic and Statistical Theory](https://mlsanity.com/paper/2605.07448/) (2026)
- [Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection](https://mlsanity.com/paper/2605.19122/) (2026)

## Abstract (arXiv)

Large-scale neuroimaging studies have been collecting brain images of study individuals, which take the form of two-dimensional, three-dimensional, or higher dimensional arrays, also known as tensors. Addressing scientific questions arising from such data demands new regression models that take multidimensional arrays as covariates. Simply turning an image array into a long vector causes extremely high dimensionality that compromises classical regression methods, and, more seriously, destroys the inherent spatial structure of array data that possesses wealth of information. In this article, we propose a family of generalized linear tensor regression models based upon the Tucker decomposition of regression coefficient arrays. Effectively exploiting the low rank structure of tensor covariates brings the ultrahigh dimensionality to a manageable level that leads to efficient estimation. We demonstrate, both numerically that the new model could provide a sound recovery of even high rank signals, and asymptotically that the model is consistently estimating the best Tucker structure approximation to the full array model in the sense of Kullback-Liebler distance. The new model is also compared to a recently proposed tensor regression model that relies upon an alternative CANDECOMP/PARAFAC (CP) decomposition.