# STORE: Sparse Tensor Response Regression and Neuroimaging Analysis

arXiv: https://arxiv.org/abs/1609.04523 · HTML: https://mlsanity.com/paper/1609.04523/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2016.

## Built on by (most cited first, 11 of 11)

- [Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplay](https://mlsanity.com/paper/2206.08756/) (2022)
- [Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence](https://mlsanity.com/paper/2104.12031/) (2021)
- [Tensor Principal Component Analysis in High Dimensional CP Models](https://mlsanity.com/paper/2108.04428/) (2021)
- [Factor Augmented Tensor-on-Tensor Neural Networks](https://mlsanity.com/paper/2405.19610/) (2024)
- [Computational and Statistical Guarantees for Tensor-on-Tensor Regression with Tensor Train Decomposition](https://mlsanity.com/paper/2406.06002/) (2024)
- [Transfer learning for tensor Gaussian graphical models](https://mlsanity.com/paper/2211.09391/) (2022)
- [Bayesian longitudinal tensor response regression for modeling neuroplasticity](https://mlsanity.com/paper/2309.10065/) (2023)
- [Decomposable Sparse Tensor on Tensor Regression](https://mlsanity.com/paper/2212.05024/) (2022)
- [Tensor PCA from basis in tensor space](https://mlsanity.com/paper/2305.02803/) (2023)
- [Efficient Synthetic Network Generation via Latent Embedding Reconstruction](https://mlsanity.com/paper/2606.00934/) (2026)
- [Structured Adaptive Tensor Prediction for Streaming Data](https://mlsanity.com/paper/2606.10085/) (2026)

## Abstract (arXiv)

Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity and low-rankness. It can handle both a non-symmetric and a symmetric tensor response, and thus is applicable to both structural and functional neuroimaging data. We formulate the parameter estimation as a non-convex optimization problem, and develop an efficient alternating updating algorithm. We establish a non-asymptotic estimation error bound for the actual estimator obtained from the proposed algorithm. This error bound reveals an interesting interaction between the computational efficiency and the statistical rate of convergence. When the distribution of the error tensor is Gaussian, we further obtain a fast estimation error rate which allows the tensor dimension to grow exponentially with the sample size. We illustrate the efficacy of our model through intensive simulations and an analysis of the Autism spectrum disorder neuroimaging data.