# Boosted Sparse and Low-Rank Tensor Regression

arXiv: https://arxiv.org/abs/1811.01158 · HTML: https://mlsanity.com/paper/1811.01158/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2018.

## Built on by (most cited first, 9 of 9)

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- [BrainNNExplainer: An Interpretable Graph Neural Network Framework for Brain Network based Disease Analysis](https://mlsanity.com/paper/2107.05097/) (2021)
- [Multiplex Graph Networks for Multimodal Brain Network Analysis](https://mlsanity.com/paper/2108.00158/) (2021)
- [Position: Tensor Networks are a Valuable Asset for Green AI](https://mlsanity.com/paper/2205.12961/) (2022)
- [Tensor-Based Multi-Modality Feature Selection and Regression for Alzheimer's Disease Diagnosis](https://mlsanity.com/paper/2209.11372/) (2022)
- [Simultaneous Best Subset Selection and Dimension Reduction via Primal-Dual Iterations](https://mlsanity.com/paper/2211.15889/) (2022)
- [Decomposable Sparse Tensor on Tensor Regression](https://mlsanity.com/paper/2212.05024/) (2022)
- [Supervised Deep Multimodal Matrix Factorization for Interpretable Brain Network Analysis](https://mlsanity.com/paper/2605.13312/) (2026)
- [Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection](https://mlsanity.com/paper/2605.19122/) (2026)

## Abstract (arXiv)

We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both parsimonious and highly interpretable, as it implies that the outcome is related to the features through a few distinct pathways, each of which may only involve subsets of feature dimensions. We take a divide-and-conquer strategy to simplify the task into a set of sparse unit-rank tensor regression problems. To make the computation efficient and scalable, for the unit-rank tensor regression, we propose a stagewise estimation procedure to efficiently trace out its entire solution path. We show that as the step size goes to zero, the stagewise solution paths converge exactly to those of the corresponding regularized regression. The superior performance of our approach is demonstrated on various real-world and synthetic examples.