# Decomposable Sparse Tensor on Tensor Regression

arXiv: https://arxiv.org/abs/2212.05024 · HTML: https://mlsanity.com/paper/2212.05024/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 9 Dec 2022.

## Builds on (most cited first, 6 of 6)

- [Tensor-on-tensor regression](https://mlsanity.com/paper/1701.01037/) (2017)
- [Parsimonious Tensor Response Regression](https://mlsanity.com/paper/1501.07815/) (2015)
- [Provable Sparse Tensor Decomposition](https://mlsanity.com/paper/1502.01425/) (2015)
- [Learning from Multiway Data: Simple and Efficient Tensor Regression](https://mlsanity.com/paper/1607.02535/) (2016)
- [STORE: Sparse Tensor Response Regression and Neuroimaging Analysis](https://mlsanity.com/paper/1609.04523/) (2016)
- [Boosted Sparse and Low-Rank Tensor Regression](https://mlsanity.com/paper/1811.01158/) (2018)

## Abstract (arXiv)

Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors X and responses Y are both high-dimensional tensors. By demonstrating that the general inner product or the contracted product on a unit rank tensor can be decomposed into standard inner products and outer products, the problem can be simply transformed into a tensor to scalar regression followed by a tensor decomposition. So we propose a fast solution based on stagewise search composed by contraction part and generation part which are optimized alternatively. We successfully demonstrate our method can out perform current methods in terms of accuracy and predictors selection by effectively incorporating the structural information.