# Covariate-Adjusted Tensor Classification in High-Dimensions

arXiv: https://arxiv.org/abs/1805.04421 · HTML: https://mlsanity.com/paper/1805.04421/

## Key facts

- Cited by 10 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 11 May 2018.

## Built on by (most cited first, 10 of 10)

- [Covariate-assisted Sparse Tensor Completion](https://mlsanity.com/paper/2103.06428/) (2021)
- [Transfer learning for tensor Gaussian graphical models](https://mlsanity.com/paper/2211.09391/) (2022)
- [Jointly Modeling and Clustering Tensors in High Dimensions](https://mlsanity.com/paper/2104.07773/) (2021)
- [Multiway sparse distance weighted discrimination](https://mlsanity.com/paper/2110.05377/) (2021)
- [TEC: Tensor Ensemble Classifier for Big Data](https://mlsanity.com/paper/2103.00025/) (2021)
- [Linear Discriminant Analysis with High-dimensional Mixed Variables](https://mlsanity.com/paper/2112.07145/) (2021)
- [Coupled Support Tensor Machine Classification for Multimodal Neuroimaging Data](https://mlsanity.com/paper/2201.07683/) (2022)
- [Elliptically-Contoured Tensor-variate Distributions with Application to Improved Image Learning](https://mlsanity.com/paper/2211.06940/) (2022)
- [Alteration Detection of Tensor Dependence Structure via Sparsity-Exploited Reranking Algorithm](https://mlsanity.com/paper/2310.08798/) (2023)
- [Nonparametric Linear Discriminant Analysis for High Dimensional Matrix-Valued Data](https://mlsanity.com/paper/2507.19028/) (2025)

## Abstract (arXiv)

In contemporary scientific research, it is of great interest to predict a categorical response based on a high-dimensional tensor (i.e. multi-dimensional array) and additional covariates. This mixture of different types of data leads to challenges in statistical analysis. Motivated by applications in science and engineering, we propose a comprehensive and interpretable discriminant analysis model, called CATCH model (in short for Covariate-Adjusted Tensor Classification in High-dimensions), which efficiently integrates the covariates and the tensor to predict the categorical outcome. The CATCH model jointly models the relationships among the covariates, the tensor predictor, and the categorical response. More importantly, it preserves and utilizes the structures of the data for maximum interpretability and optimal prediction. To tackle the new computational and statistical challenges arising from the intimidating tensor dimensions, we propose a penalized approach to select a subset of tensor predictor entries that has direct discriminative effect after adjusting for covariates. We further develop an efficient algorithm that takes advantage of the tensor structure. Theoretical results confirm that our method achieves variable selection consistency and optimal classification error, even when the tensor dimension is much larger than the sample size. The superior performance of our method over existing methods is demonstrated in extensive simulated and real data examples.