# Efficient Decision Trees for Tensor Regressions

arXiv: https://arxiv.org/abs/2408.01926 · HTML: https://mlsanity.com/paper/2408.01926/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 69 references that are in the map.
- First posted on arXiv 4 Aug 2024.

## Builds on (most cited first, 23 of 23)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [Randomized Numerical Linear Algebra : A Perspective on the Field With an Eye to Software](https://mlsanity.com/paper/2302.11474/) (2023)
- [Bayesian Regression Tree Ensembles that Adapt to Smoothness and Sparsity](https://mlsanity.com/paper/1707.09461/) (2017)
- [Randomization as Regularization: A Degrees of Freedom Explanation for Random Forest Success](https://mlsanity.com/paper/1911.00190/) (2019)
- [Large Scale Prediction with Decision Trees](https://mlsanity.com/paper/2104.13881/) (2021)
- [Tucker Tensor Regression and Neuroimaging Analysis](https://mlsanity.com/paper/1304.5637/) (2013)
- [Tensor-on-tensor regression](https://mlsanity.com/paper/1701.01037/) (2017)
- [Bayesian Tensor Regression](https://mlsanity.com/paper/1509.06490/) (2015)
- [Parsimonious Tensor Response Regression](https://mlsanity.com/paper/1501.07815/) (2015)
- [Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplay](https://mlsanity.com/paper/2206.08756/) (2022)
- [Scalable Tucker Factorization for Sparse Tensors - Algorithms and Discoveries](https://mlsanity.com/paper/1710.02261/) (2017)
- [A novel approach for fusion of heterogeneous sources of data](https://mlsanity.com/paper/1803.00138/) (2018)
- [Tensor Regression Meets Gaussian Processes](https://mlsanity.com/paper/1710.11345/) (2017)
- [Non-smooth Bayesian Optimization in Tuning Problems](https://mlsanity.com/paper/2109.07563/) (2021)
- [Medoid splits for efficient random forests in metric spaces](https://mlsanity.com/paper/2306.17031/) (2023)
- [Sharded Bayesian Additive Regression Trees](https://mlsanity.com/paper/2306.00361/) (2023)
- [Hybrid Parameter Search and Dynamic Model Selection for Mixed-Variable Bayesian Optimization](https://mlsanity.com/paper/2206.01409/) (2022)
- [Bayesian Tensor-on-Tensor Regression with Efficient Computation](https://mlsanity.com/paper/2210.11363/) (2022)
- [Soft Tensor Regression](https://mlsanity.com/paper/1910.09699/) (2019)
- [Tensor Gaussian Process with Contraction for Multi-Channel Imaging Analysis](https://mlsanity.com/paper/2301.11203/) (2023)
- [Bayesian Methods in Tensor Analysis](https://mlsanity.com/paper/2302.05978/) (2023)
- [Contrastive inverse regression for dimension reduction](https://mlsanity.com/paper/2305.12287/) (2023)

## Built on by (most cited first, 1 of 1)

- [Ranking Perspective for Tree-based Methods with Applications to Symbolic Feature Selection](https://mlsanity.com/paper/2410.02623/) (2024)

## Abstract (arXiv)

We proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variable are tensors (i.e., multi-way arrays). We devised and implemented fast randomized and deterministic algorithms for efficient fitting of scalar-on-tensor trees, making TT competitive against tensor-input GP models. Based on scalar-on-tensor tree models, we extend our method to tensor-on-tensor problems using additive tree ensemble approaches. Theoretical justification and extensive experiments on real and synthetic datasets are provided to illustrate the performance of TT.