# SMART: A Flexible Approach to Regression using Spline-Based Multivariate Adaptive Regression Trees

arXiv: https://arxiv.org/abs/2410.05597 · HTML: https://mlsanity.com/paper/2410.05597/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 21 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 4 of 4)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Local Linear Forests](https://mlsanity.com/paper/1807.11408/) (2018)
- [Linear Aggregation in Tree-based Estimators](https://mlsanity.com/paper/1906.06463/) (2019)

## Abstract (arXiv)

Decision trees are powerful for predictive modeling but often suffer from high variance when modeling continuous relationships. While algorithms like Multivariate Adaptive Regression Splines (MARS) excel at capturing such continuous relationships, they perform poorly when modeling discontinuities. To address the limitations of both approaches, we introduce Spline-based Multivariate Adaptive Regression Trees (SMART), which uses a decision tree to identify subsets of data with distinct continuous relationships and then leverages MARS to fit these relationships independently. Unlike other methods that rely on the tree structure to model interaction and higher-order terms, SMART leverages MARS's native ability to handle these terms, allowing the tree to focus solely on identifying discontinuities in the relationship. We test SMART on various datasets, demonstrating its improvement over state-of-the-art methods in such cases. Additionally, we provide an open-source implementation of our method to be used by practitioners.