# Nonparametric Variable Screening with Optimal Decision Stumps

arXiv: https://arxiv.org/abs/2011.02683 · HTML: https://mlsanity.com/paper/2011.02683/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2020.

## Built on by (most cited first, 4 of 4)

- [Optimal Sparse Recovery with Decision Stumps](https://mlsanity.com/paper/2303.04301/) (2023)
- [Regression Trees Know Calculus](https://mlsanity.com/paper/2405.13846/) (2024)
- [Transfer Learning with Distance Covariance for Random Forest: Error Bounds and an EHR Application](https://mlsanity.com/paper/2510.10870/) (2025)
- [Covariance-Driven Regression Trees: Reducing Overfitting in CART](https://mlsanity.com/paper/2601.07281/) (2026)

## Abstract (arXiv)

Decision trees and their ensembles are endowed with a rich set of diagnostic tools for ranking and screening variables in a predictive model. Despite the widespread use of tree based variable importance measures, pinning down their theoretical properties has been challenging and therefore largely unexplored. To address this gap between theory and practice, we derive finite sample performance guarantees for variable selection in nonparametric models using a single-level CART decision tree (a decision stump). Under standard operating assumptions in variable screening literature, we find that the marginal signal strength of each variable and ambient dimensionality can be considerably weaker and higher, respectively, than state-of-the-art nonparametric variable selection methods. Furthermore, unlike previous marginal screening methods that attempt to directly estimate each marginal projection via a truncated basis expansion, the fitted model used here is a simple, parsimonious decision stump, thereby eliminating the need for tuning the number of basis terms. Thus, surprisingly, even though decision stumps are highly inaccurate for estimation purposes, they can still be used to perform consistent model selection.