Nonparametric Variable Screening with Optimal Decision Stumps

TL;DR

This paper establishes theoretical guarantees for using simple decision stumps in nonparametric variable screening, showing they can effectively identify relevant variables despite their simplicity.

Contribution

It provides finite sample performance guarantees for variable selection using decision stumps, highlighting their effectiveness and simplicity compared to existing methods.

Findings

Decision stumps can reliably perform variable screening in nonparametric models.

The method tolerates weaker signals and higher dimensionality than previous approaches.

Decision stumps eliminate the need for tuning basis expansion parameters.

Abstract

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.