Nonparametric Variable Screening with Optimal Decision Stumps
This work addresses a gap in theory for practitioners using tree-based variable screening, offering a simpler and more robust method for variable selection in nonparametric models.
The paper tackles the challenge of providing theoretical guarantees for tree-based variable importance measures by deriving finite sample performance guarantees for variable selection using a single-level CART decision tree (decision stump). It shows that this method allows for weaker marginal signal strength and higher ambient dimensionality compared to state-of-the-art nonparametric variable selection methods, while eliminating the need for tuning basis terms.
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.