2020/07/07 by Vasilis Syrgkanis, Syrgkanis, Vasilis, Manolis Zampetakis +1 · 1 citation
Mathematics · #Advanced Causal Inference Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2007.03210
openalex publication_date 2020/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the finite sample mean squared error (MSE) performance of regression trees and forests in the high dimensional regime with binary features, under a sparsity constraint. We prove that if only r of the d features are relevant for the mean outcome function, then shallow trees built greedily via the CART empirical MSE criterion achieve MSE rates that depend only logarithmically on the ambient dimension d. We prove upper bounds, whose exact dependence on the number relevant variables r depends on the correlation among the features and on the degree of relevance. For strongly relevant features, we also show that fully grown honest forests achieve fast MSE rates and their predictions are also asymptotically normal, enabling asymptotically valid inference that adapts to the sparsity of the regression function.