On the Pointwise Behavior of Recursive Partitioning and Its Implications for Heterogeneous Causal Effect Estimation

Abstract: Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of experiments, where tree estimation and inference is conducted at specific values of the covariates. In this paper, we call into question the use of decision trees (trained by adaptive recursive partitioning) for such purposes by demonstrating that they can fail to achieve polynomial rates of convergence in uniform norm with non-vanishing probability, even with pruning. Instead, the convergence may be arbitrarily slow or, in some important special cases, such as honest regression trees, fail completely. We show that random forests can remedy the situation, turning poor performing trees into nearly optimal procedures, at the cost of losing interpretability and introducing two additional tuning parameters. The two hallmarks of random forests, subsampling and the random feature selection mechanism, are seen to each distinctively contribute to achieving nearly optimal performance for the model class considered. 

 

Bio: Matias D. Cattaneo is a Professor of Operations Research and Financial Engineering at Princeton University, where he is also an Associated Faculty in the School of Public and International Affairs (SPIA), the Department of Economics, and the Program in Latin American Studies (PLAS), and an Affiliated Faculty in the Data-Driven Social Science (DDSS) initiative, the AI at Princeton initiative, and the Center for Statistics and Machine Learning (CSML). His research spans econometrics, statistics, data science, and decision science, with applications to program evaluation and causal inference. Most of his work is interdisciplinary and motivated by quantitative problems in the social, behavioral, and biomedical sciences. As part of his main research agenda, he has developed novel nonparametric, semiparametric, high-dimensional, and machine learning estimation and inference procedures with demonstrably superior robustness to tuning parameter and other implementation choices.