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.
About the Speaker:
Matias D. Cattaneo is a Professor of Operations Research and Financial Engineering (ORFE) 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. His work is interdisciplinary, and often motivated by quantitative problems in the social, behavioral, and biomedical sciences. His research often integrates nonparametric, semiparametric, high-dimensional, and machine learning methods to develop robust estimation and inference techniques.
Matias is an elected Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and the International Association for Applied Econometrics.
He serves on the editorial boards of leading journals, including Journal of the American Statistical Association, Econometrica, Operations Research, Statistical Science, the Econometrics Journal, the Journal of Econometrics, Econometric Theory, and the Journal of Causal Inference. He is also an Amazon Scholar and has advised numerous governmental, multilateral, non-profit, and private organizations around the world.
Matias earned his Ph.D. in Economics (2008) and M.A. in Statistics (2005) from the University of California, Berkeley, as well as an M.A. in Economics from Universidad Torcuato Di Tella (2003) and a B.A. in Economics from Universidad de Buenos Aires (2000). Before joining Princeton in 2019, he was a faculty member in the departments of economics and statistics at the University of Michigan.
Your participation is warmly welcomed!
欢迎扫码关注北大统计科学中心公众号，了解更多讲座信息!
