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On the Pointwise Behavior of Recursive Partitioning and Its Implications for Heterogeneous Causal Effect Estimation
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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.
Forward citations
Cited by 5 Pith papers
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On the pointwise and sup-norm errors for local regression estimators
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Accuracy Limits of Causal Trees for Individualized Treatment Effects
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Honest estimation in causal forests can reduce CATE accuracy and require up to 27% more data, especially when effect heterogeneity is strong and detectable.
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Randomizing split directions in forests helps when variance dominates bias, which occurs at low signal-to-noise ratio and with correlated covariates, but hurts when irrelevant covariates or fat-tailed features make bi...
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