A Unified Framework for Random Forest Prediction Error Estimation

We introduce a unified framework for random forest prediction error estimation based on a novel estimator of the conditional prediction error distribution function. Our framework enables immediate estimation of key prediction uncertainty metrics, including conditional mean squared prediction errors, conditional biases, and conditional quantiles, by a straightforward plug-in routine. Our approach is particularly well-adapted for prediction interval estimation, which has received less attention in the random forest literature despite its practical utility; we show via simulations that our proposed prediction intervals are competitive with, and in some settings outperform, existing methods. To establish theoretical grounding for our framework, we prove pointwise uniform consistency of a more stringent version of our estimator of the conditional prediction error distribution. In addition to providing a suite of measures of prediction uncertainty, our general framework is applicable to many variants of the random forest algorithm. The estimators introduced here are implemented in the R package forestError.