Targeted tuning of random forests for quantile estimation and prediction intervals

TL;DR

This paper introduces a new tuning method for random forests that enhances quantile estimation accuracy and produces more reliable, narrower prediction intervals, especially for censored data, by minimizing quantile coverage loss.

Contribution

The paper proposes a novel QCL tuning procedure for RFs that improves quantile coverage accuracy and adapts to censored data, outperforming traditional methods.

Findings

QCL tuning yields more accurate quantile coverage probabilities.

QCL tuning reduces bias and MSE of coverage estimates.

Method produces valid, narrower prediction intervals.

Abstract

We present a novel tuning procedure for random forests (RFs) that improves the accuracy of estimated quantiles and produces valid, relatively narrow prediction intervals. While RFs are typically used to estimate mean responses (conditional on covariates), they can also be used to estimate quantiles by estimating the full distribution of the response. However, standard approaches for building RFs often result in excessively biased quantile estimates. To reduce this bias, our proposed tuning procedure minimizes "quantile coverage loss" (QCL), which we define as the estimated bias of the marginal quantile coverage probability estimate based on the out-of-bag sample. We adapt QCL tuning to handle censored data and demonstrate its use with random survival forests. We show that QCL tuning results in quantile estimates with more accurate coverage probabilities than those achieved using default parameter values or traditional tuning (using MSPE for uncensored data and C-index for censored data), while also reducing the estimated MSE of these coverage probabilities. We discuss how the superior performance of QCL tuning is linked to its alignment with the estimation goal. Finally, we explore the validity and width of prediction intervals created using this method.