Evaluation of six methods for correcting bias in estimates from ensemble tree machine learning regression models

Abstract

Ensemble-tree machine learning (ML) regression models can be prone to systematic bias: small values are overestimated and large values are underestimated. Additional bias can be introduced if the dependent variable is a transform of the original data. Six methods were evaluated for their ability to correct systematic and introduced bias. Method performance was evaluated using four case studies of groundwater quality: the units of the dependent variable were pH in two and log-concentration in the others. When performance metrics (bias and RMSE for both points and the CDF) were computed using the same units as those in the ML model, empirical distribution matching (EDM) provided the best results. When the metrics were computed using retransformed concentration, EDM and a method incorporating Duan's smearing estimate were both effective. A method based on the Z-score transform approximates EDM if the correlation coefficient between rank-ordered ML estimates and rank-ordered observations approaches one.