A statistical learning framework for groundwater nitrate models of the Central Valley, California, USA

We used a statistical learning framework to evaluate the ability of three machine-learning methods to predict nitrate concentration in shallow groundwater of the Central Valley, California: boosted regression trees (BRT), artificial neural networks (ANN), and Bayesian networks (BN). Machine learning methods can learn complex patterns in the data but because of overfitting may not generalize well to new data. The statistical learning framework involves cross-validation (CV) training and testing data and a separate hold-out data set for model evaluation, with the goal of optimizing predictive performance by controlling for model overfit. The order of prediction performance according to both CV testing R² and that for the hold-out data set was BRT > BN > ANN. For each method we identified two models based on CV testing results: that with maximum testing R² and a version with R² within one standard error of the maximum (the 1SE model). The former yielded CV training R² values of 0.94–1.0. Cross-validation testing R² values indicate predictive performance, and these were 0.22–0.39 for the maximum R² models and 0.19–0.36 for the 1SE models. Evaluation with hold-out data suggested that the 1SE BRT and ANN models predicted better for an independent data set compared with the maximum R² versions, which is relevant to extrapolation by mapping. Scatterplots of predicted vs. observed hold-out data obtained for final models helped identify prediction bias, which was fairly pronounced for ANN and BN. Lastly, the models were compared with multiple linear regression (MLR) and a previous random forest regression (RFR) model. Whereas BRT results were comparable to RFR, MLR had low hold-out R² (0.07) and explained less than half the variation in the training data. Spatial patterns of predictions by the final, 1SE BRT model agreed reasonably well with previously observed patterns of nitrate occurrence in groundwater of the Central Valley.