Large-scale evaluation of k-fold cross-validation ensembles for uncertainty estimation

Abstract

Abstract It is insightful to report an estimator that describes how certain a model is in a prediction, additionally to the prediction alone. For regression tasks, most approaches implement a variation of the ensemble method, apart from few exceptions. Instead of a single estimator, a group of estimators yields several predictions for an input. The uncertainty can then be quantified by measuring the disagreement between the predictions, for example by the standard deviation. In theory, ensembles should not only provide uncertainties, they also boost the predictive performance by reducing errors arising from variance. Despite the development of novel methods, they are still considered the “golden-standard” to quantify the uncertainty of regression models. Subsampling-based methods to obtain ensembles can be applied to all models, regardless whether they are related to deep learning or traditional machine learning. However, little attention has been given to the question whether the ensemble method is applicable to virtually all scenarios occurring in the field of cheminformatics. In a widespread and diversified attempt, ensembles are evaluated for 32 datasets of different sizes and modeling difficulty, ranging from physicochemical properties to biological activities. For increasing ensemble sizes with up to 200 members, the predictive performance as well as the applicability as uncertainty estimator are shown for all combinations of five modeling techniques and four molecular featurizations. Useful recommendations were derived for practitioners regarding the success and minimum size of ensembles, depending on whether predictive performance or uncertainty quantification is of more importance for the task at hand.

Keywords

• Cross-validation
• Deep learning
• Ensemble learning
• Machine learning
• Uncertainty quantification
• Validation