Evaluation of multiple prediction models: A novel view on model selection and performance assessment.

Model selection and performance assessment for prediction models are important tasks in machine learning, e.g. for the development of medical diagnosis or prognosis rules based on complex data. A common approach is to select the best model via cross-validation and to evaluate this final model on an independent dataset. In this work, we propose to instead evaluate several models simultaneously. These may result from varied hyperparameters or completely different learning algorithms. Our main goal is to increase the probability to correctly identify a model that performs sufficiently well. In this case, adjusting for multiplicity is necessary in the evaluation stage to avoid an inflation of the family wise error rate. We apply the so-called maxT-approach which is based on the joint distribution of test statistics and suitable to (approximately) control the family-wise error rate for a wide variety of performance measures. We conclude that evaluating only a single final model is suboptimal. Instead, several promising models should be evaluated simultaneously, e.g. all models within one standard error of the best validation model. This strategy has proven to increase the probability to correctly identify a good model as well as the final model performance in extensive simulation studies.