A Multicriteria Approach to Find Predictive and Sparse Models with Stable Feature Selection for High-Dimensional Data

Finding a good predictive model for a high-dimensional data set can be challenging. For genetic data, it is not only important to find a model with high predictive accuracy, but it is also important that this model uses only few features and that the selection of these features is stable. This is because, in bioinformatics, the models are used not only for prediction but also for drawing biological conclusions which makes the interpretability and reliability of the model crucial. We suggest using three target criteria when fitting a predictive model to a high-dimensional data set: the classification accuracy, the stability of the feature selection, and the number of chosen features. As it is unclear which measure is best for evaluating the stability, we first compare a variety of stability measures. We conclude that the Pearson correlation has the best theoretical and empirical properties. Also, we find that for the stability assessment behaviour it is most important that a measure contains a correction for chance or large numbers of chosen features. Then, we analyse Pareto fronts and conclude that it is possible to find models with a stable selection of few features without losing much predictive accuracy.