Stabilizing l1-norm prediction models by supervised feature grouping

Emerging Electronic Medical Records (EMRs) have reformed the modern healthcare. These records have great potential to be used for building clinical prediction models. However, a problem in using them is their high dimensionality. Since a lot of information may not be relevant for prediction, the underlying complexity of the prediction models may not be high. A popular way to deal with this problem is to employ feature selection. Lasso and l1-norm based feature selection methods have shown promising results. But, in presence of correlated features, these methods select features that change considerably with small changes in data. This prevents clinicians to obtain a stable feature set, which is crucial for clinical decision making. Grouping correlated variables together can improve the stability of feature selection, however, such grouping is usually not known and needs to be estimated for optimal performance. Addressing this problem, we propose a new model that can simultaneously learn the grouping of correlated features and perform stable feature selection. We formulate the model as a constrained optimization problem and provide an efficient solution with guaranteed convergence. Our experiments with both synthetic and real-world datasets show that the proposed model is significantly more stable than Lasso and many existing state-of-the-art shrinkage and classification methods. We further show that in terms of prediction performance, the proposed method consistently outperforms Lasso and other baselines. Our model can be used for selecting stable risk factors for a variety of healthcare problems, so it can assist clinicians toward accurate decision making.