Integrated path stability selection

Stability selection is a popular method for improving feature selection algorithms. One of its key attributes is that it provides theoretical upper bounds on the expected number of false positives, E(FP), enabling false positive control in practice. However, stability selection often selects few features because existing bounds on E(FP) are relatively loose. In this paper, we introduce a novel approach to stability selection based on integrating stability paths rather than maximizing over them. This yields upper bounds on E(FP) that are much stronger than previous bounds, leading to significantly more true positives in practice for the same target E(FP). Furthermore, our method requires no more computation than the original stability selection algorithm. We demonstrate the method on simulations and real data from two cancer studies.