A new definition for feature selection stability analysis

Feature selection (FS) stability is an important topic of recent interest. Finding stable features is important for creating reliable, non-overfitted feature sets, which in turn can be used to generate machine learning models with better accuracy and explanations and are less prone to adversarial attacks. There are currently several definitions of FS stability that are widely used. In this paper, we demonstrate that existing stability metrics fail to quantify certain key elements of many datasets such as resilience to data drift or non-uniformly distributed missing values. To address this shortcoming, we propose a new definition for FS stability inspired by Lyapunov stability in dynamic systems. We show the proposed definition is statistically different from the classical record-stability on (n=90) datasets. We present the advantages and disadvantages of using Lyapunov and other stability definitions and demonstrate three scenarios in which each one of the three proposed stability metrics is best suited.