Extending greedy feature selection algorithms to multiple solutions

Most feature selection methods identify only a single solution. This is acceptable for predictive purposes, but is not sufficient for knowledge discovery if multiple solutions exist. We propose a strategy to extend a class of greedy methods to efficiently identify multiple solutions, and show under which conditions it identifies all solutions. We also introduce a taxonomy of features that takes the existence of multiple solutions into account. Furthermore, we explore different definitions of statistical equivalence of solutions, as well as methods for testing equivalence. A novel algorithm for compactly representing and visualizing multiple solutions is also introduced. In experiments we show that (a) the proposed algorithm is significantly more computationally efficient than the TIE* algorithm, the only alternative approach with similar theoretical guarantees, while identifying similar solutions to it, and (b) that the identified solutions have similar predictive performance.