Empirically-estimable multi-class classification bounds

Abstract

In this paper, we extend previously developed non-parametric bounds on the Bayes risk in binary classification problems to multi-class problems. In comparison with the well-known Bhattacharyya bound which is typically calculated by employing parametric assumptions, the bounds proposed in this paper are directly estimable from data, provably tighter, and more robust to different types of data. We verify the tightness and validity of this bound using an illustrative synthetic example, and further demonstrate its value by incorporating it into a feature selection algorithm which we apply to the real-world problem of distinguishing between different neuro-motor disorders based on sentence-level speech data.