Bayes-optimal Hierarchical Classification over Asymmetric Tree-Distance Loss


Hierarchical classification is supervised multi-class classification problem over the set of class labels organized according to a hierarchy. In this project, we study the work by Ramaswamy et al. on hierarchical classification over symmetric tree distance loss. We extend the consistency of hierarchical classification algorithm over asymmetric tree distance loss. We design a O(nk log n) algorithm to find bayes optimal classification for a k-ary tree as hierarchy. We show that under reasonable assumptions over asymmetric loss function, the Bayes optimal classification over this asymmetric loss can be found in O(k log n). We exploit this insight and attempt to extend the Ova-Cascade algorithm Ramaswamy et al. for hierarchical classification over asymmetric loss