Bayes-optimal Hierarchical Classification over Asymmetric Tree-Distance Loss

TL;DR

This paper extends hierarchical classification methods to asymmetric tree-distance loss, providing an efficient algorithm to find Bayes optimal classifiers in k-ary hierarchies, improving upon previous symmetric loss approaches.

Contribution

It introduces a novel algorithm for Bayes optimal classification under asymmetric tree-distance loss and extends existing hierarchical classification algorithms to this new setting.

Findings

The algorithm runs in O(nk log n) time for k-ary trees.

Bayes optimal classification can be computed in O(k log n) under certain conditions.

Extension of Ova-Cascade algorithm to asymmetric loss.

Abstract

Hierarchical classification is supervised multi-class classification problem over the set of class labels organized according to a hierarchy. In this report, 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 $\mathcal{O}(nk\log{}n)$ algorithm to find Bayes optimal classification for a k-ary tree as a hierarchy. We show that under reasonable assumptions over asymmetric loss function, the Bayes optimal classification over this asymmetric loss can be found in $\mathcal{O}(k\log{}n)$. We exploit this insight and attempt to extend the Ova-Cascade algorithm \citet{ramaswamy2015convex} for hierarchical classification over the asymmetric loss.