The risk of trivial solutions in bipartite top ranking

Abstract

Given a sample of instances with binary labels, the bipartite top ranking problem is to produce a ranked list of instances whose head is dominated by positives. One popular existing approach to this problem is based on constructing surrogates to a performancemeasure known as the fraction of positives of the top (PTop). In this paper, we theoretically show that the measure and its surrogates have an undesirable property: for certain noisy distributions, it is optimal to trivially predict the same score for all instances.We propose a simple rectification which avoids such trivial solutions, while still focussing on the head of the ranked list and being as easy to optimise.