The risk of trivial solutions in bipartite top ranking

Aditya Krishna Menon

doi:10.1007/s10994-018-5759-4

The risk of trivial solutions in bipartite top ranking

Aditya Krishna Menon^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 performance measure 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.

Original language	English
Pages (from-to)	627-658
Number of pages	32
Journal	Machine Learning
Volume	108
Issue number	4
DOIs	https://doi.org/10.1007/s10994-018-5759-4
Publication status	Published - 15 Apr 2019

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AB - 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 performance measure 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.

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The risk of trivial solutions in bipartite top ranking

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