A plug-in approach to maximising precision at the top and recall at the top

TL;DR

This paper demonstrates that in information retrieval and binary classification, optimal precision at the top and recall at the top are achieved by thresholding the posterior probability, based on a generalized cost-sensitive error minimization.

Contribution

It introduces a plug-in method for maximizing precision and recall at the top by linking these metrics to posterior probability thresholding, extending previous theoretical results.

Findings

Optimal top precision and recall are achieved by thresholding posterior probabilities.

The approach generalizes earlier results on cost-sensitive error minimization.

Provides a practical method for improving ranking performance in retrieval tasks.

Abstract

For information retrieval and binary classification, we show that precision at the top (or precision at k) and recall at the top (or recall at k) are maximised by thresholding the posterior probability of the positive class. This finding is a consequence of a result on constrained minimisation of the cost-sensitive expected classification error which generalises an earlier related result from the literature.