A plug-in approach to maximising precision at the top and recall at the top
This provides a theoretical foundation for optimizing top-k metrics in retrieval and classification tasks, though it is incremental as it builds on prior work.
The paper demonstrates that thresholding the posterior probability of the positive class maximizes precision at the top and recall at the top in information retrieval and binary classification, generalizing an earlier result on constrained minimization of cost-sensitive expected classification error.
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.