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An exact analytical relation among recall , precision , and classification accuracy in information retrieval

From a machine learning perspective, information retrieval may be viewed as a problem of classifying items into one of two classes corresponding to interesting and uninteresting items respectively. A natural performance metric in this context is classification accuracy, defined as the fraction of the system’s interesting/uninteresting predictions that agree with the user’s assessments. On the other hand, the field of information retrieval has two classical performance evaluation metrics: precision, the fraction of the items retrieved by the system that are interesting to the user, and recall, the fraction of the items of interest to the user that are retrieved by the system. In the present paper we present for the first time a general mathematical relation linking classification accuracy with precision and recall. Our relation provides an analytical tool that promises to be useful in theoretical and applied work in information retrieval. As a significant example in this direction, we show that our relation implies a trade-off between recall and precision under certain conditions on the accuracy.