Recall-precision trade-off: A derivation

Abstract

The inexact nature of document retrieval gives rise to a fundamental recall precision trade-off: generally, recall improves at the expense of precision, or precision improves at the expense of recall. This trade-off is borne out empirically and has qualitatively intuitive explanations. In thls artkle, we explore this relationship mathematically to explain it further. We see that the recall-precision trade-off hinges on a deceleration in the proportion of relevant documents which are retrieved, successively, over time. Further, we examine several mathematical functions sharing this property and conclude that the equation that best models recall as a function of time is the logarlthm of a quadratlc function. Our conclusion meets the following requirements: the function we derlve predicts non-decreasing recall over time until the last relevant document is retrieved (regardless of the density of relevant documents in the collection) without imposing any artificial restrictions on elther what percentage of the collection would need to be examined to achieve perfect recall or what the level of precision would be at that time. Other models examined fail to meet one or more of these criteria.

Area under the Precision-Recall Curve: Point Estimates and Confidence Intervals

“…Since larger output values are assumed to be associated with positive examples, as c decreases, Recall(c) increases to one and P rec(c) decreases to π. As c increases, P rec(c) reaches one as Recall(c) approaches zero under the condition that "the first document retrieved is relevant" [9]. In other words, whether the example with the largest output value is positive or negative greatly changes the PR curve (approaching (0, 1) if positive and (0, 0) if negative).…”

Compound key word generation from document databases using a hierarchical clustering ART model

“…Already in these early experiments a trade-off was detected between recall and precision: if recall is too improved, precision worsens and conversely. This inverse relation has been corroborated in recent studies [18,21,24]. An additional problem when using relevance and precision measures is the need to know which documents are relevant for queries formulated to the database.…”

Topic correlation model for cross-modal multimedia information retrieval

“…The retrieval results are compared to the existing state-of-the-art approaches for the following tasks: (1) given an image query from the test set, the retrieval system returns a ranked set of all texts from the training dataset, and (2) query a text to obtain a ranked list of images. The mean average precision (MAP) [37] and precision-recall (PR) curves [38] are adopted to measure the retrieval performance.…”