Unachievable Region in Precision-Recall Space and Its Effect on Empirical Evaluation
This addresses a methodological issue for researchers and practitioners using precision-recall metrics, particularly in skewed datasets, but is incremental as it builds on known properties of PR curves.
The paper identifies a previously unrecognized unachievable region in precision-recall space that depends solely on class skew, precisely characterizing its size and discussing implications for empirical evaluation in machine learning.
Precision-recall (PR) curves and the areas under them are widely used to summarize machine learning results, especially for data sets exhibiting class skew. They are often used analogously to ROC curves and the area under ROC curves. It is known that PR curves vary as class skew changes. What was not recognized before this paper is that there is a region of PR space that is completely unachievable, and the size of this region depends only on the skew. This paper precisely characterizes the size of that region and discusses its implications for empirical evaluation methodology in machine learning.