  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.
