It was first introduced by Henri Theil[citation needed] and is based on the concept of information entropy.
The above expression makes clear that the uncertainty coefficient is a normalised mutual information I(X;Y).
The uncertainty coefficient is useful for measuring the validity of a statistical classification algorithm and has the advantage over simpler accuracy measures such as precision and recall in that it is not affected by the relative fractions of the different classes, i.e., P(x).
[4] It also has the unique property that it won't penalize an algorithm for predicting the wrong classes, so long as it does so consistently (i.e., it simply rearranges the classes).
The roles can be reversed and a symmetrical measure thus defined as a weighted average between the two:[2] Although normally applied to discrete variables, the uncertainty coefficient can be extended to continuous variables[1] using density estimation.