TY - JOUR
T1 - <em>R</em><sup>2</sup>-equitability is satisfiable
JF - Proceedings of the National Academy of Sciences
JO - Proc Natl Acad Sci USA
SP - E2160
LP - E2160
DO - 10.1073/pnas.1403623111
VL - 111
IS - 21
AU - Murrell, Ben
AU - Murrell, Daniel
AU - Murrell, Hugh
Y1 - 2014/05/27
UR - http://www.pnas.org/content/111/21/E2160.abstract
N2 - Kinney and Atwal (1) make excellent points about mutual information, the maximal information coefficient (2, 3), and “equitability.” One of their central claims, however, is that, “No nontrivial dependence measure can satisfy R2-equitability.” We argue that this is the result of a poorly constructed definition, which we quote:“A dependence measure D[X;Y] is R2-equitable if and only if, when evaluated on a joint probability distribution p(X,Y) that corresponds to a noisy functional relationship between two real random variables X and Y, the following relation holds:D[X;Y]=g(R2[f(X);Y]).Here, g is a function that does not depend on p(X,Y) and f is the function defining the noisy functional relationship, i.e.,Y=f(X)+η … ↵1To whom correspondence should be addressed. E-mail: bmurrell{at}ucsd.edu.
ER -