The original presentation of information theory by Shannon applied specifically to the transmission of a message of length N from a source to a destination across a noisy channel. In the time since the original publication, information theory has been applied to a wide variety of applications . To generalize beyond the communication problem, we will assume that a bivariate set of data z i = (x i , y i ), i = 1, ..., N has been gathered. The data sets x or y can be of any dimension. We will assume that each of the N elements of the data are independent and identically distributed realizations of the random variables Z = (X, Y ), and that the they are distributed according to µ(x, y), a proper smooth function. The marginal densities are µ(x) = µ(x, y)dy and µ(y) = µ(x, y)dx