# Mutual information between sets of variables

I found in this paper (PDF) a mutual information between groups of variables such as these:

• I(X;Y|F)
• I(F;Y)
• I(F;Y|G)

where F is a set of variables, and G is a set of sets of variables. I am neither statistician nor mathematician, but I have a fair knowledge about mutual information, and I do know how to calculate mutual information between two variables I(X;Y) if we have $n$ samples of X and Y. Can anyone help me do the same for the formulas above? Thanks.

• It may impact the kinds of answers that may be relevant -- what kind of approach would you tend to use to calculate $I(X; Y)$ between the $X$ and $Y$ observations in a sample of $n$ observations on $(X,Y)$? – Glen_b Mar 18 '14 at 19:34
• I intend to use this formula. Th joint and marginal probabilities can be estimated by a kernel function (e.g. Gaussian or epanechnikov) – Osama Salah Mar 18 '14 at 19:54