Look at the relationship between MI and correlation for binary vars (since it's quicker than doing the maths)

compCorrMI.R

#Check the relationship between correlation and mutual information for binary vars
store<-NULL
for (i in 1:1000){
  prob.1<-runif(1)
  prob.2<-runif(1)
  x<-rbinom(10000, 1, prob.1)
  y<-rbinom(10000, 1, prob.2)
  c<-cor(x,y)
  m<-mi.empirical(table(x,y))
  store<-rbind(store, data.frame(c=c, m=m))
}
plot(store)