Nonlinear Association

Why we need nonlinear association

Correlation cannot reveal nonlinear relation between variables: exponential, logistic, quadric, cubic...

Which methods can measure nonlinear association

Distance Correlation

Distance Correlation is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension:

d C o r (X, Y) = \frac{d C o v (X, Y)}{\sqrt{d V a r (X) d V a r (Y)}}

ranging from 0 to 1: 0 = no association
symmetric: dCor(X, Y) = dCor(Y, X)
comparing to Pearson's correlation

Mutual information

see Information theory and Entropy in Neuroscience#Mutual Information

cons: no range limit, hard to interpret