Inferring the finest pattern of mutual independence from data
G. Marrelec A. Giron
For a random variable $X$, we are interested in the blind extraction of its
finest mutual independence pattern $\mu ( X )$. We introduce a specific kind of
independence that we call dichotomic. If $\Delta ( X )$ stands for the set of
all patterns of dichotomic independence that hold for $X$, we show that $\mu (
X )$ can be obtained as the intersection of all elements of $\Delta ( X )$. We
then propose a method to estimate $\Delta ( X )$ when the data are independent
and identically (i.i.d.) realizations of a multivariate normal distribution. If
$\hat{\Delta} ( X )$ is the estimated set of valid patterns of dichotomic
independence, we estimate $\mu ( X )$ as the intersection of all patterns of
$\hat{\Delta} ( X )$. The method is tested on simulated data, showing its
advantages and limits. We also consider an application to a toy example as well
as to experimental data.