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For a random variable $X$, we are interested in the blind extraction of itsfinest mutual independence pattern $\mu ( X )$. We introduce a specific kind ofindependence that we call dichotomic. If $\Delta ( X )$ stands for the set ofall patterns of dichotomic independence that hold for $X$, we show that $\mu (X )$ can be obtained as the intersection of all elements of $\Delta ( X )$. Wethen propose a method to estimate $\Delta ( X )$ when the data are independentand identically (i.i.d.) realizations of a multivariate normal distribution. If$\hat{\Delta} ( X )$ is the estimated set of valid patterns of dichotomicindependence, we estimate $\mu ( X )$ as the intersection of all patterns of$\hat{\Delta} ( X )$. The method is tested on simulated data, showing itsadvantages and limits. We also consider an application to a toy example as wellas to experimental data.

Inferring the finest pattern of mutual independence from data