Inferring the finest pattern of mutual independence from data

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 mu(X) when the data are independent and identically (i.i.d.) realizations of a multivariate normal distribution. If (Delta) over cap (X) is the estimated set of valid patterns of dichotomic independence, we estimate mu( X) as the intersection of all patterns of (Delta) over cap( 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.