Inferring the finest pattern of mutual independence from data
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For a random variable X, we are interested in the blind extraction of its finest mutual independence pattern μ ( X ). We introduce a specific kind of independence that we call dichotomic. If Δ ( X ) stands for the set of all patterns of dichotomic independence that hold for X, we show that μ ( X ) can be obtained as the intersection of all elements of Δ ( X ). We then propose a method to estimate Δ ( X ) when the data are independent and identically (i.i.d.) realizations of a multivariate normal distribution. If Δ̂ ( X ) is the estimated set of valid patterns of dichotomic independence, we estimate μ ( X ) as the intersection of all patterns of Δ̂ ( 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.
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