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.

翻译：对于随机变量 $X$，我们关注其最精细相互独立模式 $\mu ( X )$ 的盲提取。我们引入一种称为二分独立性的特定独立性类型。若 $\Delta ( X )$ 表示 $X$ 所满足的所有二分独立模式构成的集合，我们证明 $\mu ( X )$ 可表示为 $\Delta ( X )$ 中所有元素的交集。进而，当数据为多元正态分布的独立同分布（i.i.d.）实现时，我们提出一种估计 $\Delta ( X )$ 的方法。设 $\hat{\Delta} ( X )$ 为估计得到的有效二分独立模式集合，我们通过取 $\hat{\Delta} ( X )$ 中所有模式的交集来估计 $\mu ( X )$。该方法在模拟数据上进行了测试，展示了其优势与局限性。此外，我们还考虑了该方法的玩具示例及实验数据的应用。