I am running the pc-algorithm for causal networks. In this algorithm, I need to verify if two arrays $X$ and $Y$ are independent given a set of arrays $Z_1,\ldots, Z_n$. In papers, it is usually assumed gaussian independence tests, which I am trying not to use in favor of a more generic approach. I tried to use mutual information, but as can be seen in my discussion of yesterday, mutual information doesn't seem to be a good approach.
Question.Is there a rule or property which allows me to evaluate if $X$ and $Y$ are independent given $Z = Z_1,\ldots, Z_n$? All sources I found so far concern only the case in which $Z$ has the same dimension as $X$ and $Y$.

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  • $\begingroup$ Sorry, as stated your problem is completely unintelligible. Otherwise, if as in mathoverflow.net/questions/364546/… $Z = X + Y$ with (there) independent random vectors $X$ and $Y$, then if $(X$ and $Y$ are not "too simple" (f.i. constant), then $X$ and $Y$ are not conditionally independent. I think that's not what you want to know, but what? The pc-algorithm is completely irrelevant in this situation. $\endgroup$ – Dieter Kadelka yesterday

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