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Working with multiple variables they usually contain difficult to controlcomplex dependencies. This article proposes extraction of their individualinformation, e.g. $\overline{X|Y}$ as random variable containing informationfrom $X$, but with removed information about $Y$, by using $(x,y)\leftrightarrow (\bar{x}=\textrm{CDF}_{X|Y=y}(x),y)$ reversible normalization.One application can be decoupling of individual information of variables:reversibly transform $(X_1,\ldots,X_n)\leftrightarrow(\tilde{X}_1,\ldots\tilde{X}_n)$ together containing the same information, but being independent:$\forall_{i\neq j} \tilde{X}_i\perp \tilde{X}_j, \tilde{X}_i\perp X_j$. Itrequires detailed models of complex conditional probability distributions - itis generally a difficult task, but here can be done through multiple dependencyreducing iterations, using imperfect methods (here HCR: HierarchicalCorrelation Reconstruction). It could be also used for direct mutualinformation - evaluating direct information transfer: without use ofintermediate variables. For causality direction there is discussedmulti-feature Granger causality, e.g. to trace various types of individualinformation transfers between such decoupled variables, including propagationtime (delay).

Extracting individual variable information for their decoupling, direct mutual information and multi-feature Granger causality