Working with multiple variables they usually contain difficult to control complex dependencies. This article proposes extraction of their individual information, e.g. $\overline{X|Y}$ as random variable containing information from $X$, 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: $\forall_{i\neq j} \tilde{X}_i\perp \tilde{X}_j, \tilde{X}_i\perp X_j$. It requires detailed models of complex conditional probability distributions - it is generally a difficult task, but here can be done through multiple dependency reducing iterations, using imperfect methods (here HCR: Hierarchical Correlation Reconstruction). It could be also used for direct mutual information - evaluating direct information transfer: without use of intermediate variables. For causality direction there is discussed multi-feature Granger causality, e.g. to trace various types of individual information transfers between such decoupled variables, including propagation time (delay).

翻译：处理多变量时，通常存在难以控制的复杂依赖关系。本文提出提取变量个体信息的方法，例如将 $\overline{X|Y}$ 作为包含 $X$ 信息但去除 $Y$ 信息的随机变量，通过 $(x,y) \leftrightarrow (\bar{x}=\textrm{CDF}_{X|Y=y}(x),y)$ 可逆归一化实现。其应用之一是实现变量个体信息的去耦：通过可逆变换 $(X_1,\ldots,X_n)\leftrightarrow(\tilde{X}_1,\ldots \tilde{X}_n)$ 使变量集包含相同信息但相互独立，即 $\forall_{i\neq j} \tilde{X}_i\perp \tilde{X}_j, \tilde{X}_i\perp X_j$。该过程需要复杂条件概率分布的精细建模——这通常是一项困难任务，但可通过多重依赖递减迭代（使用非完美方法，本文采用HCR：层次化相关性重建）实现。该方法还可用于直接互信息计算，即评估直接信息传递（避免使用中介变量）。在因果关系方向方面，本文讨论多特征格兰杰因果关系，例如追溯此类去耦变量间各种类型的个体信息传递（包含传播时间延迟）。