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Why is conditional independence more important than marginal independence?
Graphical models are based on the idea of representing certain types of conditional independences in a (joint) distribution via a graph, and are an active research area.
As argued (correctly I believe ...
2
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Canonical Correlation as a measure of multivariate dependence
Canonical correlation is used as a measure of dependence between multivariate vectors $\mathbf{X}$ and $\mathbf{Y}$, by finding vectors $\mathbf{a}$ and $\mathbf{b}$, respectively, such that $corr(\...