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When a bivariate distribution is jointly Gaussian, it means that the dependence structure is correlation. Therefore, mutual information and correlation magnitude between the marginals become synonyms. Note, however, that the mutual information does not give you the direction of correlation (nor should it).


This quantity seems to have an interpretation in terms of top canonical correlation, from 19.7 of Matrix Tricks for Linear Statistical Models: Our Personal Top Twenty 2011th edition,

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