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Abstract:
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In this talk four natural axioms of dependent measures D(X,Y)for Hilbert space valued random variables X and Y will be stated: (i) D(X,Y) = 0 iff X and Y are independent, (ii) D(X,X) = 1, (iii) D is invariant with respect to similarity transformations of the Hilbert space, (iv)D is continuous with respect to weak convergence of bounded sequences of random variables. --- We will see that classical measures of dependence, like correlation, maximal correlation, etc. do not satisfy some of these axioms. The same holds for the newly introduced maximal information coefficient. Distance correlation introduced by the speaker twelve years ago does satisfy all axioms above.
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