Alternating conditional expectations: Difference between revisions

Revision as of 13:51, 8 August 2018

Revision as of 23:05, 4 January 2019

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==Bivariate case==

The opticaloptimal transformation <math>\theta^*(Y), \varphi^*(X)</math> for <math>p=1</math> satisfies

: <math> \rho^*(X, Y) = \rho^*(\theta^*, \varphi^*) = \max_{\theta, \varphi} \rho(\theta(Y), \varphi(X))</math>

where <math>\rho</math> is [[Pearson correlation coefficient]]. <math> \rho^*(X, Y)</math> is known as the maximal correlation between <math>X</math> and <math>Y</math>. It can be used as a general measure of dependence.