An empirical dependence mesaures based on residual variance estimation

In this paper, a solution to empirical dependency measure is proposed. The main idea is to use the notion of predictability as a basis for dependency definition. Considering any nonlinear regression function between two random variables, the power of regression residuals or noise variance defines the desired dependency measure. The residuals variance can be directly computed by estimators without finding the best fit curve. The paper shows the conditions on which two random variables are independent according to the estimated residuals variance. The existence of residual variance, or noise variance estimators make it possible to define such practical measure for dependency. The dependency measure finds wide areas of applications in signal processing and machine learning. In this paper, solutions for Independent Component Analysis and input selection using the proposed dependency measure are discussed.