We consider the use of nonparametric evaluation of mutual information to determine the relationship between random variables. It is shown that in the presence of a nonlinear relationship between random variables, the correlation coefficient can give an incorrect result. A method is proposed for constructing an evaluation of mutual information from empirical data in an abstract reproducing-kernel Hilbert space. Using the generalized representer theorem, a method for nonparametric evaluation of mutual information is proposed. The operability of the method is demonstrated using the examples of the analysis of artificial data. The application of the method in predicting the stability of pentapeptides is described.