Kernel regression with autocorrelation prior

In this paper, we discuss a function reconstruction problem by kernel regressors in which the autocorrelation of the unknown true function is given a priori. In general, a reconstructed function in the kernel regression problem, using a certain reproducing kernel Hilbert space, is represented by a linear combination of the corresponding kernel specified by each input point. We introduce a framework to reflect the autocorrelation prior of the unknown true function on the estimation of the coefficients for the linear combination; and give a closed-form solution of the optimal coefficients. We also give numerical examples, using the popular Gaussian kernel, to confirm the behavior of the proposed method.