Non-parametric learning algorithms in time-varying environments

Abstract

A non-parametric recursive algorithm is investigated from the viewpoint of learning properties in a time-varying environment. The algorithm is based on the kernels used in the non-parametric estimation of probability density and regression functions. The procedure possesses tracking properties as the sample size grows large and the conditions for the mean square error convergence and the almost sure convergence are given. Applications to non-parametric learning of time-varying probability densities and non-parametric prediction of time-varying conditional means are discussed. An illustrative simulation example is presented to show that the algorithm converges even if a time-varying function to be tracked diverges. A great advantage of the approach is that it does not require a finite parametrization of unknown time-varying functions. The method is applicable for relatively slow non-stationary changes.