Predicting Time-Varying Functions with Local Models

Abstract

Data analysis applications which have to cope with changing environments require adaptive models. In these cases, it is not sufficient to train e.g. a neural network off-line with no further learning during the actual operation. Therefore, we are concerned with developing algorithms for approximating time-varying functions from data. We assume that the data arrives sequentially and we require an immediate update of the approximating function. The algorithm presented in this paper uses local linear regression models with adaptive kernel functions describing the validity region of a local model. As we would like to anticipate changes instead of just following the time-varying function, we use the time explicitly as an input. An example is given to demonstrate the learning capabilities of the algorithm.