Modeling by Non-Parametric Regression

Abstract

In the previous chapter on the adaptive modeling of natural laws it was stated that tasks associated with such modeling included the estimation and storage of the probability distribution, as well as the development of a method for its effective application. The fundamental problem related to the application of a natural law is the formulation of a method by which some unknown property of Nature can be predicted on the basis of information obtained by partial observation and a known natural law. If a natural law which is expressed as a functional relationship between various physical variables is to be applied, the task is to find the values of some variables from the given values of others by arithmetic procedures. If a natural law is represented by a model contained in a certain physical system then this task corresponds to the projection of a set of inputs into a set of outputs. However, this concept must be generalized when a natural law is represented by a probability density. To do this, we use some of the fundamental concepts of prediction theory which will be briefly reviewed in the next part of this section. The main goal of this chapter is to demonstrate the solution of several problems related with an optimal application of empirical information, stored as a set of representative points in a discrete memory of a modeler.