On the generating process and the class typicality measure

In this paper, we consider the stochastic generating process—one of the key concepts of the Evolving Transformation System model [1]—from the formal perspective. First, we give an informal definition of the generating process supported by some intuitive assumptions and consider several examples. Then, we formally define the concept of the generating process as a continuous parameter (c.p.) Markov chain. Some important random variables associated with this c.p. Markov chain are introduced next, followed by the definition of the typicality measure. Two methods for the computation of the typicality measure are proposed. In conclusion, we discuss the problem of compactification of the state space for the c.p. Markov chain. This problem is not only interesting from the points of view of topology and of the c.p. Markov chains theory, but also has important implications for the ETS model, since it is related to the problem of class comparison and to the proper formulation of the learning problem.