Genetic Programming for Inductive Inference of Chaotic Series

In the context of inductive inference Solomonoff complexity plays a key role in correctly predicting the behavior of a given phenomenon. Unfortunately, Solomonoff complexity is not algorithmically computable. This paper deals with a Genetic Programming approach to inductive inference of chaotic series, with reference to Solomonoff complexity, that consists in evolving a population of mathematical expressions looking for the `optimal' one that generates a given series of chaotic data. Validation is performed on the Logistic, the Henon and the Mackey-Glass series. The results show that the method is effective in obtaining the analytical expression of the first two series, and in achieving a very good approximation and forecasting of the Mackey-Glass series.