A genetic programming approach to Solomonoff's probabilistic induction

In the context of Solomonoff's Inductive Inference theory, Induction operator plays a key role in modeling and correctly predicting the behavior of a given phenomenon. Unfortunately, this operator is not algorithmically computable. The present paper deals with a Genetic Programming approach to Inductive Inference, with reference to Solomonoff's algorithmic probability theory, that consists in evolving a population of mathematical expressions looking for the 'optimal' one that generates a collection of data and has a maximal a priori probability. Validation is performed on Coulomb's Law, on the Henon series and on the Arosa Ozone time series. The results show that the method is effective in obtaining the analytical expression of the first two problems, and in achieving a very good approximation and forecasting of the third.