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.
KeywordsProduction Rule Inductive Inference Kolmogorov Complexity Derivation Tree Probabilistic Induction
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- 3.Solomonoff, R.J.: Progress in incremental machine learning. In: NIPS Workshop on Universal Learning Algorithms and Optimal Search, Whistler, B.C (2002)Google Scholar
- 6.Cramer, N.L.: A representation for the adaptive generation of simple sequential programs. In: Grefenstette, J.J. (ed.) Int. Conf. on Genetic Algorithms and Their Applications, Lawrence Erlbaum Ass., Hillsdale, N.J, pp. 183–187 (1985)Google Scholar
- 7.Whigham, P.A.: Grammatical Bias for Evolutionary Learning. PhD thesis, School of Computer Science. University of New South Wales, Australia (1996)Google Scholar
- 9.Hipel, K.W., McLeod, A.I.: Time Series Modelling of Water Resources and Environmental Systems. Elsevier, Amsterdam (1994)Google Scholar