Solomonoff's inductive learning model is a powerful, universal and highly elegant theory of sequence prediction. Its critical flaw is that it is incomputable and thus cannot be used in practice. It is sometimes suggested that it may still be useful to help guide the development of very general and powerful theories of prediction which are computable. In this paper it is shown that although powerful algorithms exist, they are necessarily highly complex. This alone makes their theoretical analysis problematic, however it is further shown that beyond a moderate level of complexity the analysis runs into the deeper problem of Gödel incompleteness. This limits the power of mathematics to analyse and study prediction algorithms, and indeed intelligent systems in general.
Unfortunately this model is incomputable, and in REF it is shown furthermore that some sequences can only be predicted by very complex predictors which cannot be discovered mathematically due to problems of Gödel incompleteness.
Is there an Elegant Universal Theory of Prediction?
ArXiv
ArXiv
Computer Science