An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Non-stochastic infinite and finite sequences
Theoretical Computer Science - Special issue Kolmogorov complexity
Introduction to Reinforcement Learning
Introduction to Reinforcement Learning
Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
On the foundations of universal sequence prediction
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Fisher information and stochastic complexity
IEEE Transactions on Information Theory
The context-tree weighting method: basic properties
IEEE Transactions on Information Theory
ALT'11 Proceedings of the 22nd international conference on Algorithmic learning theory
Making solomonoff induction effective: or: you can learn what you can bound
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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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.