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AbstractClassical probability theory considers probability distributions that assign probabilities to all events (at least in the finite case). However, there are natural situations where only part of the process is controlled by some probability distribution while for the other part we know only the set of possibilities without any probabilities assigned. We adapt the notions of algorithmic information theory (complexity, algorithmic randomness, martingales, a priori probability) to this framework and show that many classical results are still valid.
CitationChernov, A., Shen, A., Vereshchagin, N. and Vovk , V., (2008) 'On-Line Probability, Complexity and Randomness' in Algorithmic Learning Theory, proceedings on the 19th International Conference, ALT 2008, vol. 5254: 138-153
JournalAlgorithmic Learning Theory
TypeConference papers, meetings and proceedings