On-Line Probability, Complexity and Randomness
Abstract
Classical 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.
Cite
Text
Chernov et al. "On-Line Probability, Complexity and Randomness." International Conference on Algorithmic Learning Theory, 2008. doi:10.1007/978-3-540-87987-9_15Markdown
[Chernov et al. "On-Line Probability, Complexity and Randomness." International Conference on Algorithmic Learning Theory, 2008.](https://mlanthology.org/alt/2008/chernov2008alt-online/) doi:10.1007/978-3-540-87987-9_15BibTeX
@inproceedings{chernov2008alt-online,
title = {{On-Line Probability, Complexity and Randomness}},
author = {Chernov, Alexey V. and Shen, Alexander and Vereshchagin, Nikolai K. and Vovk, Vladimir},
booktitle = {International Conference on Algorithmic Learning Theory},
year = {2008},
pages = {138-153},
doi = {10.1007/978-3-540-87987-9_15},
url = {https://mlanthology.org/alt/2008/chernov2008alt-online/}
}