## Abstract

The notions of predictive complexity and of corresponding amount of information are considered. Predictive complexity is a generalization of Kolmogorov complexity which bounds the ability of any algorithm to predict elements of a sequence of outcomes. We consider predictive complexity for a wide class of bounded loss functions which are generalizations of square-loss function. Relations between unconditional KG(x) and conditional KG(x|y) predictive complexities are studied. We define an algorithm which has some "expanding property". It transforms with positive probability sequences of given predictive complexity into sequences of essentially bigger predictive complexity. A concept of amount of predictive information IG(y:x) is studied. We show that this information is noncommutative in a very strong sense and present asymptotic relations between values IG(y:x), IG(x:y), KG(x) and KG(y).

Original language | English |
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Pages (from-to) | 539-554 |

Number of pages | 16 |

Journal | Journal of Computer and System Sciences |

Volume | 70 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jun 2005 |

Externally published | Yes |

## Keywords

- Algorithmic prediction
- Expanding property
- Kolmogorov complexity
- Loss functions
- Machine learning
- Predictive complexity
- Predictive information