On-line probability, complexity and randomness

Alexey Chernov; Alexander Shen; Nikolai Vereshchagin; Vladimir Vovk

doi:10.1007/978-3-540-87987-9_15

On-line probability, complexity and randomness

Alexey Chernov
, Alexander Shen
, Nikolai Vereshchagin
, Vladimir Vovk

University of Bedfordshire

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

11 Citations (Scopus)

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.

Original language	English
Title of host publication	nan
Publisher	Springer
ISBN (Electronic)	9783540879862
ISBN (Print)	9783540879862
DOIs	https://doi.org/10.1007/978-3-540-87987-9_15
Publication status	Published - 1 Jan 2008
Event	Algorithmic Learning Theory 2008 - Duration: 1 Jan 2008 → …

Conference

Conference	Algorithmic Learning Theory 2008
Period	1/01/08 → …
Other	Algorithmic Learning Theory 2008

Keywords

randomness

Access to Document

10.1007/978-3-540-87987-9_15

http://link.springer.com/chapter/10.1007/978-3-540-87987-9_15

Handle.net

Persistent link

Cite this

@inproceedings{ebee39bae098474fb35effc8fa625c3c,

title = "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.",

keywords = "randomness",

author = "Alexey Chernov and Alexander Shen and Nikolai Vereshchagin and Vladimir Vovk",

year = "2008",

month = jan,

day = "1",

doi = "10.1007/978-3-540-87987-9\_15",

language = "English",

isbn = "9783540879862",

booktitle = "nan",

publisher = "Springer",

address = "Germany",

note = "Algorithmic Learning Theory 2008 ; Conference date: 01-01-2008",

}

TY - GEN

T1 - On-line probability, complexity and randomness

AU - Chernov, Alexey

AU - Shen, Alexander

AU - Vereshchagin, Nikolai

AU - Vovk, Vladimir

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 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.

AB - 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.

KW - randomness

U2 - 10.1007/978-3-540-87987-9_15

DO - 10.1007/978-3-540-87987-9_15

M3 - Conference contribution

SN - 9783540879862

BT - nan

PB - Springer

T2 - Algorithmic Learning Theory 2008

Y2 - 1 January 2008

ER -

On-line probability, complexity and randomness

Abstract

Conference

Keywords

Access to Document

Handle.net

Fingerprint

Cite this