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On impossibility of sequential algorithmic forecasting

Authors: Vladimir V'Yugin

Published in: Dagstuhl Seminar Proceedings, Volume 6051, Kolmogorov Complexity and Applications (2006)


Abstract
The problem of prediction future event given an individual sequence of past events is considered. Predictions are given in form of real numbers $p_n$ which are computed by some algorithm $varphi$ using initial fragments $omega_1,dots, omega_{n-1}$ of an individual binary sequence $omega=omega_1,omega_2,dots$ and can be interpreted as probabilities of the event $omega_n=1$ given this fragment. According to Dawid's {it prequential framework} %we do not consider %numbers $p_n$ as conditional probabilities generating by some %overall probability distribution on the set of all possible events. we consider partial forecasting algorithms $varphi$ which are defined on all initial fragments of $omega$ and can be undefined outside the given sequence of outcomes. We show that even for this large class of forecasting algorithms combining outcomes of coin-tossing and transducer algorithm it is possible to efficiently generate with probability close to one sequences for which any partial forecasting algorithm is failed by the method of verifying called {it calibration}.

Cite as

Vladimir V'Yugin. On impossibility of sequential algorithmic forecasting. In Kolmogorov Complexity and Applications. Dagstuhl Seminar Proceedings, Volume 6051, pp. 1-7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)


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@InProceedings{vyugin:DagSemProc.06051.11,
  author =	{V'Yugin, Vladimir},
  title =	{{On impossibility of sequential algorithmic forecasting}},
  booktitle =	{Kolmogorov Complexity and Applications},
  pages =	{1--7},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6051},
  editor =	{Marcus Hutter and Wolfgang Merkle and Paul M.B. Vitanyi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06051.11},
  URN =		{urn:nbn:de:0030-drops-6305},
  doi =		{10.4230/DagSemProc.06051.11},
  annote =	{Keywords: Universal forecasting, computable calibration, Dawid's prequential framework, algorithmic randomness, defensive forecasting}
}
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