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DOI: 10.4230/DagSemProc.06051.11
URN: urn:nbn:de:0030-drops-6305
URL: https://drops.dagstuhl.de/opus/volltexte/2006/630/
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V'Yugin, Vladimir

On impossibility of sequential algorithmic forecasting

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06051.VYuginVladimir.Paper.630.pdf (0.2 MB)


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}.

BibTeX - Entry

@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.dagstuhl.de/opus/volltexte/2006/630},
  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}
}

Keywords: Universal forecasting, computable calibration, Dawid's prequential framework, algorithmic randomness, defensive forecasting
Collection: 06051 - Kolmogorov Complexity and Applications
Issue Date: 2006
Date of publication: 31.07.2006


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