V'Yugin, Vladimir
On impossibility of sequential algorithmic forecasting
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 $omega_1,dots, omega_{n1}$
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 cointossing 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:DSP:2006:630,
author = {Vladimir V'Yugin},
title = {On impossibility of sequential algorithmic forecasting},
booktitle = {Kolmogorov Complexity and Applications},
year = {2006},
editor = {Marcus Hutter and Wolfgang Merkle and Paul M.B. Vitanyi},
number = {06051},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Internationales Begegnungs und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2006/630},
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 
Seminar: 

06051  Kolmogorov Complexity and Applications

Issue date: 

2006 
Date of publication: 

31.07.2006 