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On impossibility of sequential algorithmic forecasting

Author Vladimir V'Yugin



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Vladimir V'Yugin

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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)
https://doi.org/10.4230/DagSemProc.06051.11

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}.
Keywords
  • Universal forecasting
  • computable calibration
  • Dawid's prequential framework
  • algorithmic randomness
  • defensive forecasting

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