Almost sure and mean convergence of extended stochastic complexity

Masayuki Goto, Toshiyasu Matsushima, Shigeichi Hirasawa

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    Abstract

    We analyze the extended stochastic complexity (ESC) which has been proposed by K. Yamanishi. The ESC can be applied to learning algorithms for on-line prediction and batch-learning settings. Yamanishi derived the upper bound of ESC satisfying uniformly for all data sequences and that of the asymptotic expectation of ESC. However, Yamanishi concentrates mainly on the worst case performance and the lower bound has not been derived. In this paper, we show some interesting properties of ESC which are similar to Bayesian statistics: the Bayes rule and the asymptotic normality. We then derive the asymptotic formula of ESC in the meaning of almost sure and mean convergence within an error of o(1) using these properties.

    Original languageEnglish
    Pages (from-to)2129-2134
    Number of pages6
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    VolumeE82-A
    Issue number10
    Publication statusPublished - 1999

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    Keywords

    • Asymptotic normality
    • Bayesian statistics
    • Extended stochastic complexity
    • Stochastic complexity

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Hardware and Architecture
    • Information Systems

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