Almost sure and mean convergence of extended stochastic complexity

Masayuki Gotoh*, Toshiyasu Matsushima, Shigeichi Hirasawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number10
Publication statusPublished - 1999 Jan 1


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

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


Dive into the research topics of 'Almost sure and mean convergence of extended stochastic complexity'. Together they form a unique fingerprint.

Cite this