Almost sure and mean convergence of extended stochastic complexity

摘要

We analyze the extended stochastic complex- ity(ESC)which has beenproposed by K. Yamanishi. The ESC can be applied to learningalgorithm for on-line prediction and batch-learning settings.Yamanishi derived the upper bound of ESC satisfying uniformly for alldata sequences and that of the Asymptotic expectation of ESC.However, Yamanishi concen- Trates mainly on the worst caseperformance and the lower bound Has not been derived. In this paper,we show some interesting Properties of ESC which are similar toBayesian statistics: the Bayes rule and the asymptotic normality.