Experimental Study of Ergodic Learning Curve in Hidden Markov Models

  • Masashi Matsumoto
  • Sumio Watanabe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5506)


A number of learning machines used in information science are not regular, but rather singular, because they are non-identifiable and their Fisher information matrices are singular. Even for singular learning machines, the learning theory was developed for the case in which training samples are independent. However, if training samples have time-dependency, then learning theory is not yet established. In the present paper, we define an ergodic generalization error for a time-dependent sequence and study its behavior experimentally in hidden Markov models. The ergodic generalization error is clarified to be inversely proportional to the number of training samples, but the learning coefficient depends strongly on time-dependency.


Training Sample Hide Markov Model True Parameter Hide State Predictive Distribution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Masashi Matsumoto
    • 1
  • Sumio Watanabe
    • 2
  1. 1.Department of Computational Intelligence and Systems ScienceTokyo Institute of TechnologyYokohamaJapan
  2. 2.Precision and Intelligence LaboratoryTokyo Institute of TechnologyYokohamaJapan

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