PAC-Learning of Markov Models with Hidden State

  • Ricard Gavaldà
  • Philipp W. Keller
  • Joelle Pineau
  • Doina Precup
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4212)

Abstract

The standard approach for learning Markov Models with Hidden State uses the Expectation-Maximization framework. While this approach had a significant impact on several practical applications (e.g. speech recognition, biological sequence alignment) it has two major limitations: it requires a known model topology, and learning is only locally optimal. We propose a new PAC framework for learning both the topology and the parameters in partially observable Markov models. Our algorithm learns a Probabilistic Deterministic Finite Automata (PDFA) which approximates a Hidden Markov Model (HMM) up to some desired degree of accuracy. We discuss theoretical conditions under which the algorithm produces an optimal solution (in the PAC-sense) and demonstrate promising performance on simple dynamical systems.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ricard Gavaldà
    • 1
  • Philipp W. Keller
    • 2
  • Joelle Pineau
    • 2
  • Doina Precup
    • 2
  1. 1.Universitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.School of Computer ScienceMcGill UniversityMontrealCanada

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