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Probabilistic independence networks for hidden Markov probability models

P Smyth1, D Heckerman, M I Jordan

  • 1Department of Information and Computer Science, University of California at Irvine 92697-3425, USA.

Neural Computation
|February 15, 1997
PubMed
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This study unifies hidden Markov models (HMMs) and probabilistic independence networks (PINs) using graphical models. It shows HMM algorithms are special cases of general PIN inference, offering new analysis tools for complex models.

Area of Science:

  • Statistics
  • Artificial Intelligence
  • Speech Recognition
  • Genetics
  • Statistical Physics
  • Image Processing

Background:

  • Graphical models are used across diverse fields to represent dependencies between random variables.
  • Formalisms for these models developed independently in various research communities.
  • Hidden Markov Models (HMMs) are a prominent example of such graphical models.

Purpose of the Study:

  • To present a unified framework for understanding Hidden Markov Models (HMMs) within Probabilistic Independence Networks (PINs).
  • To demonstrate that established HMM algorithms are specific instances of more general inference methods for PINs.
  • To introduce advanced analysis tools for HMM practitioners by leveraging the broader graphical model framework.

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Main Methods:

  • Review of the fundamental principles of Probabilistic Independence Networks (PINs).
  • Demonstration of HMM algorithms (Forward-Backward, Viterbi) as special cases of general PIN inference algorithms.
  • Application of general graphical model inference and estimation algorithms to HMMs.

Main Results:

  • Established that Forward-Backward and Viterbi algorithms for HMMs are particular cases of general inference algorithms for PINs.
  • Showcased the utility of general graphical models for analyzing more complex HMM structures.
  • Illustrated the advantages of the unified graphical model approach with examples in sensor fusion and speech coarticulation.

Conclusions:

  • Hidden Markov Models can be effectively represented and analyzed within the broader framework of Probabilistic Independence Networks.
  • The general inference and estimation algorithms for graphical models offer powerful new analytical capabilities for HMMs.
  • This unified approach facilitates the exploration and handling of more complex dependency structures in various applications, including speech recognition.