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Factorial hidden Markov models and the generalized backfitting algorithm.

Robert A Jacobs1, Wenxin Jiang, Martin A Tanner

  • 1Department of Brain and Cognitive Sciences, University of Rochester, Rochester, NY 14627, USA. robbie@bcs.rochester.edu

Neural Computation
|October 25, 2002
PubMed
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This study introduces a new, simpler learning algorithm for factorial hidden Markov models (FHMMs) that improves analysis of sequential data. The generalized backfitting algorithm makes FHMMs more accessible and versatile for various data types.

Area of Science:

  • Machine Learning
  • Statistical Modeling
  • Time Series Analysis

Background:

  • Conventional hidden Markov models (HMMs) have been extended for sequential data using distributed state representations.
  • Factorial hidden Markov models (FHMMs) allow approximate inference and parameter estimation, but existing algorithms are complex and data-type limited.

Purpose of the Study:

  • To propose an alternative, more accessible method for approximate inference and parameter estimation in FHMMs.
  • To generalize FHMMs by connecting them to Generalized Additive Models (GAMs).
  • To develop a learning algorithm that is easier to understand and implement.

Main Methods:

  • Developed the generalized backfitting algorithm, inspired by statistical techniques for GAMs.
  • The algorithm computes customized error signals for each hidden Markov chain.

Related Experiment Videos

  • Trains each chain individually using conventional HMM techniques.

    • Main Results:

    • The generalized backfitting algorithm provides a more statistically grounded perspective on FHMMs.
    • The method extends FHMM applicability to diverse time-series data, including Bernoulli and multinomial.
    • Simulation results indicate FHMMs trained with this algorithm are effective for sequential data analysis.

    Conclusions:

    • The generalized backfitting algorithm offers a practical and powerful tool for analyzing sequential data.
    • This approach enhances the understanding and implementation of FHMMs.
    • FHMMs are generalized and made more versatile through this novel perspective and algorithm.