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Related Experiment Videos

Variational learning for switching state-space models.

Z Ghahramani1, G E Hinton

  • 1Gatsby Computational Neuroscience Unit, University College London, London WC1N 3AR, U.K.

Neural Computation
|April 19, 2000
PubMed
Summary
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This study introduces a novel statistical model for time series analysis, combining hidden Markov models and linear dynamical systems. Variational approximation offers a viable method for inference in these complex switching state-space models.

Area of Science:

  • Statistics
  • Time Series Analysis
  • Machine Learning

Background:

  • Widely used stochastic time-series models include hidden Markov models (HMMs) and linear dynamical systems (LDS).
  • These models are prevalent in control and econometrics, with extensions like recurrent mixture of experts networks.
  • Computational intractability hinders exact inference in advanced dynamical models.

Purpose of the Study:

  • To introduce a new statistical model for time series that segments data into regimes with linear dynamics.
  • To combine and generalize HMMs and LDS into a unified framework.
  • To develop a computationally feasible inference method for this novel model.

Main Methods:

  • Developed a novel statistical model generalizing HMMs and LDS for time series segmentation.

Related Experiment Videos

  • Proposed a variational approximation algorithm to overcome computational intractability of exact inference.
  • Utilized forward-backward recursions (HMMs) and Kalman filter recursions (LDS) within the variational approach.

    • Main Results:

    • The proposed variational approximation effectively handles inference and learning in switching state-space models.
    • Demonstrated the model's efficacy on both artificial and real-world data (sleep apnea respiration force).
    • Variational methods are shown to be a viable approach for complex time series modeling.

    Conclusions:

    • The new statistical model provides a powerful tool for analyzing time series with regime shifts.
    • Variational approximation offers a practical solution for inference in computationally challenging models.
    • The approach is applicable to various fields requiring dynamic system analysis.