Factorial Fractional Hidden Markov Models

Lakhdar Aggoun
(Recommended by Prof. E. Dshalalow)

ABSTRACT

Conventional hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive Gaussian noise. A lesser known extension of this class of models, is the so called Factorial Hidden Model (FHMM). FHMM's also have numerous applications, notably in machine learning and speech recognition. In this article we consider FHMM's with additive fractional Gaussian noise in the observed process.

KEYWORDS

factorial hidden Markov chains, change of measure, fractional Gaussian noise

REFERENCES

  1. Aggoun, L. and  Elliott, R.J. (2004), “Measure Theory and Filtering: Introduction with Applications”,  Cam­bridge Series In Statistical and Probabilistic Mathematics.
  2. Elliott, R.J., Aggoun, L. and  Moore, J.B. (1995), “Hidden Markov Models: Estimation and Control” Applications of Mathematics, no. 29.
  3. MacDonald, I.L. and Zucchini, W. (1997), Hidden Markov and Other Model for Discrete-Valued Time Series, Chapman and Hall, London, Great Britain.
  4. Aggoun, L. (2011), “Partially observed discrete-valued time series in fractional Gaussian noise”,  Elektronnoe modelirovanie, Vol. 33, no. 3 pp. 13-21.
  5. Brand, M.  (1997), “Coupled hidden Markov models for modeling interacting processes MIT Media Lab Perceptual Computing”, Learning and Common Sense Technical Report 405 (Revised), June, 1997.
  6. Elliott, R.J. and Deng, J. (2010), “A filter for a state space model with fractional Gaussian noise”, Automatica, Vol. 46, pp. 1689-1695.
  7. Elliott, R.J. and Deng, J. (2011), “A filter for a hidden Markov chain observed in fractional Gaussian noise”, Systems and Control Letters, Vol. 60, pp. 93-100.
  8. Ghahramani, Z. and Jordan, M. (1996), “Factorial Hidden Markov Models”, Computational Cognitive Sci­ence Technical Report 9502 (Revised), July, 1996.
  9. Logan, B. and Pedro, J.M. (1997), “Factorial Hidden Markov Models for Speech Recognition: Prelimi­nary Experiments”, Cambridge Research Laboratory, September, 1997.
  10. Malcolm, W.P., Quadrianto, N. and Aggoun, L. (2010), “State estimation schemes for independent compo­nent coupled hidden Markov models”, Stochastic Analysis and Appl., Vol. 28, no. 3, pp. 430-446.
  11. Zhong, S. and  Ghosh, J. (2001), “Coupled Hidden Markov Models”, Tech. Report, June, 2001.

 

Full text: PDF (in Russian)