Hidden semi-Markov model

Statistical Model

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A hidden semi-Markov model (HSMM) is a statistical model with the same structure as a hidden Markov model except that the unobservable process is semi-Markov rather than Markov. This means that the probability of there being a change in the hidden state depends on the amount of time that has elapsed since entry into the current state. This is in contrast to hidden Markov models where there is a constant probability of changing state given survival in the state up to that time.[1]

For instance Sansom & Thomson (2001) modelled daily rainfall using a hidden semi-Markov model.[2] If the underlying process (e.g. weather system) does not have a geometrically distributed duration, an HSMM may be more appropriate.

Hidden semi-Markov models can be used in implementations of statistical parametric speech synthesis to model the probabilities of transitions between different states of encoded speech representations. They are often used along with other tools such artificial neural networks, connecting with other components of a full parametric speech synthesis system to generate the output waveforms.[3]

The model was first published by Leonard E. Baum and Ted Petrie in 1966.[4][5]

Statistical inference for hidden semi-Markov models is more difficult than in hidden Markov models, since algorithms like the Baum–Welch algorithm are not directly applicable, and must be adapted requiring more resources.

## See also

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* Markov renewal process

## References

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1. ^ Yu, Shun-Zheng (2010), "Hidden Semi-Markov Models", Artificial Intelligence, 174 (2): 215–243, doi:10.1016/j.artint.2009.11.011, S2CID 1899849.
2. ^ Sansom, J.; Thomson, P. J. (2001), "Fitting hidden semi-Markov models to breakpoint rainfall data", J. Appl. Probab., 38A: 142–157, doi:10.1239/jap/1085496598, S2CID 123113970.
3. ^ Tokuda, Keiichi; Hashimoto, Kei; Oura, Keiichiro; Nankaku, Yoshihiko (2016), "Temporal modeling in neural network based statistical parametric speech synthesis" (PDF), 9th ISCA Speech Synthesis Workshop, 9: 1, archived from the original (PDF) on 2021-03-13
4. ^ Barbu, V.; Limnios, N. (2008). "Hidden Semi-Markov Model and Estimation". Semi-Markov Chains and Hidden Semi-Markov Models toward Applications. Lecture Notes in Statistics. Vol. 191\. p. 1\. doi:10.1007/978-0-387-73173-5_6. ISBN 978-0-387-73171-1.
5. ^ Baum, L. E.; Petrie, T. (1966). "Statistical Inference for Probabilistic Functions of Finite State Markov Chains". The Annals of Mathematical Statistics. 37 (6): 1554. doi:10.1214/aoms/1177699147.

* Shun-Zheng Yu, "Hidden Semi-Markov Models: Theory, Algorithms and Applications", 1st Edition, 208 pages, Publisher: Elsevier, Nov. 2015 ISBN 978-0128027677.

## Further reading

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* Chiappa, Silvia (2014), "Explicit-duration Markov switching models" (PDF), Foundations and Trends in Machine Learning, 7 (6): 803–886, arXiv:1909.05800, doi:10.1561/2200000054, S2CID 51858970.
* Guédon, Y. (2003), "Estimating hidden semi-Markov chains from discrete sequences" (PDF), Journal of Computational and Graphical Statistics, 12 (3): 604–639, doi:10.1198/1061860032030, S2CID 34116959.
* Murphy, Kevin P. (2002), Hidden semi-Markov Models (HSMMs) (PDF)
* Liu, X. L.; Liang, Y.; Lou, Y. H.; Li, H.; Shan, B. S. (2010), "Noise-Robust Voice Activity Detector Based on Hidden Semi-Markov Models", Proc. ICPR'10 (PDF), pp. 81–84, archived from the original (PDF) on 2011-06-17.
* Bulla, J.; Bulla, I.; Nenadiç, O. (2010), "hsmm – an R Package for Analyzing Hidden Semi-Markov Models", Computational Statistics & Data Analysis, 54 (3): 611–619, doi:10.1016/j.csda.2008.08.025.

## External links

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* Shun-Zheng Yu, HSMM – Online bibliography[permanent dead link‍] and Matlab source code[permanent dead link‍]

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