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Statistics and Computing

, Volume 26, Issue 1–2, pp 61–71 | Cite as

Inference in finite state space non parametric Hidden Markov Models and applications

  • E. Gassiat
  • A. Cleynen
  • S. Robin
Article

Abstract

Hidden Markov models (HMMs) are intensively used in various fields to model and classify data observed along a line (e.g. time). The fit of such models strongly relies on the choice of emission distributions that are most often chosen among some parametric family. In this paper, we prove that finite state space non parametric HMMs are identifiable as soon as the transition matrix of the latent Markov chain has full rank and the emission probability distributions are linearly independent. This general result allows the use of semi- or non-parametric emission distributions. Based on this result we present a series of classification problems that can be tackled out of the strict parametric framework. We derive the corresponding inference algorithms. We also illustrate their use on few biological examples, showing that they may improve the classification performances.

Keywords

Identifiability Hidden Markov Models Non-parametric 

Notes

Acknowledgments

The authors want to thank Caroline Bérard for providing the transcriptomic tiling array data. Part of this work was supported by the ABS4NGS ANR project (ANR-11-BINF-0001-06).

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Laboratoire de MathématiqueUniversité Paris-SudOrsayFrance
  2. 2.Laboratoire de MathématiqueCNRSOrsayFrance
  3. 3.AgroParisTech, MIA 518ParisFrance
  4. 4.INRA, MIA 518ParisFrance

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