AUTHOR(S): I. Gorynin, L. Crelier, H. Gangloff, E. Monfrini, W. Pieczynski

TITLE Performance comparison across hidden, pairwise and triplet Markov models’ estimators 
ABSTRACT In a hidden Markov model (HMM), one observes a sequence of emissions (Y) but lacks a Markovian sequence of states (X) the model went through to generate these emissions. The hidden Markov chain allows recovering the sequence of states from the observed data. The classic HMM formulation is too restrictive but extends to the pairwise Markov models (PMMs) where we assume that the pair (X, Y) is Markovian. Since (X) is not necessarily Markovian in such a model, a PMM is generally not a hidden Markov model. However, since (X) is conditionally Markovian in the PMM, an HMMlike fast processing is available. Similarly, the triplet Markov models (TMMs) extend the PMMs by introducing an additional unobserved discretevalued process (U). The triplet (X, U, Y) is Markovian in a TMM. Such a model is more inclusive than the PMM and offers the same possibilities of fast processing. The aim of the paper is to present numerical studies which evaluate how these models may behave compared to the classic HMM. In other words, we compare different models in terms of the Bayesian Maximum Posterior Mode (MPM) error rate. We show that the misclassification percentage decreases by a half when using these advanced models. 
KEYWORDS Bayesian classification, Hidden Markov models, Maximum Posterior Mode, PMM, TMM 
REFERENCES [1] O. Cappé, E. Moulines, T. Rydén, Inference in Hidden Markov Models, Springer Verlag, 2005. [1] O. Cappé, E. Moulines, T. Rydén, Inference in Hidden Markov Models, Springer Verlag, 2005. 
Cite this paper I. Gorynin, L. Crelier, H. Gangloff, E. Monfrini, W. Pieczynski. (2016) Performance comparison across hidden, pairwise and triplet Markov models’ estimators. Mathematical and Computational Methods, 1, 253258 
