Hybrid hidden Markov model for mixed continuous/continuous and discrete/continuous data modeling

Hybrid hidden Markov model for mixed continuous/continuous and discrete/continuous data modeling. Epaillard, E. & Bouguila, N. In 2015 IEEE 17th International Workshop on Multimedia Signal Processing (MMSP), pages 1–6, October, 2015.
doi abstract bibtex

We propose a hybrid hidden Markov model (HMM) for mixed continuous/continuous and discrete/continuous outcomes. The Expectation-Maximization (EM) procedure used for the parameters estimation relies on a combination of local and global quantities that relate to outcomes of a specific type and to all outcomes, respectively. The new model is implemented for discrete outcomes and continuous outcomes that follow Gaussian, Dirichlet, and Gamma distributions. Experiments led with synthetic data show same or better modeling accuracy compared to a fully Gaussian HMM, with less parameters and thus a shorter convergence time for high dimensional data. Finally, the approach is validated with real data in a change detection scenario between a pair of images, one of which has been captured by an optic sensor and the other by a synthesis aperture radar (SAR) sensor. Based on the properties of the noises corrupting these images, a hybrid Gamma-Gaussian HMM is trained and the likelihood of the data with respect to the model is used to detect changes. The obtained results are in line with the most recent approaches for this task with the advantage of providing a very compact representation of the data.

@inproceedings{epaillard_hybrid_2015,
	title = {Hybrid hidden {Markov} model for mixed continuous/continuous and discrete/continuous data modeling},
	doi = {10.1109/MMSP.2015.7340853},
	abstract = {We propose a hybrid hidden Markov model (HMM) for mixed continuous/continuous and discrete/continuous outcomes. The Expectation-Maximization (EM) procedure used for the parameters estimation relies on a combination of local and global quantities that relate to outcomes of a specific type and to all outcomes, respectively. The new model is implemented for discrete outcomes and continuous outcomes that follow Gaussian, Dirichlet, and Gamma distributions. Experiments led with synthetic data show same or better modeling accuracy compared to a fully Gaussian HMM, with less parameters and thus a shorter convergence time for high dimensional data. Finally, the approach is validated with real data in a change detection scenario between a pair of images, one of which has been captured by an optic sensor and the other by a synthesis aperture radar (SAR) sensor. Based on the properties of the noises corrupting these images, a hybrid Gamma-Gaussian HMM is trained and the likelihood of the data with respect to the model is used to detect changes. The obtained results are in line with the most recent approaches for this task with the advantage of providing a very compact representation of the data.},
	booktitle = {2015 {IEEE} 17th {International} {Workshop} on {Multimedia} {Signal} {Processing} ({MMSP})},
	author = {Epaillard, Elise and Bouguila, Nizar},
	month = oct,
	year = {2015},
	keywords = {Data models, Estimation, Hidden Markov models, Mathematical model, Optical imaging, Parameter estimation},
	pages = {1--6},
}

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