Asymmetric Hidden Markov Models with Continuous Variables

Puerto-Santana, Carlos; Bielza, Concha; Larrañaga, Pedro

doi:10.1007/978-3-030-00374-6_10

Cited by 2 publications

(4 citation statements)

References 12 publications

(15 reference statements)

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“…( 30) is then used together with the greedy-forward algorithm described in [4]. However, we emphasize that any other heuristic or meta-heuristic can used for the model search, such as the tabu search in [3], or the simulated annealing of [31].…”

Section: Learning the Context-specific Bayesian Networkmentioning

confidence: 99%

Context-specific kernel-based hidden Markov model for time series analysis

Puerto-Santana¹,

Bielza²,

Larrañaga³

et al. 2023

Preprint

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Traditional hidden Markov models have been a useful tool to understand and model stochastic dynamic linear data; in the case of non-Gaussian data or not linear in mean data, models such as mixture of Gaussian hidden Markov models suffer from the computation of precision matrices and have a lot of unnecessary parameters. As a consequence, such models often perform better when it is assumed that all variables are independent, a hypothesis that may be unrealistic. Hidden Markov models based on kernel density estimation is also capable of modeling non Gaussian data, but they assume independence between variables. In this article, we introduce a new hidden Markov model based on kernel density estimation, which is capable of introducing kernel dependencies using context-specific Bayesian networks. The proposed model is described, together with a learning algorithm based on the expectation-maximization algorithm. Additionally, the model is compared with related HMMs using synthetic and real data. From the results, the benefits in likelihood and classification accuracy from the proposed model are quantified and analyzed.

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Section: Learning the Context-specific Bayesian Networkmentioning

confidence: 99%

Context-specific kernel-based hidden Markov model for time series analysis

Puerto-Santana¹,

Bielza²,

Larrañaga³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…However, again only models with discrete observable variables were allowed. In [27], this issue was addressed with the asymmetric linear Gaussian HMMs (AsLG-HMMs), where the emission probabilities were modeled as conditional linear Gaussian Bayesian networks. The estimation of the model parameters was performed with the EM algorithm.…”

Section: Asymmetric Modelsmentioning

confidence: 99%

“…In this paper, we extend asymmetric HMMs for continuous variables of [27], where the model during its learning phase can estimate for each variable the order of the AR process as well as its parameters depending on the context or value of the hidden variable. Thus, we couple for the first time asymmetric linear Gaussian HMMs with AR processes.…”

Section: Asymmetric Modelsmentioning

confidence: 99%

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Autoregressive Asymmetric Linear Gaussian Hidden Markov Models

Puerto-Santana

Larrañaga

Bielza

2021

IEEE Trans. Pattern Anal. Mach. Intell.

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In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil this dynamical requirement and provide a framework where the trend of the process can be expressed as a latent variable. In this paper, we modify these recent asymmetric hidden Markov models to have an asymmetric autoregressive component in the case of continuous variables, allowing the model to choose the order of autoregression that maximizes its penalized likelihood for a given training set. Additionally, we show how inference, hidden states decoding and parameter learning must be adapted to fit the proposed model. Finally, we run experiments with synthetic and real data to show the capabilities of this new model.

show abstract

Asymmetric Hidden Markov Models with Continuous Variables

Cited by 2 publications

References 12 publications

Context-specific kernel-based hidden Markov model for time series analysis

Context-specific kernel-based hidden Markov model for time series analysis

Autoregressive Asymmetric Linear Gaussian Hidden Markov Models

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