Asymmetric hidden Markov models

Bueno, Marcos L. P.; Hommersom, Arjen; Lucas, Peter; Linard, Alexis

doi:10.1016/j.ijar.2017.05.011

Cited by 16 publications

(18 citation statements)

References 25 publications

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“…However, the model was specified only for discrete variables. More recently, asymmetric hidden Markov models (As-HMMs) were proposed in [5], where a local graphical model was associated with each value of the hidden variable, and the graphical model was not restricted to Chow-Liu trees. However, again only models with discrete observable variables were allowed.…”

Section: Asymmetric Modelsmentioning

confidence: 99%

“…= ln q 0:T ∈R(Q p * :T ) P (q p * :T , x p * :T |x 0:p * −1 , λ). (4) For this proposed HMM model which is, as explained below, asymmetric autoregressive with linear Gaussian emission probabilities (AR-AsLG-HMM), we modify the emission probabilities {b i (x t )} N i=1 such that they can be factorized into linear Gaussian Bayesian networks [33] with an asymmetric component [5], i.e., each variable X m for each state i ∈ R(Q) is associated with a set of parents Pa i (X m ) = {U im1 , ..., U imkim } ⊂ {X 1 , ..., X M } of size k im (apart from Q) which influences its mean in a linear form. Additionally, the emission probabilities are now conditional probabilities given p im ≤ p * past values of the variables X t m , m = 1, ..., M (AR terms) for each state i ∈ R(Q).…”

Section: Autoregressive Asymmetric Linear Gaussian Hidden Markov Modelsmentioning

confidence: 99%

“…Other algorithms have been used to search in the graph space during the SEM algorithm, e.g., [5] used a tabu search algorithm [34], and [27] used a simulated annealing algorithm [35]. In general, any meta-heuristic or heuristic can be used to search in the space of graphs.…”

Section: The Sem Algorithm In Ar-aslg-hmmsmentioning

confidence: 99%

“…The idea of asymmetric HMMMs is introduced in [4] and [5]. These models imply that depending on the value of certain variables, the distribution of the remaining variables may change.…”

Section: Introductionmentioning

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.

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Section: Asymmetric Modelsmentioning

confidence: 99%

Section: Autoregressive Asymmetric Linear Gaussian Hidden Markov Modelsmentioning

confidence: 99%

Section: The Sem Algorithm In Ar-aslg-hmmsmentioning

confidence: 99%

“…The idea of asymmetric HMMMs is introduced in [4] and [5]. These models imply that depending on the value of certain variables, the distribution of the remaining variables may change.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Autoregressive Asymmetric Linear Gaussian Hidden Markov Models

Puerto-Santana

Larrañaga

Bielza

2021

IEEE Trans. Pattern Anal. Mach. Intell.

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“…Context-specific independence in Bayesian networks [1] have tree structured conditional probability distributions with a d-separation-based algorithm to determine statistical dependencies between variables according to contexts. It has been shown that the use of these asymmetries within the model can improve the inference and learning procedures [2].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Hidden Markov Models with Continuous Variables

Puerto-Santana

Bielza

Larrañaga

2018

Advances in Artificial Intelligence

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Hidden Markov models have been successfully applied to model signals and dynamic data. However, when dealing with many variables, traditional hidden Markov models do not take into account asymmetric dependencies, leading to models with overfitting and poor problem insight. To deal with the previous problem, asymmetric hidden Markov models were recently proposed, whose emission probabilities are modified to follow a state-dependent graphical model. However, only discrete models have been developed. In this paper we introduce asymmetric hidden Markov models with continuous variables using state-dependent linear Gaussian Bayesian networks. We propose a parameter and structure learning algorithm for this new model. We run experiments with real data from bearing vibration. Since vibrational data is continuous, with the proposed model we can avoid any variable discretization step and perform learning and inference in an asymmetric information frame.

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A Data-Driven Exploration of Hypotheses on Disease Dynamics

Bueno

Hommersom

Lucas

et al. 2019

Artificial Intelligence in Medicine

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Unsupervised learning is often used to obtain insight into the underlying structure of medical data. In this paper, we show that unsupervised methods, in particular hidden Markov models, can go beyond this by guiding the generation of clinical outcome measures and hypotheses, which play a crucial role in medical research. The usage of the datadriven approach facilitates selecting which hypotheses to further investigate. We demonstrate this by using clinical trial data for psychotic depression treatment as a case study. The discovered latent structure and proposed outcome are shown to provide new insight into the heterogeneity of psychotic depression in terms of predictive symptoms.

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Asymmetric hidden Markov models

Cited by 16 publications

References 25 publications

Autoregressive Asymmetric Linear Gaussian Hidden Markov Models

Autoregressive Asymmetric Linear Gaussian Hidden Markov Models

Asymmetric Hidden Markov Models with Continuous Variables

A Data-Driven Exploration of Hypotheses on Disease Dynamics

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