Feature Saliencies in Asymmetric Hidden Markov Models.

Many real-life problems are stated as nonlabeled high-dimensional data. Current strategies to select features are mainly focused on labeled data, which reduces the options to select relevant features for unsupervised problems, such as clustering. Recently, feature saliency models have been introduced and developed as clustering models to select and detect relevant variables/features as the model is learned. Usually, these models assume that all variables are independent, which narrows their applicability. This article introduces asymmetric hidden Markov models with feature saliencies, i.e., models capable of simultaneously determining during their learning phase relevant variables/features and probabilistic relationships between variables. The proposed models are compared with other state-of-the-art approaches using synthetic data and real data related to grammatical face videos and wear in ball bearings. We show that the proposed models have better or equal fitness than other state-of-the-art models and provide further data insights.

Autoregressive Asymmetric Linear Gaussian Hidden Markov Models.

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.