Autoregressive Asymmetric Linear Gaussian Hidden Markov Models
This work addresses the need for flexible inference models in dynamic processes, but it is incremental as it builds upon existing asymmetric hidden Markov models.
The authors tackled the problem of modeling time-evolving processes with changing variable relationships by introducing an autoregressive component into asymmetric hidden Markov models, allowing adaptive order selection based on penalized likelihood, and demonstrated its capabilities through experiments on synthetic and real data.
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, 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.