Autoregressive Asymmetric Linear Gaussian Hidden Markov Models

TL;DR

This paper introduces an enhanced asymmetric hidden Markov model with an autoregressive component, enabling better modeling of evolving processes with changing relationships among variables, and demonstrates its effectiveness through experiments.

Contribution

It proposes a novel asymmetric autoregressive hidden Markov model with adaptive order selection, extending existing models for improved dynamic process inference.

Findings

Effective modeling of real-world processes with changing relationships

Improved inference and decoding methods for the new model

Successful validation on synthetic and real datasets

Abstract

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.