Autoregressive Asymmetric Linear Gaussian Hidden Markov Models.

Area of Science:

• Statistics
• Machine Learning
• Time Series Analysis

Background:

• Real-life processes evolve, causing variable relationships to change over time.
• Dynamic inference models are needed to capture these evolving relationships.
• Asymmetric Hidden Markov Models (AHMMs) offer a framework for modeling such processes with latent trends.

Purpose of the Study:

• To enhance AHMMs by incorporating an asymmetric autoregressive component for continuous variables.
• To enable the model to automatically select the optimal autoregression order.
• To adapt inference, hidden state decoding, and parameter learning for the proposed model.

Main Methods:

• Modification of existing Asymmetric Hidden Markov Models.
• Introduction of an asymmetric autoregressive component for continuous data.
• Development of adapted algorithms for inference, parameter learning, and hidden state decoding.
• Validation using both synthetic and real-world datasets.

Main Results:

• The proposed model successfully adapts the autoregression order based on penalized likelihood maximization.
• Demonstrated effective inference, hidden state decoding, and parameter learning for the modified AHMMs.
• Experimental results showcase the model's capabilities on diverse datasets.

Conclusions:

• The enhanced AHMM with an asymmetric autoregressive component provides a powerful tool for modeling dynamic processes with changing variable relationships.
• The model's ability to automatically select autoregression order improves flexibility and performance.
• The adapted inference and learning methods are crucial for the model's practical application.