Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time...

Area of Science:

• Statistics
• Machine Learning
• Time Series Analysis

Background:

• Latent-variable graphical models are crucial for analyzing complex multivariate time series data.
• Identifying the sparsity pattern of the spectral density matrix inverse is key for model interpretability and efficiency.
• Existing methods often involve subjective user choices, impacting model selection consistency.

Purpose of the Study:

• To generalize an existing algorithm for identifying sparsity patterns in the inverse spectral density matrix of multivariate time series.
• To develop and evaluate novel information-theoretic (IT) criteria for selecting the best model from candidate models.
• To reduce the computational complexity associated with these graphical models.

Main Methods:

• Generalization of an algorithm for finding zeros in the covariance matrix inverse to identify spectral density matrix sparsity.
• Application of information-theoretic criteria, including a newly proposed one, for model selection.
• Exploration of computational burden reduction techniques tested via numerical examples.

Main Results:

• The generalized algorithm successfully identifies sparsity patterns in multivariate time series.
• The novel IT criterion aids in effective model selection.
• Proposed computational reduction methods show promise in numerical tests.
• Empirical comparison demonstrates competitive or superior performance against state-of-the-art methods.

Conclusions:

• The developed approach offers a robust method for latent-variable graphical model selection in multivariate time series.
• The algorithm's reduced reliance on user subjectivity represents a significant advantage over existing techniques.
• This work contributes to more objective and efficient time series analysis.