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

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This study introduces a generalized algorithm for identifying sparsity patterns in multivariate time series, improving latent-variable graphical model selection. The method enhances accuracy by reducing user subjectivity in model choice.

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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.