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Maximum Pseudolikelihood Estimation for Model-Based Clustering of Time Series Data.

Hien D Nguyen1, Geoffrey J McLachlan2, Pierre Orban3

  • 1Department of Mathematics and Statistics, La Trobe University, Victoria, Bundoora 3086, Australia hien1988@gmail.com.

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|January 18, 2017
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Summary
This summary is machine-generated.

We introduce a maximum pseudolikelihood (MPL) estimation method for Mixture of Autoregressions (MoAR) models, overcoming numerical challenges in time series clustering. This consistent estimator is computable via the Expectation-Maximization (EM) algorithm.

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Area of Science:

  • Statistics
  • Machine Learning
  • Time Series Analysis

Background:

  • Mixture of Autoregressions (MoAR) models are used for time series clustering.
  • Maximum Likelihood (ML) estimation for MoAR models faces numerical instability with increasing time series length.
  • This instability makes standard ML estimation infeasible without complex numerical methods.

Purpose of the Study:

  • To propose a Maximum Pseudolikelihood (MPL) estimation approach for MoAR models.
  • To provide a computationally feasible and statistically sound alternative to ML estimation.
  • To demonstrate the application of MPL estimation in clustering real-world time series data.

Main Methods:

  • Developed a Maximum Pseudolikelihood (MPL) estimation method for MoAR models.
  • Proved the consistency of the MPL estimator.
  • Utilized the Expectation-Maximization (EM) algorithm for computing the MPL estimator.
  • Conducted simulations to compare MPL with ML estimation where feasible.

Main Results:

  • The MPL estimator is consistent and computable using the EM algorithm.
  • MPL estimation overcomes the numerical infeasibility of ML estimation for long time series.
  • Simulations demonstrated the effectiveness of the MPL approach.
  • Applied the MPL method to cluster resting-state fMRI data.

Conclusions:

  • MPL estimation offers a viable and robust alternative for MoAR model-based time series clustering.
  • The proposed method addresses critical computational challenges in estimating MoAR models.
  • The approach is effective for analyzing complex neuroimaging data like fMRI.