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Updated: Sep 6, 2025

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Bayesian time-aligned factor analysis of paired multivariate time series.

Arkaprava Roy1, Jana Schaich Borg2, David B Dunson3

  • 1Department of Biostatistics, University of Florida, Gainnesville, FL 32611, USA.

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|June 27, 2022
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Summary

We introduce Time Aligned Common and Individual Factor Analysis (TACIFA), a novel Bayesian dynamic factor model. This method effectively estimates shared and individual variability in time-series matrix data, even with temporal misalignment.

Keywords:
CIFADynamic factor modelHamiltonian Monte CarloJIVEMonotonicityPaired time seriesSocial mimicryTime alignmentWarping

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Area of Science:

  • Statistics
  • Machine Learning
  • Time Series Analysis

Background:

  • Analyzing dynamic matrix data requires methods to distinguish shared and individual variability.
  • Existing static methods are insufficient for time-varying datasets.
  • Dynamic settings lack robust approaches for modeling coupled matrix time series.

Purpose of the Study:

  • To develop a Bayesian dynamic factor model for analyzing pairs of time-varying matrices.
  • To characterize common and individual features in dynamic matrix collections.
  • To address the challenge of temporal misalignment in time-series data.

Main Methods:

  • Proposed Time Aligned Common and Individual Factor Analysis (TACIFA) framework.
  • Incorporated uncertainty in time alignment via an unknown warping function.
  • Utilized a Hamiltonian Monte Carlo (HMC) algorithm for efficient computation.

Main Results:

  • Provided theoretical support, demonstrating model identifiability and posterior concentration.
  • Achieved excellent performance in simulation studies.
  • Successfully applied TACIFA to analyze a social mimicry experiment.

Conclusions:

  • TACIFA offers a robust framework for analyzing dynamic matrix data with shared and individual components.
  • The model effectively handles temporal misalignment, a common issue in real-world time-series.
  • This approach advances the analysis of complex, time-varying multivariate observations.