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Latent deformation models for multivariate functional data and time-warping separability.

Cody Carroll1, Hans-Georg Müller2

  • 1Department of Mathematics and Statistics, University of San Francisco, San Francisco, California, USA.

Biometrics
|March 6, 2023
PubMed
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This study introduces a new model for multivariate functional data, addressing challenges like time warping. The model simplifies complex data, enabling better analysis of growth and environmental data.

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component processescross-component registrationfunctional data analysislongitudinal studiesmultivariate functional datatime warping

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Area of Science:

  • Statistics
  • Data Science

Background:

  • Multivariate functional data presents unique challenges compared to univariate data.
  • Component functions in multivariate data can be positive and subject to mutual time warping, indicating shared shape with systematic phase variations.

Purpose of the Study:

  • To develop a novel model for multivariate functional data that accounts for mutual time warping.
  • To connect mutual time warping to a latent-deformation framework using a time-warping separability assumption.

Main Methods:

  • Proposed a latent deformation model for multivariate functional data.
  • Incorporated a time-warping separability assumption for interpretation and dimension reduction.
  • Combined random amplitude factors with population-based registration and a latent population function.

Main Results:

  • The latent deformation model effectively represents commonly encountered functional vector data.
  • Developed estimators for model components, enabling data representation and downstream analyses like Fréchet regression.
  • Established convergence rates for fully observed and error-contaminated data.

Conclusions:

  • The proposed model offers a robust framework for analyzing multivariate functional data with time warping.
  • Demonstrated the model's utility through simulations and applications to human growth and environmental pollution data.