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TENSOR QUANTILE REGRESSION WITH LOW-RANK TENSOR TRAIN ESTIMATION.

Zihuan Liu1, Cheuk Yin Lee2, Heping Zhang1

  • 1Department of Biostatistics, Yale University.

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Summary
This summary is machine-generated.

This study introduces a novel tensor train (TT) decomposition method for analyzing magnetic resonance imaging (MRI) data to predict human intelligence. The TT approach efficiently handles high-dimensional neuroimaging data, offering a more stable and interpretable model.

Keywords:
conditional quantiletensor regressiontensor train (TT) decompositiontotal variation

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Area of Science:

  • Neuroimaging
  • Statistical modeling
  • Machine learning

Background:

  • Neuroimaging studies frequently predict outcomes from complex, high-dimensional image data (tensors).
  • Magnetic resonance imaging (MRI) is crucial for investigating brain structures and their relation to cognitive functions like intelligence.
  • Existing methods face computational challenges due to the high dimensionality of tensor data.

Purpose of the Study:

  • To develop a computationally efficient and stable framework for predicting scalar outcomes from MRI tensor data.
  • To investigate the association between MRI images and human intelligence using a novel statistical approach.
  • To improve the interpretability of neuroimaging models by leveraging spatial tensor structures.

Main Methods:

  • Formulation of a scalar-on-image quantile regression framework tailored for neuroimaging data.
  • Proposal of a low-rank coefficient array estimation algorithm based on tensor train (TT) decomposition.
  • Incorporation of a generalized Lasso penalty and total variation regularization to enhance dimensionality reduction and interpretability.

Main Results:

  • The proposed TT decomposition method effectively reduces the dimensionality of the coefficient tensor, making analysis feasible and efficient.
  • The TT-based method demonstrates superior stability and efficiency compared to traditional Canonic Polyadic rank approximation.
  • Theoretical properties (consistency, asymptotic normality) of the TT estimator are established, supported by numerical studies on synthetic and real MRI data.

Conclusions:

  • The tensor train (TT) decomposition offers a powerful and efficient approach for analyzing high-dimensional neuroimaging data in statistical modeling.
  • The proposed method enhances model stability, interpretability, and computational performance in predicting outcomes from MRI data.
  • This framework advances the ability to explore complex relationships between brain structure and cognitive abilities like intelligence.