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  3. Regularized Tensor Quantile Regression With Applications To Neuroimaging Data Analysis.
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  3. Regularized Tensor Quantile Regression With Applications To Neuroimaging Data Analysis.

Related Experiment Video

Basics of Multivariate Analysis in Neuroimaging Data
06:35

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Published on: July 24, 2010

Regularized Tensor Quantile Regression With Applications to Neuroimaging Data Analysis.

Matthew Pietrosanu1, Dengdeng Yu2, Ivan Mizera1,3

  • 1Mathematical & Statistical Sciences, University of Alberta, Edmonton, Canada.

Statistics in Medicine
|May 18, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a novel regularized linear quantile regression model for tensor-valued data. The method offers superior performance and interpretability compared to existing tensor frameworks, especially when standard regression assumptions fail.

Keywords:
block relaxationempirical processestensor regressiontensor regularization

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Area of Science:

  • Statistics
  • Machine Learning
  • Neuroimaging Analysis

Background:

  • Traditional regression models often fail when assumptions are violated.
  • Analyzing complex, high-dimensional data like tensors requires specialized methods.
  • Quantile regression offers robustness but can be challenging with tensor covariates.

Purpose of the Study:

  • To propose a novel regularized linear quantile regression model for scalar response and tensor-valued covariates.
  • To develop a method that uniquely regularizes tensor effects for improved analysis.
  • To demonstrate the computational and statistical properties of the new model and its estimators.

Main Methods:

  • Developed a regularized linear quantile regression model.
  • Employed tensor estimation for regularizing low-dimensional tensor effect decomposition parameters.
  • Established computational and statistical properties, accounting for quantile loss function complexities.

    • Main Results:

    • The proposed model demonstrates superior performance over existing tensor frameworks in simulations, particularly when standard regression assumptions are violated.
    • The method provides enhanced interpretability, as shown in a real-world neuroimaging analysis.
    • Established theoretical properties for the algorithm and estimators.

    Conclusions:

    • The novel regularized quantile regression model effectively handles tensor-valued covariates.
    • This approach offers significant advantages in performance and interpretability for complex data analysis.
    • The model is particularly beneficial in scenarios where traditional regression assumptions do not hold.