Regularized Tensor Quantile Regression With Applications to Neuroimaging Data Analysis

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.