Partial Quantile Tensor Regression.

Area of Science:

• Statistics
• Machine Learning
• Neuroimaging

Background:

• Tensors are common in scientific studies, requiring advanced analytical methods.
• Quantile regression is valuable for understanding covariate effects across response distributions.
• Existing methods may struggle with high-dimensional tensor covariates in quantile regression.

Purpose of the Study:

• To propose a novel Partial Quantile Tensor Regression (PQTR) framework.
• To enable effective dimension reduction for quantile regression with tensor covariates.
• To provide a computationally efficient and scalable solution for analyzing large tensor data.

Main Methods:

• Developed a PQTR framework integrating partial least squares principles.
• Established a latent variable model representation for PQTR.
• Investigated the connection with envelope quantile tensor regression (EQTR) models.
• Proved root-n consistency of the PQTR estimator under the EQTR model.

Main Results:

• The PQTR algorithm is computationally efficient and scalable.
• PQTR offers a population interpretation through its latent variable representation.
• Simulation studies show superior finite-sample performance compared to benchmarks.
• Application to PTSD neuroimaging data yielded neurobiologically meaningful results.

Conclusions:

• PQTR provides an effective and interpretable method for quantile regression with tensor covariates.
• The method demonstrates practical utility in neuroimaging studies.
• PQTR offers advantages over existing methods in terms of interpretability and performance.