Bayesian scalar-on-tensor regression using the Tucker decomposition for sparse spatial modeling.

Area of Science:

• Statistical modeling
• Machine learning
• Neuroimaging analysis

Background:

• High-dimensional data and inherent sparsity in tensors pose challenges for statistical modeling.
• Existing methods struggle to effectively characterize associations between tensor covariates and scalar responses.
• Regularization techniques are often necessary but can be complex to implement.

Purpose of the Study:

• To propose an efficient Bayesian method for modeling scalar responses with tensor covariates.
• To leverage Tucker tensor decomposition to preserve spatial relationships and reduce model parameters.
• To apply regularization methods within a Bayesian framework for robust analysis.

Main Methods:

• Utilizing Tucker tensor decomposition to handle the spatial structure of tensor coefficients.
• Implementing a Bayesian approach for efficient parameter estimation and uncertainty quantification.
• Comparing the proposed method with existing tensor regression techniques using simulated data.

Main Results:

• The proposed Bayesian method demonstrates efficient modeling of scalar responses with tensor covariates.
• Tucker decomposition effectively retains spatial information while reducing model complexity.
• Simulated data analysis shows competitive or improved performance compared to other methods.
• Neuroimaging analysis using Alzheimer's Data Neuroimaging Initiative data shows enhanced inferential performance.

Conclusions:

• The developed Bayesian method offers an effective solution for analyzing high-dimensional, sparse tensor data.
• Tucker tensor decomposition is a valuable tool for preserving spatial relationships in tensor coefficients.
• The method shows promise for applications in neuroimaging and other fields requiring complex statistical modeling.