Graph-Regularized Tensor Regression: A Domain-Aware Framework for Interpretable Modeling of Multiway Data on Graphs.

Area of Science:

• Data Science
• Machine Learning
• Applied Mathematics

Background:

• High-dimensional data poses challenges for traditional machine learning due to the curse of dimensionality.
• Tensor decomposition (TD) offers computational benefits but often lacks domain knowledge integration.
• Existing tensor models struggle to incorporate prior information into model compression.

Purpose of the Study:

• To introduce a novel graph-regularized tensor regression (GRTR) framework.
• To integrate domain knowledge into high-dimensional models using graph Laplacian regularization.
• To enhance model interpretability and reduce computational complexity in data analytics.

Main Methods:

• Developed a graph-regularized tensor regression (GRTR) framework.
• Incorporated domain knowledge via a graph Laplacian matrix as a regularization term.
• Utilized tensor algebra for coefficient-wise and dimension-wise model interpretability.

Main Results:

• The GRTR framework demonstrated improved performance in multiway regression settings.
• Achieved significant reductions in computational costs compared to competing models.
• Validated the model's ability to promote physically meaningful structures in model parameters.

Conclusions:

• GRTR offers a powerful and interpretable approach for analyzing high-dimensional data.
• The framework effectively balances model compression with the incorporation of domain expertise.
• GRTR presents a promising solution for computationally intensive data analytics challenges.