An ensemble approach to tensor learning

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Tensor regression modeling is a developing field.
• Determining the appropriate rank for CANDECOMP/PARAFAC (CP) decomposition is challenging.
• Tensor data often exhibits spatially varying structural complexity.

Purpose of the Study:

• To propose a novel Tensor Ensemble Learning (TEL) approach.
• To address uncertainties in CP rank determination and tensor block structure.
• To enhance predictive performance for complex tensor data analysis.

Main Methods:

• Developed different tensor partition strategies to divide tensors into disjoint blocks, forming candidate models.
• Implemented a model ensemble method to explore uncertainties in tensor block structure and CP rank.
• Utilized the predictability, computability, and stability framework for assigning weights to candidate models.

Main Results:

• Simulation studies demonstrated TEL's effectiveness under varying tensor complexity.
• TEL showed superiority over existing methods in numerical studies.
• TEL was successfully applied to glaucoma management and Alzheimer's disease cognitive ability prediction.

Conclusions:

• TEL offers a promising approach for analyzing complex tensor data.
• The method effectively handles uncertainties in tensor structure and CP decomposition.
• TEL demonstrates strong performance in both simulated and real-world applications.