Tensor learning for regression.

Area of Science:

• Machine Learning
• Computer Vision
• Data Science

Background:

• Traditional regression models often struggle with high-dimensional data.
• Tensorial representations offer a powerful alternative for capturing complex multi-modal relationships.

Purpose of the Study:

• To propose and evaluate novel tensor learning models for regression tasks.
• To leverage canonical/parallel-factor decomposition for enhanced predictive accuracy.

Main Methods:

• Developed tensor learning models based on canonical/parallel-factor decomposition.
• Investigated square loss and ε-insensitive loss functions, leading to Tensor Ridge Regression (TRR) and Support Tensor Regression (STR).
• Employed Frobenius norm and group-sparsity norm for regularization, enabling automatic rank selection.

Main Results:

• Proposed TRR and STR models demonstrated superiority over vector-based approaches.
• Achieved optimal-rank tensor regression through automatic rank selection.
• Validated effectiveness on head-pose, human-age, and 3-D body-pose estimation tasks using real-world data.

Conclusions:

• Tensor learning models provide significant advantages over traditional vector methods for regression.
• The proposed algorithms are efficient and effective for complex estimation problems.
• Automatic rank selection enhances model performance and interpretability.