Efficient Decision Trees for Tensor Regressions

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Tensor data, represented as multi-way arrays, presents unique challenges in statistical modeling.
• Existing methods for regression with tensor inputs can be computationally intensive.
• There is a need for efficient and robust methods to analyze scalar-on-tensor and tensor-on-tensor relationships.

Purpose of the Study:

• To propose the tensor-input tree (TT) method for scalar-on-tensor regression.
• To extend the TT method for tensor-on-tensor regression problems.
• To provide efficient algorithms and demonstrate the performance of TT on various datasets.

Main Methods:

• Development of scalar-output regression tree models with tensor inputs.
• Implementation of fast randomized and deterministic algorithms for fitting scalar-on-tensor trees.
• Extension to tensor-on-tensor regression using additive tree ensemble techniques.

Main Results:

• The TT method demonstrates competitive performance against established tensor-input Gaussian process models.
• The method shows robustness to entrywise input tensor noise.
• Extensive experiments on synthetic and real datasets validate the efficacy of TT.

Conclusions:

• The tensor-input tree (TT) method offers an efficient and effective approach for scalar-on-tensor and tensor-on-tensor regression.
• TT provides a valuable tool for analyzing complex, multi-way array data.
• The open-source implementation facilitates broader adoption and further research.