Reproduce “Efficient Decision Trees for Tensor Regressions” on OpenResearch
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About this paper
Hengrui Luo, Akira Horiguchi, Li Ma
Researchers at Rice University, UC Davis, and the University of Chicago developed Tensor-Input Trees (TT), a non-parametric framework for regression that directly handles multi-way array inputs and outputs. The method captures complex non-linear relationships within tensor data while demonstrating enhanced computational efficiency over existing tensor Gaussian Process models.
Key insights
- The Low-Rank Regression Error (LRE) splitting criterion generally leads to superior predictive performance for tensor inputs compared to traditional variance-based criteria, as it is better tuned to the underlying tensor structure.
- Tensor-Input Tree models demonstrate significantly improved computational scalability, achieving complexities of O(n² * d² * log k) for LRE/LAE, which is substantially faster than the O(n³) complexity of methods like Tensor Gaussian Processes.
- Ensemble methods utilizing TT models provide a flexible and effective means to perform non-parametric tensor-on-tensor regression, capable of predicting multi-way array outputs from multi-way array inputs.
Summary by alphaXiv.
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