Efficient Decision Trees for Tensor Regressions
This work addresses regression tasks for high-dimensional tensor data, offering efficient tree-based methods that are incremental improvements over existing approaches.
The authors tackled regression problems with tensor inputs by proposing tensor-input tree (TT) methods for scalar-on-tensor and tensor-on-tensor cases, achieving competitive performance against tensor-input GP models through fast algorithms and extensive experiments.
We proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variable are tensors (i.e., multi-way arrays). We devised and implemented fast randomized and deterministic algorithms for efficient fitting of scalar-on-tensor trees, making TT competitive against tensor-input GP models. Based on scalar-on-tensor tree models, we extend our method to tensor-on-tensor problems using additive tree ensemble approaches. Theoretical justification and extensive experiments on real and synthetic datasets are provided to illustrate the performance of TT.