Efficient Decision Trees for Tensor Regressions
提出张量输入树方法，解决标量对张量和张量对张量回归问题，通过快速随机和确定性算法实现高效拟合，并在真实和合成数据上验证了鲁棒性。
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 variables 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 (Sun et al., 2023; Yu et al., 2018). 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, including testing robustness to entrywise input tensor noise, are provided on real and synthetic datasets to illustrate the performance of TT. Our implementation is provided at http://www.github.com/hrluo.