  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.
