Efficient Decision Trees for Tensor Regressions

2024/08/04 by Luo, Hengrui, Horiguchi, Akira, Ma, Li
#15A69 #62G08 #FOS: Computer and information sciences #G.3 #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2408.01926

Abstract

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.

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