Boosted Sparse and Low-Rank Tensor Regression
Boosted Sparse and Low-Rank Tensor Regression
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发表时间：
2018-11
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通讯作者：
Lifang He;Kun Chen;Wanwan Xu;Jiayu Zhou;Fei Wang
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作者：
Lifang He;Kun Chen;Wanwan Xu;Jiayu Zhou;Fei Wang
我们提出了一个稀疏和低秩张量回归模型，将单变量结果与特征张量相关联，其中来自系数张量的CP分解的每个单位秩张量被假设为稀疏的。这种结构既简约又高度可解释，因为它意味着结果通过几个不同的途径与特征相关，每个途径可能只涉及特征维度的子集。我们采取分而治之的策略，简化成一组稀疏的单位秩张量回归问题的任务。为了使计算效率和可扩展性，对于单位秩张量回归，我们提出了一个逐步估计过程，以有效地跟踪其整个解决方案的路径。我们表明，当步长为零，逐步解决方案的路径收敛到相应的正则化回归。我们的方法的上级性能表现在各种现实世界和合成的例子。
We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both parsimonious and highly interpretable, as it implies that the outcome is related to the features through a few distinct pathways, each of which may only involve subsets of feature dimensions. We take a divide-and-conquer strategy to simplify the task into a set of sparse unit-rank tensor regression problems. To make the computation efficient and scalable, for the unit-rank tensor regression, we propose a stagewise estimation procedure to efficiently trace out its entire solution path. We show that as the step size goes to zero, the stagewise solution paths converge exactly to those of the corresponding regularized regression. The superior performance of our approach is demonstrated on various real-world and synthetic examples.