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.

本篇论文提出了一种基于稀疏且低秩张量回归模型的方法，其中系数张量的每个单元秩张量都被假定为是稀疏的，通过分治策略，可以简化任务，并使用分阶段的估计过程来高效地跟踪其整个解决方案路径。在多种真实和合成实例中展示了我们方法的卓越性能。