论文标题
张量回归的分解稀疏张量
Decomposable Sparse Tensor on Tensor Regression
论文作者
论文摘要
大多数正规张量回归研究的重点是具有标量响应的张量预测变量，或者对张量响应的向量预测指标。我们考虑张张量回归的稀疏等级张量，其中预测因子$ \ MATHCAL {x} $和响应$ \ Mathcal {y} $都是高维张量。通过证明可以将一般的内部产品或单位等级张量的收缩产品分解为标准的内部产品和外部产品，可以将问题简单地转换为张量为标量回归，然后进行张量分解。因此，我们提出了一个基于收缩部分和生成部分组成的阶段搜索的快速解决方案，该解决方案被优化。我们成功地证明我们的方法可以通过有效纳入结构信息来实现准确性和预测因子选择方面的当前方法。
Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and responses $\mathcal{Y}$ are both high-dimensional tensors. By demonstrating that the general inner product or the contracted product on a unit rank tensor can be decomposed into standard inner products and outer products, the problem can be simply transformed into a tensor to scalar regression followed by a tensor decomposition. So we propose a fast solution based on stagewise search composed by contraction part and generation part which are optimized alternatively. We successfully demonstrate our method can out perform current methods in terms of accuracy and predictors selection by effectively incorporating the structural information.
