论文标题
小组斜率惩罚的低级张量回归
Group SLOPE Penalized Low-Rank Tensor Regression
论文作者
论文摘要
本文旨在寻求针对多变量协变量和矩阵响应的一类张量回归问题的选择和估计程序，这可以为有限样本中的模型选择提供理论保证。考虑到系数张量中遗传的额叶切片的稀疏性和低级别，我们将回归程序制定为基于正交分解（即tgslope）的组斜率惩罚的低率张量优化问题。该过程证明可以控制新引入的张量组错误发现率（TGFDR），但前提是预测器矩阵是列的正交。此外，我们建立了相对于TGSlope估计风险的渐近最小收敛。为了有效的问题解决，我们等效地将TGSLOPE问题转换为具有级别可矫正目标函数的范围差异（DC）程序。这使我们能够通过具有全球收敛性的有效近端DC算法（DCA）解决TGSlope的重新制定问题。对合成数据和实际人脑连接数据进行的数值研究说明了提出的TGSLOPE估计程序的功效。
This article aims to seek a selection and estimation procedure for a class of tensor regression problems with multivariate covariates and matrix responses, which can provide theoretical guarantees for model selection in finite samples. Considering the frontal slice sparsity and low-rankness inherited in the coefficient tensor, we formulate the regression procedure as a group SLOPE penalized low-rank tensor optimization problem based on an orthogonal decomposition, namely TgSLOPE. This procedure provably controls the newly introduced tensor group false discovery rate (TgFDR), provided that the predictor matrix is column-orthogonal. Moreover, we establish the asymptotically minimax convergence with respect to the TgSLOPE estimate risk. For efficient problem resolution, we equivalently transform the TgSLOPE problem into a difference-of-convex (DC) program with the level-coercive objective function. This allows us to solve the reformulation problem of TgSLOPE by an efficient proximal DC algorithm (DCA) with global convergence. Numerical studies conducted on synthetic data and a real human brain connection data illustrate the efficacy of the proposed TgSLOPE estimation procedure.
