Matrix form data sets arise in many areas, so there are lots of works about the matrix regression models. One special model of these models is the adaptive nuclear norm regularized trace regression, which has been proven have good statistical performances. In order to accelerate the computation of this model, we consider the technique called screening rule. According to matrix decomposition and optimal condition of the model, we develop a safe subspace screening rule that can be used to identify inactive subspace of the solution decomposition and reduce the dimension of the solution. To evaluate the efficiency of the safe subspace screening rule, we embed this result into the alternating direction method of multipliers algorithm under a sequence of the tuning parameters. Under this process, each solution under the tuning parameter provides a matrix decomposition space. Then, the safe subspace screening rule is applied to eliminate inactive subspace, reduce the solution dimension and accelerate the computation process. Some numerical experiments are implemented on simulation data sets and real data sets, which illustrate the efficiency of our screening rule.

翻译：矩阵形式数据集出现在许多领域，因此关于矩阵回归模型的研究大量存在。其中一种特殊模型是自适应核范数正则化迹回归，已被证明具有良好的统计性能。为加速该模型的计算，我们考虑了一种称为筛选规则的技术。基于矩阵分解和模型的最优条件，我们开发了一种安全子空间筛选规则，可用于识别解分解中的非活跃子空间并降低解的维度。为评估安全子空间筛选规则的效率，我们将该结果嵌入到交替方向乘子法算法中，并在一个调优参数序列下运行。在此过程中，每个调优参数对应的解提供了一个矩阵分解空间。随后，应用安全子空间筛选规则剔除非活跃子空间，降低解维度并加速计算过程。在模拟数据集和真实数据集上进行的数值实验表明了所提筛选规则的有效性。