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.

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