Abstract Heavy-tailed noise or strongly correlated predictors often go with the multivariate linear regression model. To tackle with these problems, this paper focuses on the matrix elastic-net regularized multivariate Huber regression model. This new model possesses the grouping effect property and the robustness to heavy-tailed noise. Meanwhile, it also has the ability of reducing the negative effect of outliers due to Huber loss. Furthermore, an accelerated proximal gradient algorithm is designed to solve the proposed model. Some numerical studies including a real data analysis are dedicated to show the efficiency of our method.

中文翻译：

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低秩弹性网正则化多元 Huber 回归模型

摘要 重尾噪声或强相关预测变量通常与多元线性回归模型一起使用。针对这些问题，本文重点研究了矩阵弹性网正则化多元Huber回归模型。该新模型具有分组效应特性和对重尾噪声的鲁棒性。同时，它还具有减少由于 Huber 损失引起的异常值的负面影响的能力。此外，设计了一种加速近端梯度算法来求解所提出的模型。包括真实数据分析在内的一些数值研究致力于展示我们方法的效率。