论文标题
对抗性稳健低等级矩阵估计：压缩传感和矩阵完成
Adversarial Robust Low Rank Matrix Estimation: Compressed Sensing and Matrix Completion
论文作者
论文摘要
当产出受到对抗性污染时，我们将强大的低等级矩阵估计值视为痕量回归。允许对手向任意输出添加任意值。这样的值可以取决于任何样本。我们处理矩阵压缩感测，包括套索作为部分问题和矩阵完成，然后获得尖锐的估计误差界限。为了获得不同模型（例如矩阵压缩传感和矩阵完成）的误差界限，我们根据Huber损耗函数和核定标准惩罚的组合提出了一种简单的统一方法，这与常规方法是不同的方法。本文在本文中获得的一些错误范围比过去的错误范围更加清晰。
We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with matrix compressed sensing, including lasso as a partial problem, and matrix completion, and then we obtain sharp estimation error bounds. To obtain the error bounds for different models such as matrix compressed sensing and matrix completion, we propose a simple unified approach based on a combination of the Huber loss function and the nuclear norm penalization, which is a different approach from the conventional ones. Some error bounds obtained in the present paper are sharper than the past ones.
