论文标题
针对线性回归的最佳特征操纵攻击
Optimal Feature Manipulation Attacks Against Linear Regression
论文作者
论文摘要
在本文中，我们研究了如何通过在数据集中添加精心设计的中毒数据点或修改原始数据点来操纵通过线性回归获得的系数。鉴于能源预算，我们首先提供最佳中毒数据点的封闭式解决方案，当我们的目标修改一个指定的回归系数。然后，我们将分析扩展到更具挑战性的场景，攻击者的目标是改变一个特定的回归系数，同时使其他回归系数尽可能小。对于这种情况，我们引入了一种半决赛放松方法来设计最佳的攻击方案。最后，我们研究一个更强大的对手，他可以在功能矩阵上进行排名一号的修改。我们提出了一种交替的优化方法，以找到最佳的排名一个修改矩阵。提供了数值示例，以说明本文获得的分析结果。
In this paper, we investigate how to manipulate the coefficients obtained via linear regression by adding carefully designed poisoning data points to the dataset or modify the original data points. Given the energy budget, we first provide the closed-form solution of the optimal poisoning data point when our target is modifying one designated regression coefficient. We then extend the analysis to the more challenging scenario where the attacker aims to change one particular regression coefficient while making others to be changed as small as possible. For this scenario, we introduce a semidefinite relaxation method to design the best attack scheme. Finally, we study a more powerful adversary who can perform a rank-one modification on the feature matrix. We propose an alternating optimization method to find the optimal rank-one modification matrix. Numerical examples are provided to illustrate the analytical results obtained in this paper.
