Optimal Feature Manipulation Attacks Against Linear Regression
Optimal Feature Manipulation Attacks Against Linear Regression
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DOI：
10.1109/tsp.2021.3115951
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发表时间：
2020-02
影响因子：
5.4
通讯作者：
Fuwei Li;L. Lai;Shuguang Cui
中科院分区：
文献类型：
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作者：
Fuwei Li;L. Lai;Shuguang Cui
在本文中，我们研究如何通过添加精心设计的中毒数据点的数据集或修改原始数据点，通过线性回归获得的系数进行操作。在给定能量预算的情况下，我们首先给出了当目标是修改一个指定的回归系数时最优中毒数据点的封闭解。然后，我们将分析扩展到一个更具挑战性的场景，其中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。对于这种情况下，我们引入了半定松弛方法来设计最佳的攻击方案。最后，我们研究了一个更强大的对手谁可以执行一个秩一修改的特征矩阵。我们提出了一种交替优化方法来找到最佳的秩一修改矩阵。数值例子说明了本文的分析结果。
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 modifying 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 a 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.