论文标题
基于套索的特征选择的对抗性鲁棒性
On the Adversarial Robustness of LASSO Based Feature Selection
论文作者
论文摘要
在本文中，我们研究了基于$ \ ell_1 $正规线性回归模型的特征选择的对抗性鲁棒性，即拉索。在考虑的模型中，有一个恶意对手可以观察整个数据集，然后将仔细修改响应值或特征矩阵以操纵所选功能。我们将对手的修改策略作为双层优化问题。由于$ \ ell_1 $ narm在零点的难以差异性的难度，我们将$ \ ell_1 $ norm norm norm正常器作为线性不平等约束。我们采用内点方法来解决这一重新制定的套索问题并获得梯度信息。然后，我们使用预计的梯度下降方法来设计修改策略。此外，我们证明该方法可以扩展到其他基于$ \ ell_1 $的功能选择方法，例如Group Lasso和Sparse Group Lasso。合成和实际数据的数值示例说明了我们的方法是有效的。
In this paper, we investigate the adversarial robustness of feature selection based on the $\ell_1$ regularized linear regression model, namely LASSO. In the considered model, there is a malicious adversary who can observe the whole dataset, and then will carefully modify the response values or the feature matrix in order to manipulate the selected features. We formulate the modification strategy of the adversary as a bi-level optimization problem. Due to the difficulty of the non-differentiability of the $\ell_1$ norm at the zero point, we reformulate the $\ell_1$ norm regularizer as linear inequality constraints. We employ the interior-point method to solve this reformulated LASSO problem and obtain the gradient information. Then we use the projected gradient descent method to design the modification strategy. In addition, We demonstrate that this method can be extended to other $\ell_1$ based feature selection methods, such as group LASSO and sparse group LASSO. Numerical examples with synthetic and real data illustrate that our method is efficient and effective.
