Optimal Feature Manipulation Attacks Against Linear Regression

In this paper, we investigate how to manipulate the coefficients obtained via linear regression by adding carefully designed poisoning data points dataset or modify original points. Given energy budget, first provide closed-form solution of optimal point when our target is modifying one designated coefficient. We then extend analysis more challenging scenario where attacker aims change particular coefficient while making others be changed as small possible. For scenario, introduce a semidefinite relaxation method design best attack scheme. Finally, study powerful adversary who can perform rank-one modification on feature matrix. propose an alternating optimization find Numerical examples are provided illustrate analytical results in paper.