Support Vector Machines with Randomized Response

The linear support vector machine (SVM) is a fundamental binary classification model. In many classification applications, labels are sensitive, and randomized response can ensure label differential privacy (LabelDP). This paper studies statistical inference for the linear SVM under randomized response. We construct a corrected loss to estimate the linear SVM parameter. Since the hinge loss is non-differentiable, we apply convolution smoothing to obtain a differentiable objective and the corresponding estimator. For the estimator, we analyze its asymptotic properties and establish confidence intervals. We then select the randomized response probabilities by minimizing the trace of the covariance contribution induced by randomized response within the feasible regions of $\epsilon$-LabelDP and $(\epsilon ,\delta )$-LabelDP, leading to optimal randomized response mechanisms. Simulation studies and a real-data application show that the proposed method improves parameter estimation, confidence interval coverage, and prediction accuracy.