Estimation Of Quantile Regression Models With Differential Privacy

With the vigorous development of the era of big data,relevant social institutions can obtain a large amount of data,which creates commercial value and scientific research value.However,these data often involve personal privacy,and direct analysis and research on these data will cause privacy leakage.Therefore,a tremendous challenge facing the development of big data applications is privacy protection.Differential privacy is a new type of privacy protection technology that has been applied in various fields.The research on linear regression models under differential privacy has received extensive attention.But when the data has outliers,the linear regression model is no longer applicable.The quantile regression model makes up for the deficiencies of the linear regression model when the data has outliers and can also describe the whole picture of the explained variables more comprehensively.Quantile regression models are widely applied in economics,medical care,education,and other fields.But the existing quantile regression modeling does not consider the issue of privacy protection.Therefore,it has theoretical significance and practical application value to study the estimation problem of the quantile regression model under differential privacy.Based on the empirical risk minimization method under differential privacy,this dissertation studies the estimation problem of smooth approximate quantile regression models.Under the Laplace mechanism,three differential privacy algorithms that can effectively protect data privacy are proposed:output perturbation,objective function perturbation and gradient perturbation.The effectiveness of algorithms is verified by numerical analysis,and the following conclusions are obtained:when the degree of privacy protection is high,the estimation accuracy of objective function perturbation and gradient perturbation can be close to the estimation accuracy under non-privacy protection.Under the same degree of privacy protection,the objective function perturbation outperforms the gradient perturbation.However,when the sample size is large,the gradient perturbation performs almost as well as objective function perturbation,and its calculation speed is faster than objective function perturbation.