Differential Privacy Preservation In Polynomial Regression Analysis

Polynomial regression is a statistical analysis method used in mathematical statistics to determine nonlinear quantitative relationships among multiple interdependent variables,which has a wide range of applications in big data analysis.Usually,the mined dataset contains some sensitive attributes that can cause privacy leakage without any privacy protection measures in data mining and data release.In the era of booming big data technology,privacy leakage happens more frequently,which can cause serious consequences for individuals,enterprises and countries,thus the research and development of privacy protection algorithms has become one of the hot spots in response to the call of the times.The main research points of this paper are as follows.Based on the cost function coefficient contamination mechanism,the thesis proposes four differential privacy-preserving algorithms for polynomial regression based on the requirements for data security and data availability in practical applications: Functional Mechanism on Polynomial Regression,Functional Mechanism with Different Perturbation of Coefficients on Polynomial Regression,Differentiated Privacy Budget Allocation on Polynomial Regression,and Differentiated Privacy Budget Allocation with Functional Mechanism with Different Perturbation of Coefficients on Polynomial Regression.In terms of data availability,the privacy budget allocation method is optimized by improving the formula of global sensitivity to further improve the data availability with data security ensured.In terms of data security,privacy security is improving by changing the privacy budget allocation mechanism to allocate less privacy budget to sensitive data in order to increase the noise addition to weaken the correlation of data.Based on the characteristics of the differential privacy algorithm for polynomial regressionoriented regression,the thesis also improves the process of iterative training of the data.First,the algorithm solves the overfitting problem in polynomial regression,and second,since the differential privacy algorithm adds a lot of unnecessary noise and deteriorates the training results under low privacy budget,the R-RANSAC model has a better performance in this case.Superior performance,with higher accuracy of iterative results and overall higher robustness compared to using the least squares method.