Differentially Private Empirical Risk Minimization Algorithm For β-mixing Sequences

Machine learning is one of the source of innovation of intelligent data analysis tech-nology, it brings intelligence analysis techniques and methods at the same time.There is a privacy problem to solve. When we use machine learning algorithms to do the personal or financial information medical date, and web browsing records which con-tains the private information data.So information is easy to leak people’s privacy. This means that establishing a new machine learning method is very important. In this arti-cle, we study the differentially privacy protecting model. Dwork and Kamalika define a differentially privacy model, the purpose is that the algorithm has a good output and can protect in the process. The differentially privacy is based on empirical risk min-imization theory of privacy. Privacy protection algorithm has two kinds:the output perturbation algorithm and the object perturbation algorithm. The output perturbation algorithm is to add noise on the output of the algorithm to protect private data, and the objective perturbation algorithm is to add the noise in front of optimizing classifier.Because the classical theory of privacy protection algorithm based on the indepen-dent identical distribution data. But that the data are independent assumption is very strong in theory and in application. So we do the mixing sequence and provide the differentially privacy generalization performance of the differentially privacy.We find out the reasonable classification with the input for the beta mixing se-quences in the distortion of the input data cases and the rest of the data can still retain some performance. The main purpose is to protect personal privacy. Our’s main work includes the following aspects:(1) We analysis the difference of all privacy definitions, and compare their accurate degree.(2) On the basis of the original theory, we use the classical differentially privacy protection algorithm to the β-mixing sequence. In application, we use it to the support vector machine.