Online differentially private inference for linear regression model

Abstract In the era of big data, data privacy has attracted increasing attention. Differential privacy is a state‐of‐the‐art framework for formal privacy guarantees. Many privacy‐preserving inference methods have been developed for releasing information from a wide range of data analyses in the differential privacy framework. However, differential privacy statistical inference methods for streaming data, which represent a common type of big data, are still lacking. In this paper, we propose a computationally efficient privacy‐preserving method for online updating and inference of linear regression models that is differentially private. We derive regression parameter estimates in the differential privacy framework, along with the covariance estimates based on which privacy‐preserving confidence intervals for the parameters are constructed. We provide theoretical support for the proposed differentially private method, and numerical results demonstrate the good performance of our approach.