Have the cake and eat it too: Differential Privacy enables privacy and precise analytics

Existing research in differential privacy, whose applications have exploded across functional areas in the last few years, describes an intrinsic trade-off between the privacy of a dataset and its utility for analytics. Resolving this trade-off critically impacts potential applications of differential privacy to protect privacy in datasets even while enabling analytics using them. In contrast to the existing literature, this paper shows how differential privacy can be employed to precisely-not approximately-retrieve the analytics on the original dataset. We examine, conceptually and empirically, the impact of noise addition on the quality of data analytics. We show that the accuracy of analytics following noise addition increases with the privacy budget and the variance of the independent variable. Also, the accuracy of analytics following noise addition increases disproportionately with an increase in the privacy budget when the variance of the independent variable is greater. Using actual data to which we add Laplace noise, we provide evidence supporting these two predictions. We then demonstrate our central thesis that, once the privacy budget employed for differential privacy is declared and certain conditions for noise addition are satisfied, the slope parameters in the original dataset can be accurately retrieved using the estimates in the modified dataset of the variance of the independent variable and the slope parameter. Thus, differential privacy can enable robust privacy as well as precise data analytics.