Privacy of Synthetic Data: A Statistical Framework

Privacy-preserving data analysis is emerging as a challenging problem with far-reaching impact. In particular, synthetic are promising concept toward solving the aporetic conflict between privacy and sharing. Yet, it known that accurately generating private, of certain kinds NP-hard. We develop statistical framework for differentially private data, which enables us to circumvent computational hardness problem. consider true random sample drawn from population $\Omega $ according some unknown density. then replace by much smaller subset ^{\ast}$ , we generate on reduced space fitting specified linear statistics obtained data. To ensure use common Laplacian mechanism. Employing Rényi condition number, measures how well sampling distribution correlated distribution, derive explicit bounds accuracy provided proposed method.