Calculating Function Sensitivity for Synthetic Data Algorithms

Differential privacy (DP) provides a robust framework for ensuring individual privacy while analyzing population data. To achieve DP, statistical noise is added to query results before publication, but accurately determining the required noise is challenging, especially for user-defined functions. Existing approaches often rely on limited pre-defined functions with known sensitivities, limiting the expressivity of DP systems. In this paper, we present a novel embedded domain-specific language (eDSL) in Haskell to automatically approximate the sensitivity of user-defined linear functions commonly used in synthetic data generation. Our approach leverages Haskell’s expressive type system and generic programming principles to infer function ranges, enabling us to approximate sensitivities efficiently. We demonstrate the effectiveness of our eDSL by integrating it into the Multiplicative Weights Exponential Mechanism (MWEM) for synthetic data generation. Our solution guides users when updating functions, ensuring proper sensitivity consideration, enhancing the robustness and reliability of synthetic data algorithms. By adopting this straightforward yet effective approach, we streamline the sensitivity calculation process for user-defined functions, making it more accessible and user-friendly. The contributions of our work include an eDSL capable of approximating sensitivity for linear functions and its evaluation within the context of MWEM workloads.