Task-aware Kernel Stein certificates for R\'{e}nyi differential privacy

The paper introduces task‑aware kernel Stein certificates for Rényi differential privacy, leveraging kernel Stein discrepancies based on escort distributions to provide privacy guarantees. By tailoring the kernel to focus on relevant privacy directions, the authors derive exact identities for Gaussian and Laplace mechanisms and bounds for exponential mechanisms, including task‑aware guarantees. A real‑world data example demonstrates how the protected comparison set and the released subspace jointly influence the resulting certificates.

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