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Given a differentially private unbiased estimate q̃ = q(D) +ν of a statistic q(D), we wish to obtain unbiased estimates of functions of q(D), such as 1/q(D), solely through post-processing of q̃, with no further access to the confidential dataset D. To this end, we adapt the deconvolution method used for unbiased estimation in the statistical literature, deriving unbiased estimators for a broad family of twice-differentiable functions - those that are tempered distributions - when the privacy-preserving noise ν is drawn from the Laplace distribution (Dwork et al., 2006). We further extend this technique to functions other than tempered distributions, deriving approximately optimal estimators that are unbiased for values in a user-specified interval (possibly extending to ± ∞). We use these results to derive an unbiased estimator for private means when the size n of the dataset is not publicly known. In a numerical application, we find that a mechanism that uses our estimator to return an unbiased sample size and mean outperforms a mechanism that instead uses the previously known unbiased privacy mechanism for such means (Kamath et al., 2023). We also apply our estimators to develop unbiased transformation mechanisms for per-record differential privacy, a privacy concept in which the privacy guarantee is a public function of a record’s value (Seeman et al., 2024). Our mechanisms provide stronger privacy guarantees than those in prior work (Finley et al., 2024) by using Laplace, rather than Gaussian, noise. Finally, using a different approach, we go beyond Laplace noise by deriving unbiased estimators for polynomials under the weak condition that the noise distribution has sufficiently many moments. 

Predefined demographic groups often overlook the subpopulations most impacted by model errors, leading to a growing emphasis on data-driven methods that pinpoint where models underperform. The emerging field of multi-group fairness addresses this by ensuring models perform well across a wide range of group-defining functions, rather than relying on fixed demographic categories. We demonstrate that recently introduced notions of multi-group fairness can be equivalently formulated as integral probability metrics (IPM). IPMs are the common information-theoretic tool that underlie definitions such as multiaccuracy, multicalibration, and outcome indistinguishably. For multiaccuracy, this connection leads to a simple, yet powerful procedure for achieving multiaccuracy with respect to an infinite-dimensional class of functions defined by a reproducing kernel Hilbert space (RKHS): first perform a kernel regression of a model’s errors, then subtract the resulting function from a model’s predictions. We combine these results to develop a post-processing method that improves multiaccuracy with respect to bounded-norm functions in an RKHS, enjoys provable performance guarantees, and, in binary classification benchmarks, achieves favorable multiaccuracy relative to competing methods.