# A Sieve-Accelerated Quadrature Method for Exact Privacy Accounting in the 2020 U.S. Decennial Census

arXiv: https://arxiv.org/abs/2606.29835 · HTML: https://mlsanity.com/paper/2606.29835/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 56 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 26 of 26)

- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Subsampled R'enyi Differential Privacy and Analytical Moments Accountant](https://mlsanity.com/paper/1808.00087/) (2018)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Numerical Composition of Differential Privacy](https://mlsanity.com/paper/2106.02848/) (2021)
- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016)
- [The Discrete Gaussian for Differential Privacy](https://mlsanity.com/paper/2004.00010/) (2020)
- [The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2102.06387/) (2021)
- [Deep Learning with Gaussian Differential Privacy](https://mlsanity.com/paper/1911.11607/) (2019)
- [Optimal Accounting of Differential Privacy via Characteristic Function](https://mlsanity.com/paper/2106.08567/) (2021)
- [Geographic Spines in the 2020 Census Disclosure Avoidance System](https://mlsanity.com/paper/2203.16654/) (2022)
- [Tight Differential Privacy for Discrete-Valued Mechanisms and for the Subsampled Gaussian Mechanism Using FFT](https://mlsanity.com/paper/2006.07134/) (2020)
- [The Impact of the U.S. Census Disclosure Avoidance System on Redistricting and Voting Rights Analysis](https://mlsanity.com/paper/2105.14197/) (2021)
- [Confidence-Ranked Reconstruction of Census Microdata from Published Statistics](https://mlsanity.com/paper/2211.03128/) (2022)
- [Unifying Re-Identification, Attribute Inference, and Data Reconstruction Risks in Differential Privacy](https://mlsanity.com/paper/2507.06969/) (2025)
- [Unified Enhancement of Privacy Bounds for Mixture Mechanisms via f-Differential Privacy](https://mlsanity.com/paper/2310.19973/) (2023)
- [Making the Most of Parallel Composition in Differential Privacy](https://mlsanity.com/paper/2109.09078/) (2021)
- [Bayesian and Frequentist Semantics for Common Variations of Differential Privacy: Applications to the 2020 Census](https://mlsanity.com/paper/2209.03310/) (2022)
- [A Statistical Viewpoint on Differential Privacy: Hypothesis Testing, Representation and Blackwell's Theorem](https://mlsanity.com/paper/2409.09558/) (2024)
- [Gaussian DP for Reporting Differential Privacy Guarantees in Machine Learning](https://mlsanity.com/paper/2503.10945/) (2025)
- [The 2020 US Decennial Census is more private than you (might) think](https://mlsanity.com/paper/2410.09296/) (2024)
- [Census TopDown: The Impacts of Differential Privacy on Redistricting](https://mlsanity.com/paper/2203.05085/) (2022)
- [Mitigating Privacy-Utility Trade-off in Decentralized Federated Learning via f-Differential Privacy](https://mlsanity.com/paper/2510.19934/) (2025)
- [Comment: The Essential Role of Policy Evaluation for the 2020 Census Disclosure Avoidance System](https://mlsanity.com/paper/2210.08383/) (2022)
- [Disclosure Avoidance for the 2020 Census Demographic and Housing Characteristics File](https://mlsanity.com/paper/2312.10863/) (2023)
- [SafeTab-P: Disclosure Avoidance for the 2020 Census Detailed Demographic and Housing Characteristics File A (Detailed DHC-A)](https://mlsanity.com/paper/2505.01472/) (2025)
- [Differential Perspectives: Epistemic Disconnects Surrounding the US Census Bureau's Use of Differential Privacy](https://mlsanity.com/paper/2602.18648/) (2026)

## Abstract (arXiv)

In 2020, the U.S. Census Bureau adopted differential privacy for the Decennial Census by injecting integer-valued Gaussian noise into published census tabulations. Exactly evaluating the privacy guarantees of these data releases would enable the Bureau to determine the absolute minimum noise required to satisfy a given privacy budget, preventing the injection of unnecessary excess noise and thereby substantially enhancing the statistical utility of the data for downstream applications such as federal funding allocation and political redistricting. In this paper, we introduce a computationally efficient and mathematically rigorous quadrature method to evaluate the exact privacy profile of practical, large-scale census releases under the composition of heterogeneous discrete Gaussian mechanisms. Mathematically, this problem reduces to evaluating the tail probabilities of high-dimensional convolutions of integer-valued random variables sampled from heterogeneous discrete Gaussian distributions under exceptionally stringent numerical error tolerances (e.g., 10-35). By recasting the exact privacy accounting as a numerical integration problem via the discrete Fourier transform, we explicitly exploit the exponential convergence of the trapezoidal rule for complex analytic, periodic characteristic functions. Furthermore, to overcome the computational bottleneck of evaluating highly oscillatory integrands in high dimensions, we develop a sieve algorithm that identifies and prunes negligible quadrature nodes, accelerating the computation by three orders of magnitude. Taken together, these numerical innovations enable the first exact, assumption-free privacy accounting for the 2020 Census Demographic and Housing Characteristics File, achieving a 1,824-fold speedup over prior methods while maintaining census-mandated error tolerances.