# Denoising the US Census: Succinct Block Hierarchical Regression

arXiv: https://arxiv.org/abs/2603.10099 · HTML: https://mlsanity.com/paper/2603.10099/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [The Discrete Gaussian for Differential Privacy](https://mlsanity.com/paper/2004.00010/) (2020)
- [Geographic Spines in the 2020 Census Disclosure Avoidance System](https://mlsanity.com/paper/2203.16654/) (2022)
- [The Power of Factorization Mechanisms in Local and Central Differential Privacy](https://mlsanity.com/paper/1911.08339/) (2019)
- [Optimizing error of high-dimensional statistical queries under differential privacy](https://mlsanity.com/paper/1808.03537/) (2018)
- [Factorization Norms and Hereditary Discrepancy](https://mlsanity.com/paper/1408.1376/) (2014)
- [The 2020 US Decennial Census is more private than you (might) think](https://mlsanity.com/paper/2410.09296/) (2024)
- [Optimizing Hierarchical Queries for the Attribution Reporting API](https://mlsanity.com/paper/2308.13510/) (2023)
- [A Simulated Reconstruction and Reidentification Attack on the 2010 U.S. Census](https://mlsanity.com/paper/2312.11283/) (2023)
- [Least Squares Estimation For Hierarchical Data](https://mlsanity.com/paper/2404.13164/) (2024)
- [An Approximate Monte Carlo Simulation Method for Estimating Uncertainty and Constructing Confidence Intervals for 2020 Census Statistics](https://mlsanity.com/paper/2503.19714/) (2025)

## Built on by (most cited first, 1 of 1)

- [Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees](https://mlsanity.com/paper/2605.22756/) (2026)

## Abstract (arXiv)

The US Census Bureau Disclosure Avoidance System (DAS) balances confidentiality and utility requirements for the decennial US Census (Abowd et al., 2022). The DAS was used in the 2020 Census to produce demographic datasets critically used for legislative apportionment and redistricting, federal and state funding allocation, municipal and infrastructure planning, and scientific research. At the heart of DAS is TopDown, a heuristic post-processing method that combines billions of private noisy measurements across six geographic levels in order to produce new estimates that are consistent, more accurate, and satisfy certain structural constraints on the data. In this work, we introduce BlueDown, a new post-processing method that produces more accurate, consistent estimates while satisfying the same privacy guarantees and structural constraints. We obtain especially large accuracy improvements for aggregates at the county and tract levels on evaluation metrics proposed by the US Census Bureau. From a technical perspective, we develop a new algorithm for generalized least-squares regression that leverages the hierarchical structure of the measurements and that is statistically optimal among linear unbiased estimators. This reduces the computational dependence on the number of geographic regions measured from matrix multiplication time, which would be infeasible for census-scale data, to linear time. We incorporate the additional structural constraints by combining this regression algorithm with an optimization routine that extends TDA to support correlated measurements. We further improve the efficiency of our algorithm using succinct linear-algebraic operations that exploit symmetries in the structure of the measurements and constraints. We believe our hierarchical regression and succinct operations to be of independent interest.