Geographic Spines in the 2020 Census Disclosure Avoidance System

TL;DR

The paper addresses how the internal geographic spine used by the 2020 Census Disclosure Avoidance System (DAS) shapes the accuracy of formally private outputs. It advances the design space by introducing an AIAN spine and multi-stage spine optimization (including bypassing) to bring target off-spine entities closer to the spine and reduce estimator variance, while rigorously establishing that the DP/$\rho$-zCDP guarantees hold under these spine choices. The authors derive theoretical results on when bypassing improves accuracy and demonstrate, through production-like settings, that optimized spines yield lower mean absolute errors (MAEs) for many geounits and OSEs, with AIAN spines delivering substantial gains for AIAN areas. Overall, spine optimization emerges as a practical approach to improve DP census data quality without compromising privacy, guiding future production deployments.

Abstract

The 2020 Census Disclosure Avoidance System (DAS) is a formally private mechanism that first adds independent noise to cross tabulations for a set of pre-specified hierarchical geographic units, which is known as the geographic spine. After post-processing these noisy measurements, DAS outputs a formally private database with fields indicating location in the standard census geographic spine, which is defined by the United States as a whole, states, counties, census tracts, block groups, and census blocks. This paper describes how the geographic spine used internally within DAS to define the initial noisy measurements impacts accuracy of the output database. Specifically, tabulations for geographic areas tend to be most accurate for geographic areas that both 1) can be derived by aggregating together geographic units above the block geographic level of the internal spine, and 2) are closer to the geographic units of the internal spine. After describing the accuracy tradeoffs relevant to the choice of internal DAS geographic spine, we provide the settings used to define the 2020 Census production DAS runs.

Figures (2)

• Figure 1: The redistricting AIAN spine, shown without the optional tract group geographic level between the tract and county geographic levels. This spine uses the standard census spine as a starting point and includes an AIAN branch. The optimized spine uses an AIAN spine as a starting point and redefines block groups as optimized block groups.
• Figure 2: An example of $A \otimes B$ is given above. In this example, $A$ is given by $\textup{stack}(\mathbf{1}_{2}^{\top}, I_{2}),$ which corresponds to the case in which there is one US geounit with two block geolevel child geounits. Each geounit contains a $2\times 2$ histogram, and the linear queries in $B$ are given by a total sum query ($\mathbf{1}_2^\top\otimes \mathbf{1}^\top_2$), the marginal query groups for each attribute ($I_2 \otimes \mathbf{1}_2^\top$ and $\mathbf{1}_2^\top \otimes I_2$), and the detailed cell query group ($I_2 \otimes I_2$). For each of the geounits, the total sum query is highlighted in green, the marginal query groups are highlighted in light and dark red, and the detailed cell query group is unhighlighted.

Theorems & Definitions (14)

• Definition 1
• Definition 2
• Lemma 1
• Lemma 2
• Lemma 3
• Lemma 4
• proof
• Example 1
• Theorem 1
• proof