[Paper Review] Geographic Spines in the 2020 Census Disclosure Avoidance System

Ryan Cumings-Menon, John M. Abowd+6 more|arXiv (Cornell University)|Mar 30, 2022

Data-Driven Disease Surveillance4 citations

TL;DR

This paper proposes an optimized geographic spine for the 2020 Census Disclosure Avoidance System (DAS) to improve accuracy in differentially private microdata by reducing estimation error for off-spine geographic entities. By redefining block groups and incorporating targeted geographic units—such as AIAN tribal areas, GQs, MCDs, and places—into the spine hierarchy, the method minimizes distance from the spine and controls fan-out, resulting in lower mean squared error for key statistical outputs.

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.

Motivation & Objective

• To address accuracy degradation in differentially private census outputs for geographic entities that lie far from the standard geographic spine.
• To reduce mean squared error (MSE) in tabulation estimates by minimizing the distance of key geographic entities from the internal spine used in the TopDown Algorithm (TDA).
• To manage fan-out values—especially for high-coverage geounits—by redefining block groups and tract groups to balance computational efficiency and estimation precision.
• To ensure that legally and administratively significant entities (e.g., AIAN tribal areas, incorporated places, minor civil divisions) are brought closer to the spine without compromising differential privacy guarantees.
• To develop a systematic, auditable method for spine optimization that supports consistent, high-fidelity statistical outputs across multiple census data products.

Proposed method

• The TopDown Algorithm (TDA) is used to generate differentially private histograms at hierarchical geolevels, starting from the U.S. level and progressing to finer granularities.
• The conventional geographic spine (U.S., state, county, tract, block group, block) is modified by introducing an AIAN spine branch at the state level to better represent tribal areas.
• Optimized block groups are defined by grouping blocks that share membership in the same AIAN, GQ, MCD, place, school district, or conventional block group OSE (off-spine entity).
• Fan-out values are controlled by aggregating child geounits (e.g., blocks) into higher-level units (e.g., tract subsets, optimized block groups) to prevent excessive noise accumulation.
• A bypassing algorithm (Algorithm 3) is applied to assign privacy loss budgets (PLB) to each geounit in the spine, ensuring global privacy budget is preserved while improving local accuracy.
• The spine is further refined by introducing prim geounits (from E&P Area) and tract subset geounits as intermediate levels, enabling more precise aggregation and noise control.

Experimental results

Research questions

• RQ1 How does the distance of a geographic entity from the internal spine affect the mean squared error (MSE) of its differentially private estimate?
• RQ2 What is the impact of high fan-out values on estimation accuracy in the TDA, and how can they be mitigated through strategic geounit redefinition?
• RQ3 To what extent can including off-spine entities (OSEs) such as AIAN tribal areas, GQs, MCDs, and places in the spine hierarchy reduce estimation error?
• RQ4 How does the use of optimized block groups and tract subsets improve accuracy compared to the conventional spine in the 2020 Census DAS?
• RQ5 What trade-offs exist between computational feasibility, privacy budget allocation, and estimation accuracy when designing a custom geographic spine?

Key findings

• Geographic areas that can be derived by aggregating units above the block level and are closer to the spine exhibit significantly lower mean squared error in noisy estimates.
• The AIAN spine branch reduced estimation error for tribal areas by bringing them closer to the internal spine, improving accuracy for these historically underrepresented geographies.
• The use of optimized block groups reduced fan-out values and improved estimation accuracy for key entities such as GQs, MCDs, and incorporated places.
• The final optimized spine for the 2020 Census DAS reduced estimation error across all data products, including redistricting and DHC, by aligning the spine with legally and administratively significant geographic entities.
• The bypassing algorithm in Algorithm 3 successfully allocated privacy loss budgets while preserving global privacy guarantees and improving local accuracy for high-priority geographies.
• The spine used in the DHC data product—featuring prim, tract subset, and optimized block group levels—enabled more accurate and consistent tabulations than the standard spine, particularly for small-area estimates.