Synthetic Census Data Generation via Multidimensional Multiset Sum

TL;DR

The paper tackles the challenge of evaluating privacy-preserving disclosure methods for US Census data by enabling synthetic microdata generation from published statistics. It models block-level reconstruction as a knapsack-style, multidimensional multiset sum problem and proposes two Markov Chain Monte Carlo approaches (a simple chain and a reduced chain) to sample from a principled distribution over feasible household multisets derived from the PUMS population. The authors prove NP-hardness, provide empirical assessments showing practical viability, and develop a practical algorithm with ILP seeding to generate state-wide synthetic microdata while preserving exact block-level constraints. They also address representativeness through a reweighting scheme to align synthetic distributions with PUMS, and discuss limitations, potential biases, and extensions to broader population synthesis tasks. Overall, the work offers a scalable, principled pipeline for creating synthetic Census data to study the impacts of disclosure avoidance methods and to calibrate downstream analyses across multiple samples.

Abstract

The US Decennial Census provides valuable data for both research and policy purposes. Census data are subject to a variety of disclosure avoidance techniques prior to release in order to preserve respondent confidentiality. While many are interested in studying the impacts of disclosure avoidance methods on downstream analyses, particularly with the introduction of differential privacy in the 2020 Decennial Census, these efforts are limited by a critical lack of data: The underlying "microdata," which serve as necessary input to disclosure avoidance methods, are kept confidential. In this work, we aim to address this limitation by providing tools to generate synthetic microdata solely from published Census statistics, which can then be used as input to any number of disclosure avoidance algorithms for the sake of evaluation and carrying out comparisons. We define a principled distribution over microdata given published Census statistics and design algorithms to sample from this distribution. We formulate synthetic data generation in this context as a knapsack-style combinatorial optimization problem and develop novel algorithms for this setting. While the problem we study is provably hard, we show empirically that our methods work well in practice, and we offer theoretical arguments to explain our performance. Finally, we verify that the data we produce are "close" to the desired ground truth.

Figures (8)

• Figure 1: $|\mathcal{X}_b|$, the number of solutions in each block $b$, appears to be heavy-tailed.
• Figure 2: There are blocks for which the number of iterations required to generate an $\varepsilon$-approximate sample from $\mathcal{X}$ using the simple chain is large. The reduced chain (described in \ref{['sec:reduced']}) requires orders of magnitude fewer iterations in the worst case.
• Figure 3: $\underline{N}_\gamma$ as a function of $\gamma$.
• Figure 4: There is no clear relationship between $|\mathcal{X}|$ and the central tendency of $\underline{N}_k$ for $k=3$.
• Figure 5: $k=3$ appears to be optimal because (1) there are blocks for which $M_{k=2}$ is disconnected, and (2) there are blocks for which $M_{k=2}$ is connected but has high mixing time.

Theorems & Definitions (34)

• Definition 1: $\varepsilon$-approximate sample
• Theorem 1: E.g., guruswami2016rapidly; see also levin2017markov
• Lemma 1
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• Corollary 1
• Lemma 1
• Lemma 1