  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.
