Denoising the US Census: Succinct block hierarchical regression

The 2020 United States Census adopted differential privacy to protect individual confidentiality, adding calibrated noise to summary demographic measurements that are then reconciled into population tables. We developed BlueDown, a postprocessing algorithm that combines techniques from linear regression and constrained optimization while exploiting measurement structure for efficiency. On 2020 Census data, BlueDown reduced the error of groupings by race at the county level by 21 to 36% and of all county-level groupings by 9 to 58%; at the tract level, it reduced error of groupings by housing type by 38 to 61%. These gains came at no cost to confidentiality or computational efficiency and would improve the validity of research relying on this definitive dataset and analyses used to guide the distribution of more than $1.5 trillion in annual federal spending.