DAS Queries

Most of the DAS processing revolves around queries which are selections of (optionally, coarsened) variables applied to a particular geographic region (geounit) to yield a histogram for different combinations of the variables' values. For example, the query votingage * cenrace creates a histogram with 126 individual scalar "slots", one for each combination of 'votingage' (1 or 0) and cenrace (63 possible values for the 2020 Census). The value in each slot is the number of records in the region that have those particular values (the as-enumerated number, when the query is computed on the CEF; the estimated number, when the query is a noisy measurement, or is computed from a Nonnegative Least Squares output, a Rounder output, or the final MDF).

As implemented in the DAS, the strategy queries currently used are implemented as matrices that can be efficiently represented by Kronecker products, and which have a known sensitivity bound (as described in "DAS Implementation Details"). The as-enumerated query answers are then perturbed in the redistricting production run by the Discrete Gaussian Mechanism) with a noise scale determined by the privacy-loss budget associated with the specific query and geographic level (and by the sensitivity bound known a priori). These perturbed measurements are then compressed and saved in the geographic node's attributes for use in optimization to generate privacy-protected histograms.