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Differential privacy is the dominant standard for formal and quantifiable privacy and has been used in major deployments that impact millions of people. Many differentially private algorithms for query release and synthetic data contain steps that reconstruct answers to queries from answers to other queries that have been measured privately. Reconstruction is an important subproblem for such mecha- nisms to economize the privacy budget, minimize error on reconstructed answers, and allow for scalability to high-dimensional datasets. In this paper, we introduce a principled and efficient postprocessing method ReM (Residuals-to-Marginals) for reconstructing answers to marginal queries. Our method builds on recent work on efficient mechanisms for marginal query release, based on making measurements using a residual query basis that admits efficient pseudoinversion, which is an important primitive used in reconstruction. An extension GReM-LNN (Gaussian Residuals-to-Marginals with Local Non-negativity) reconstructs marginals under Gaussian noise satisfying consistency and non-negativity, which often reduces error on reconstructed answers. We demonstrate the utility of ReM and GReM-LNN by applying them to improve existing private query answering mechanisms. 

Abstract During their nonbreeding period, many species of swallows and martins (family: Hirundinidae) congregate in large communal roosts. Some of these roosts are well-known within local birdwatching communities; however, monitoring them at large spatial scales and with day-to-day temporal resolution is challenging. Community-science platforms such as the Purple Martin Conservation Association’s project MartinRoost and eBird have addressed some of these challenges by centralizing data collected from regional communities. Additionally, due to the high densities of birds within these aggregations, their early morning dispersals are systematically detected by weather radars, which have also been used to collect data about roost timing and location. An important issue, however, limits spatiotemporal scope of previous radar-based studies: finding the roost signatures on millions of rendered reflectivity images is extremely time-consuming. Recent advances in computer vision, however, have allowed us to reduce this effort. The rise of this technology makes it necessary that we assess whether our biological definition of a roost matches what the machine-learning models are capturing. We do so by comparing eBird detections of roosts in the Great Lakes region with those obtained by a human-supervised machine-learning model from 2000 to 2022. With more than two decades of data, we assess the ability of these two tools to detect roosts on a day-to-day basis, and we compare the phenology of dispersals to investigate whether radar detections correspond to swallow and martin roosts or if they are associated with other well-known birds that form large aggregations. Our comparison of these datasets strongly suggests that swallows and martins are responsible for the dispersals we observe on the radars from July to late September; however, the alternative species we examined could be causing some of the detections in October.