Spatial counts under differential privacy mechanism on changing spatial scales

With a spatial statistical database covering a large region, how to publish differential privacy protected information is a challenge. In previous works, information was published using large fixed spatial cells. In this paper, we develop novel flexible methods to publish the spatial information, which allows the users to freely move around the large region, zoom in and zoom out at arbitrary locations, and obtain information over spatial areas both large and small. We develop two methods to publish the spatial information protected under differential privacy. First the region is divided into the smallest spatial cells, where each cell does not observe an event happening more than once. Given repeated measurements, such as multiple day data, the noise added Bernoulli probabilities are computed for all the smallest spatial cells. For larger spatial cells of high interests to users, the noisy Bernoulli probabilities are combined into noisy Poisson-Binomial distributions which also satisfy differential privacy requirement. We use the New York Taxi data in the experiments to demonstrate how our methods work. We show that both of our methods are accurate, while the noisy count probabilities directly obtained from fixed large spatial cells often generate the spatial counts much smaller than the true values.