Privacy by Projection: Federated Population Density Estimation by Projecting on Random Features

We consider the problem of population density estimation based on location data crowdsourced from mobile devices, using kernel (KDE). In a conventional, centralized setting, KDE requires users to upload their server, thus raising privacy concerns. Here, we propose Federated framework for estimating user density, which not only keeps devices but also provides probabilistic guarantees against malicious server that tries infer users' location. Our approach random Fourier feature (RFF) leverages representation solution, in each user's information is irreversibly projected onto small number spatially delocalized basis functions, making precise localization impossible while still allowing estimation. evaluate our method both synthetic and real-world datasets, show it achieves better utility (estimation performance)-vs-privacy (distance between inferred true locations) tradeoff, compared state-of-the-art baselines (e.g., GeoInd). vary functions per user, further improve privacy-utility trade-off, provide analytical bounds as function areal unit size bandwidth.