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

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With complex systems emerging in various applications, e.g., financial, biological and social networks, graphs become working horse to model and analyse these systems. Nodes within networks usually entail attributes. Due to privacy concerns and missing observations, nodal attributes may be unavailable for some nodes in real-world networks. Besides, new nodes with unknown nodal attributes may emerge at any time, which require evaluation of the corresponding attributes in real-time. In this context, the present paper reconstructs nodal attributes of unobserved ones via an estimated nodal function based on their connectivity patterns with other nodes in the graph. Unlike existing works which only consider single-hop neighbors, the present paper further explores global information and adaptively combines the effects of multi-hop neighbors together. A multikernel-based approach is developed, which is capable of leveraging global network information, and scales well with network size as well. In addition, it has the flexibility to account for different nonlinear relationship by adaptively selecting the appropriate kernel combination. Experiments on real-word datasets corroborate the merits of the proposed algorithm.

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