Graph Topology Learning Under Privacy Constraints

Kavli Affiliate: Xiang Zhang

| First 5 Authors: Xiang Zhang, , , ,

| Summary:

We consider the problem of inferring the underlying graph topology from
smooth graph signals in a novel but practical scenario where data are located
in distributed clients and are privacy-sensitive. The main difficulty of this
task lies in how to utilize the potentially heterogeneous data of all isolated
clients under privacy constraints. Towards this end, we propose a framework
where personalized graphs for local clients as well as a consensus graph are
jointly learned. The personalized graphs match local data distributions,
thereby mitigating data heterogeneity, while the consensus graph captures the
global information. We next devise a tailored algorithm to solve the induced
problem without violating privacy constraints, i.e., all private data are
processed locally. To further enhance privacy protection, we introduce
differential privacy (DP) into the proposed algorithm to resist privacy attacks
when transmitting model updates. Theoretically, we establish provable
convergence analyses for the proposed algorithms, including that with DP.
Finally, extensive experiments on both synthetic and real-world data are
carried out to validate the proposed framework. Experimental results illustrate
that our approach can learn graphs effectively in the target scenario.

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