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.

翻译：我们考虑在一种新颖但实际场景中从平滑图信号推断底层图拓扑结构的问题，该场景中数据分布于分布式客户端且具有隐私敏感性。该任务的主要难点在于如何在隐私约束下利用所有孤立客户端的潜在异质性数据。为此，我们提出一个框架，其中联合学习本地客户端的个性化图以及共识图。个性化图匹配本地数据分布，从而缓解数据异质性，而共识图则捕获全局信息。接着，我们设计一种定制的算法来求解该问题且不违反隐私约束，即所有私有数据均在本地处理。为进一步增强隐私保护，我们在所提算法中引入差分隐私（DP）以抵御模型更新传输过程中的隐私攻击。理论上，我们为所提算法（包括带DP的变体）建立了可证明的收敛性分析。最后，在合成数据和真实数据上进行了大量实验以验证所提框架的有效性。实验结果表明，我们的方法能在目标场景中有效学习图结构。