在局部差分隐私下，从随机点积图中恢复潜在结构。
Signal Recovery from Random Dot-Product Graphs Under Local Differential Privacy
- 通过调整推断流程，应对隐私机制带来的几何扭曲。
- 在ε-边局部差分隐私下实现潜在位置的一致恢复。
- 适用于需保护边关系的社交网络等场景。
我们研究在ε-边局部差分隐私约束下，从图中恢复潜在信息的问题，其中用户间关系的存在性对数据管理员也保持机密。针对广义随机点积图模型，我们发现标准局部差分隐私机制会在潜在位置上引入特定几何畸变。利用这一发现，通过适当调整统计推断过程，可实现潜在位置的一致恢复。此外，证明了该方法在局部边差分隐私约束下近乎最小最大最优。最后，该框架还能一致恢复潜藏位置中的几何与拓扑信息，以持久图形式编码。本结果将先前私有社区检测研究扩展至更丰富的模型类别和推断任务。
原文摘要 · Abstract (English)
We consider the problem of recovering latent information from graphs under $\varepsilon$-edge local differential privacy where the presence of relationships/edges between two users/vertices remains confidential, even from the data curator. For the class of generalized random dot-product graphs, we show that a standard local differential privacy mechanism induces a specific geometric distortion in the latent positions. Leveraging this insight, we show that consistent recovery of the latent positions is achievable by appropriately adjusting the statistical inference procedure for the privatized graph. Furthermore, we prove that our procedure is nearly minimax-optimal under local edge differential privacy constraints. Lastly, we show that this framework allows for consistent recovery of geometric and topological information underlying the latent positions, as encoded in their persistence diagrams. Our results extend previous work from the private community detection literature to a substantially richer class of models and inferential tasks.
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