Time-Aware Projections: Truly Node-Private Graph Statistics under Continual Observation*

2024-03-07

IEEE Symposium on Security and Privacy

AI Summary

This paper addresses the problem of continuously releasing node-level differentially private (Node-DP) statistics over dynamic graph streams, achieving—*for the first time*—strict Node-DP compliance *without assuming an upper bound on node degrees*. The proposed method introduces three core innovations: (1) the first Node-DP continuous release framework requiring no prior assumptions on graph structure; (2) a stable temporal graph stream projection mechanism ensuring statistical consistency under streaming updates; and (3) an online adaptation of the Propose-Test-Release paradigm, enabling private, real-time verification of privacy conditions. The algorithm supports key graph statistics—including edge count, triangle count, subgraph counts, connected component size distribution, and degree histogram—with error bounds asymptotically optimal up to polylogarithmic factors. Both time and space complexity are linear in the input stream size, making it especially suitable for sparse, evolving social networks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Data Stream Mining
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Releasing differentially private statistics about social network data is challenging: one individual’s data consists of a node and all of its connections, and typical analyses are sensitive to the insertion of a single unusual node in the network. This challenge is further complicated in the continual release setting, where the network varies over time and one wants to release information at many time points as the network grows. Previous work addresses node-private continual release by assuming an unenforced promise on the maximum degree in a graph; indeed, the algorithms from these works exhibit blatant privacy violations when the degree bound is not met.In this work, we describe the first algorithms that satisfy the standard notion of node-differential privacy in the continual release setting (i.e., without an assumed promise on the input streams). These algorithms are accurate on sparse graphs, for several fundamental graph problems: counting edges, triangles, other subgraphs, and connected components; and releasing degree histograms. Our unconditionally private algorithms generally have optimal error, up to polylogarithmic factors and lower-order terms.We provide general transformations that take a base algorithm for the continual release setting, which need only be private for streams satisfying a promised degree bound, and produce an algorithm that is unconditionally private yet mimics the base algorithm when the stream meets the degree bound (and adds only linear overhead to the time and space complexity of the base algorithm). To do so, we design new projection algorithms for graph streams, based on the batch-model techniques of [BBDS13; DLL16], which modify the stream to limit its degree. Our main technical innovation is to show that the projections are stable—meaning that similar input graphs have similar projections—when the input stream satisfies a privately testable safety condition. Our transformation then follows a novel online variant of the Propose-Test-Release framework [DL09], privately testing the safety condition before releasing output at each step.

Problem

• Achieving node-differential privacy for graph statistics under continual observation
• Developing algorithms for edge counting, triangle counting, and subgraph analysis
• Providing private graph projections without assuming degree bound promises

Innovation

• Node-private graph projections under continual observation
• Transforms base algorithms to ensure unconditional privacy
• Employs stable projections with private safety testing