[論文レビュー] Publishing Below-Threshold Triangle Counts under Local Weight Differential Privacy

Kevin Pfisterer, Quentin Hillebrand+1 more|arXiv (Cornell University)|Jan 5, 2026

Privacy-Preserving Technologies in Data被引用数 0

ひとこと要約

The paper proposes a two-round local weight differential privacy method to count below-threshold weighted triangles, with biased and unbiased estimators, plus optimization and smooth-sensitivity techniques to reduce error and running time.

ABSTRACT

We propose an algorithm for counting below-threshold triangles in weighted graphs under local weight differential privacy. While prior work has largely focused on unweighted graphs, edge weights are intrinsic to many real-world networks. We consider the setting in which the graph topology is publicly known and privacy is required only for the contribution of an individual to incident edge weights, capturing practical scenarios such as road and telecommunication networks. Our method uses two rounds of communication. In the first round, each node releases privatized information about its incident edge weights under local weight differential privacy. In the second round, nodes locally count below-threshold triangles using this privatized information; we introduce both biased and unbiased variants of the estimator. We further develop two refinements: (i) a pre-computation step that reduces covariance and thus lowers expected error, and (ii) an efficient procedure for computing smooth sensitivity, which substantially reduces running time relative to a straightforward implementation. Finally, we present experimental results that quantify the trade-offs between the biased and unbiased variants and demonstrate the effectiveness of the proposed improvements.

研究の動機と目的

• Motivate counting below-threshold triangles in weighted graphs under local weight DP.
• Develop a two-round communication protocol where nodes publish noisy incident weights and then count locally.
• Introduce biased and unbiased estimators for below-threshold triangles and analyze their bias/variance.
• Reduce error and computation time via a pre-computation step and an efficient smooth-sensitivity algorithm.
• Demonstrate practical accuracy improvements on real-world networks through experiments.

提案手法

• Two-round algorithm: nodes publish incident weight vectors with discrete Laplace noise to create a noisy graph, and a server assigns triangles to vertices.
• Local counting using either a biased estimator B'T or an unbiased estimator U'T for each triangle assigned to a vertex.
• Publish local counts with Laplace (or smooth-sensitivity) mechanism to achieve LWDP; aggregate at the server.
• Provide a sensitivity analysis and computable bounds for the Gaussian-style smooth sensitivity in O(d^2) time per node.
• Adapt an unbiased histogram release technique to release unbiased estimates of the number of below-threshold triangles.
• Develop an assignment rho that minimizes the number of covariance-prone C'4 instances to reduce variance.
• Present a formal comparison of biased vs. unbiased estimators in terms of error scaling under different graph regimes.

実験結果

リサーチクエスチョン

• RQ1 How can we count below-threshold triangles in weighted graphs under local weight differential privacy?
• RQ2 What estimators (biased vs unbiased) yield lower error under LWDP for this problem?
• RQ3 How can we assign triangles to nodes to minimize covariance and variance in the released counts?
• RQ4 Can we compute a scalable local smooth-sensitivity bound that improves accuracy without exploding runtime?

主な発見

• A two-round protocol enables counting below-threshold weighted triangles under local weight DP.
• Biased and unbiased estimators have different error scaling: biased error grows with number of triangles, unbiased scales with sqrt(#triangles).
• A pre-computation step reduces covariance and lowers expected error.
• An O(d^2) time method computes local beta-smooth sensitivity independent of weight magnitudes, aiding scalability.
• The unbiased estimator achieves better accuracy when the graph has many triangles; the biased estimator can perform better with smaller budgets.
• Experiments on Milan telecom and a biological network show up to two orders of magnitude reduction in relative counting error over a naive baseline.