Quentin Hillebrand

Kevin Pfisterer, Quentin Hillebrand, Vorapong Suppakitpaisarn

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.

Quentin Hillebrand, Jacob Imola, Rasmus Pagh et al.

We show that an "old dog", the classical discrete Laplace (aka.~geometric) mechanism, can "perform new tricks": 1. It can be post-processed to yield a simple, unbiased estimator of any subexponential function $f$ of the original data, giving a simple, discrete, multivariate version of the recent unbiasing result for the Laplace mechanism by Calmon et al. (FORC '25). 2. It can be post-processed to output the same distribution as the Laplace mechanism or the Staircase mechanism with identical privacy parameters. Thus, the discrete Laplace mechanism is a versatile mechanism that should be preferred over the Laplace and Staircase mechanisms whenever the data is discrete (or can be made discrete while controlling $\ell_1$-sensitivity). We show bounds on the variance of our estimator, compared to the mean square error of the biased estimator that simply evaluates the $f$ on the output of the mechanism. Though our unbiased estimator has exponential running time for worst-case functions, we show that it can often be computed in linear or polynomial time for some common functions exhibiting structure. We showcase the properties of our methods empirically with several use cases including profile and entropy estimation, as well as distributed/federated data analysis applications in which unbiasedness is key to accuracy.

Quentin Hillebrand, Vorapong Suppakitpaisarn, Tetsuo Shibuya

We suggest the use of hash functions to cut down the communication costs when counting subgraphs under edge local differential privacy. While various algorithms exist for computing graph statistics, including the count of subgraphs, under the edge local differential privacy, many suffer with high communication costs, making them less efficient for large graphs. Though data compression is a typical approach in differential privacy, its application in local differential privacy requires a form of compression that every node can reproduce. In our study, we introduce linear congruence hashing. With a sampling rate of $s$, our method can cut communication costs by a factor of $s^2$, albeit at the cost of increasing variance in the published graph statistic by a factor of $s$. The experimental results indicate that, when matched for communication costs, our method achieves a reduction in the $\ell_2$-error for triangle counts by up to 1000 times compared to the performance of leading algorithms.