arXiv subjects

Yara Schütt

Publications and source records attributed to Yara Schütt.

2 recordsLinked to original sources

arXiv2025

Understanding the Theoretical Guarantees of DPM

In this study, we conducted an in-depth examination of the utility analysis of the differentially private mechanism (DPM). The authors of DPM have already established the probability of a good split being selected and of DPM halting. In this study, we expanded the analysis of the stopping criterion and provided an interpretation of these guarantees in the context of realistic input distributions. Our findings revealed constraints on the minimum cluster size and the metric weight for the scoring function. Furthermore, we introduced an interpretation of the utility of DPM through the lens of the clustering metric, the silhouette score. Our findings indicate that even when an optimal DPM-based split is employed, the silhouette score of the resulting clustering may still decline. This observation calls into question the suitability of the silhouette score as a clustering metric. Finally, we examined the potential of the underlying concept of DPM by linking it to a more theoretical view, that of $(ξ, ρ)$-separability. This extensive analysis of the theoretical guarantees of DPM allows a better understanding of its behaviour for arbitrary inputs. From these guarantees, we can analyse the impact of different hyperparameters and different input data sets, thereby promoting the application of DPM in practice for unknown settings and data sets.

cs.CR↗

arXiv2024

DPM: Clustering Sensitive Data through Separation

Clustering is an important tool for data exploration where the goal is to subdivide a data set into disjoint clusters that fit well into the underlying data structure. When dealing with sensitive data, privacy-preserving algorithms aim to approximate the non-private baseline while minimising the leakage of sensitive information. State-of-the-art privacy-preserving clustering algorithms tend to output clusters that are good in terms of the standard metrics, inertia, silhouette score, and clustering accuracy, however, the clustering result strongly deviates from the non-private KMeans baseline. In this work, we present a privacy-preserving clustering algorithm called DPM that recursively separates a data set into clusters based on a geometrical clustering approach. In addition, DPM estimates most of the data-dependent hyper-parameters in a privacy-preserving way. We prove that DPM preserves Differential Privacy and analyse the utility guarantees of DPM. Finally, we conduct an extensive empirical evaluation for synthetic and real-life data sets. We show that DPM achieves state-of-the-art utility on the standard clustering metrics and yields a clustering result much closer to that of the popular non-private KMeans algorithm without requiring the number of classes.

cs.CR↗