The European Health Data Space (EHDS) aims to enable the sharing of health data across Europe to improve healthcare and research. While the EHDS mandates anonymization or pseudonymization of shared health data, these techniques may still allow adversaries to re-identify individuals. Local differential privacy (LDP) has been proposed as a formal privacy guarantee that can help mitigate this issue. In this paper, we consider a common problem when analyzing health data: estimating means for different groups. We discuss a generic privacy-preserving method for approximating the means of different groups in a decentralized setting where both the group and the value are considered private. We show that four concrete instantiations of the method based on existing mean estimation methods (Laplace, Bernoulli, Piecewise, and NPRR) are locally differentially private. We evaluate their performance on synthetic and real-world medical datasets. Our results show that the proposed methods can accurately estimate the group means, while maintaining privacy. However, similar to other LDP algorithms, our approach requires a sufficient amount of data (in our case a sufficient amount of samples per group) combined with a sufficiently large privacy budget ε to produce accurate results. We discuss concrete practical issues like choosing an appropriate input range, dealing with large privacy budgets through the use of the shuffle model of differential privacy, and the need for further analysis techniques to make LDP solutions applicable to practical medical data analysis.

Outlier detection stands as a critical cornerstone in the field of data mining, with a wide range of applications spanning from fraud detection to network security. However, real-world scenarios often lack labeled data for training, necessitating unsupervised outlier detection methods. This study centers on Unsupervised Outlier Model Selection (UOMS), with a specific focus on the family of Internal, Relative Evaluation of Outlier Solutions (IREOS) algorithms. IREOS measures outlier candidate separability by evaluating multiple maximum-margin classifiers and, while effective, it is constrained by its high computational demands. We investigate the impact of several different separation methods in UOMS in terms of ranking quality and runtime. Surprisingly, our findings indicate that different separability measures have minimal impact on IREOS’ effectiveness. However, using linear separation methods within IREOS significantly reduces its computation time. These insights hold significance for real-world applications where efficient outlier detection is critical. In the context of this work, we provide the code for the IREOS algorithm and our separability techniques.

Clustering is at the very core of machine learning, and its applications proliferate with the increasing availability of data. However, as datasets grow, comparing clusterings with an adjustment for chance becomes computationally difficult, preventing unbiased ground-truth comparisons and solution selection. We propose FastAMI, a Monte Carlo-based method to efficiently approximate the Adjusted Mutual Information (AMI) and extend it to the Standardized Mutual Information (SMI). The approach is compared with the exact calculation and a recently developed variant of the AMI based on pairwise permutations, using both synthetic and real data. In contrast to the exact calculation our method is fast enough to enable these adjusted information-theoretic comparisons for large datasets while maintaining considerably more accurate results than the pairwise approach.

Popular metrics for clustering comparison, like the Adjusted Rand Index and the Adjusted Mutual Information, are type II biased. The Standardized Mutual Information removes this bias but suffers from counterintuitive non-monotonicity and poor computational efficiency. We introduce the $p$-value adjusted Rand Index ($\operatorname{PMI}_2$), the first cluster comparison method that is type II unbiased and provably monotonous. The $\operatorname{PMI}_2$ has fast approximations that outperform the Standardized Mutual information. We demonstrate its unbiased clustering selection, approximation quality, and runtime efficiency on synthetic benchmarks. In experiments on image and social network datasets, we show how the $\operatorname{PMI}_2$ can help practitioners choose better clustering and community detection algorithms.