Local Differential Privacy (LDP) provides a formal guarantee of privacy that enables the collection and analysis of sensitive data without revealing any individual's data. While LDP methods have been extensively studied, there is a lack of a systematic and empirical comparison of LDP methods for descriptive statistics. In this paper, we first provide a systematization of LDP methods for descriptive statistics, comparing their properties and requirements. We demonstrate that several mean estimation methods based on sampling from a Bernoulli distribution are equivalent in the one-dimensional case and introduce methods for variance estimation. We then empirically compare methods for mean, variance, and frequency estimation. Finally, we provide recommendations for the use of LDP methods for descriptive statistics and discuss their limitations and open questions.

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.

Abstract Progress in making neural networks more robust against adversarial attacks is mostly marginal, despite the great efforts of the research community. Moreover, the robustness evaluation is often imprecise, making it challenging to identify promising approaches. We do an observational study on the classification decisions of 19 different state-of-the-art neural networks trained to be robust against adversarial attacks. This analysis gives a new indication of the limits of the robustness of current models on a common benchmark. In addition, our findings suggest that current untargeted adversarial attacks induce misclassification toward only a limited amount of different classes. Similarly, we find that previous attacks under-explore the perturbation space during optimization. This leads to unsuccessful attacks for samples where the initial gradient direction is not a good approximation of the final adversarial perturbation direction. Additionally, we observe that both over- and under-confidence in model predictions result in an inaccurate assessment of model robustness. Based on these observations, we propose a novel loss function for adversarial attacks that consistently improves their efficiency and success rate compared to prior attacks for all 30 analyzed models.

The reliability of neural networks is essential for their use in safety-critical applications. Existing approaches generally aim at improving the robustness of neural networks to either real-world distribution shifts (e.g., common corruptions and perturbations, spatial transformations, and natural adversarial examples) or worst-case distribution shifts (e.g., optimized adversarial examples). In this work, we propose the Decision Region Quantification (DRQ) algorithm to improve the robustness of any differentiable pre-trained model against both real-world and worst-case distribution shifts in the data. DRQ analyzes the robustness of local decision regions in the vicinity of a given data point to make more reliable predictions. We theoretically motivate the DRQ algorithm by showing that it effectively smooths spurious local extrema in the decision surface. Furthermore, we propose an implementation using targeted and untargeted adversarial attacks. An extensive empirical evaluation shows that DRQ increases the robustness of adversarially and non-adversarially trained models against real-world and worst-case distribution shifts on several computer vision benchmark datasets.

The vulnerability of deep neural networks to small and even imperceptible perturbations has become a central topic in deep learning research. Although several sophisticated defense mechanisms have been introduced, most were later shown to be ineffective. However, a reliable evaluation of model robustness is mandatory for deployment in safety-critical scenarios. To overcome this problem we propose a simple yet effective modification to the gradient calculation of state-of-the-art first-order adversarial attacks. Normally, the gradient update of an attack is directly calculated for the given data point. This approach is sensitive to noise and small local optima of the loss function. Inspired by gradient sampling techniques from non-convex optimization, we propose Dynamically Sampled Nonlocal Gradient Descent (DSNGD). DSNGD calculates the gradient direction of the adversarial attack as the weighted average over past gradients of the optimization history. Moreover, distribution hyperparameters that define the sampling operation are automatically learned during the optimization scheme. We empirically show that by incorporating this nonlocal gradient information, we are able to give a more accurate estimation of the global descent direction on noisy and non-convex loss surfaces. In addition, we show that DSNGD-based attacks are on average 35% faster while achieving 0.9% to 27.1% higher success rates compared to their gradient descent-based counterparts.

The susceptibility of deep neural networks to untrustworthy predictions, including out-of-distribution (OOD) data and adversarial examples, still prevent their widespread use in safety-critical applications. Most existing methods either require a retraining of a given model to achieve robust identification of adversarial attacks or are limited to out-of-distribution sample detection only. In this work, we propose a geometric gradient analysis (GGA) to improve the identification of untrustworthy predictions without retraining of a given model. GGA analyzes the geometry of the loss landscape of neural networks based on the saliency maps of their respective input. We observe considerable differences between the input gradient geometry of trustworthy and untrustworthy predictions. Using these differences, GGA outperforms prior approaches in detecting OOD data and adversarial attacks, including state-of-the-art and adaptive attacks.