We study the propagation of outliers in cyclic causal graphs with linear structural equations, tracing them back to one or several "root cause" nodes. We show that it is possible to identify a short list of potential root causes provided that the perturbation is sufficiently strong and propagates according to the same structural equations as in the normal mode. This shortlist consists of the true root causes together with those of its parents lying on a cycle with the root cause. Notably, our method does not require prior knowledge of the causal graph.

Out-of-distribution (OOD) detection plays a crucial role in ensuring the robustness and reliability of machine learning systems deployed in real-world applications. Recent approaches have explored the use of unlabeled data, showing potential for enhancing OOD detection capabilities. However, effectively utilizing unlabeled in-the-wild data remains challenging due to the mixed nature of both in-distribution (InD) and OOD samples. The lack of a distinct set of OOD samples complicates the task of training an optimal OOD classifier. In this work, we introduce Medix, a novel framework designed to identify potential outliers from unlabeled data using the median operation. We use the median because it provides a stable estimate of the central tendency, as an OOD detection mechanism, due to its robustness against noise and outliers. Using these identified outliers, along with labeled InD data, we train a robust OOD classifier. From a theoretical perspective, we derive error bounds that demonstrate Medix achieves a low error rate. Empirical results further substantiate our claims, as Medix outperforms existing methods across the board in open-world settings, confirming the validity of our theoretical insights.

Ensuring the safety of self-driving cars remains a major challenge due to the complexity and unpredictability of real-world driving environments. Traditional testing methods face significant limitations, such as the oracle problem, which makes it difficult to determine whether a system's behavior is correct, and the inability to cover the full range of scenarios an autonomous vehicle may encounter. In this paper, we introduce a digital twin-driven metamorphic testing framework that addresses these challenges by creating a virtual replica of the self-driving system and its operating environment. By combining digital twin technology with AI-based image generative models such as Stable Diffusion, our approach enables the systematic generation of realistic and diverse driving scenes. This includes variations in weather, road topology, and environmental features, all while maintaining the core semantics of the original scenario. The digital twin provides a synchronized simulation environment where changes can be tested in a controlled and repeatable manner. Within this environment, we define three metamorphic relations inspired by real-world traffic rules and vehicle behavior. We validate our framework in the Udacity self-driving simulator and demonstrate that it significantly enhances test coverage and effectiveness. Our method achieves the highest true positive rate (0.719), F1 score (0.689), and precision (0.662) compared to baseline approaches. This paper highlights the value of integrating digital twins with AI-powered scenario generation to create a scalable, automated, and high-fidelity testing solution for autonomous vehicle safety.