Causal discovery aims to learn causal relationships between variables from targeted data, making it a fundamental task in machine learning. However, causal discovery algorithms often rely on unverifiable causal assumptions, which are usually difficult to satisfy in real-world data, thereby limiting the broad application of causal discovery in practical scenarios. Inspired by these considerations, this work extensively benchmarks the empirical performance of various mainstream causal discovery algorithms, which assume i.i.d. data, under eight model assumption violations. Our experimental results show that differentiable causal discovery methods exhibit robustness under the metrics of Structural Hamming Distance and Structural Intervention Distance of the inferred graphs in commonly used challenging scenarios, except for scale variation. We also provide the theoretical explanations for the performance of differentiable causal discovery methods. Finally, our work aims to comprehensively benchmark the performance of recent differentiable causal discovery methods under model assumption violations, and provide the standard for reasonable evaluation of causal discovery, as well as to further promote its application in real-world scenarios.

This paper presents the MinUnc method to construct m-/belief functions in the framework of the Dempster-Shafer theory to represent the uncertainty in a given body of evidence. Using the Aprinciple of minimum uncertainty and the concepts of entropy and non-specificity, the MinUnc method specifies a partition of a finite interval on the real line and assigns belief masses to the uniform subintervals. The proposed MinUnc method is illustrated using a simple example and applied to uncertainty representation of air flight arrival delay data set.