Article publicat / Published paper: Hong, C.; et al. Efficient calculation of the robustness measure R for complex networks.
AbstractIn a recent work [Proc. Natl. Acad. Sci. USA, 108 (2011) 3838], Schneider et al. proposed a new measure R for network robustness, where the value of R is calculated within the entire process of malicious node attacks. In this paper, we present an approach to improve the calculation efficiency of R, in which a computationally efficient robustness measure R ′ is introduced when the fraction of failed nodes reaches to a critical threshold q c . Simulation results on three different types of network models and three real networks show that these networks all exhibit a computationally efficient robustness measure R ′ . The relationships between R ′ and the network size N and the network average degree ⟨k⟩ are also explored. It is found that the value of R ′ decreases with N while increases with ⟨k⟩. Our results would be useful for improving the calculation efficiency of network robustness measure R for complex networks.
Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world datasets. As a result, many existing causal discovery methods can fail under limited data. In this work, we propose Bayesian-augmented frequentist independence tests to improve the performance of constraint-based causal discovery methods under insufficient data: 1) We firstly introduce a Bayesian method to estimate mutual information (MI), based on which we propose a robust MI based independence test; 2) Secondly, we consider the Bayesian estimation of hypothesis likelihood and incorporate it into a well-defined statistical test, resulting in a robust statistical testing based independence test. We apply proposed independence tests to constraint-based causal discovery methods and evaluate the performance on benchmark datasets with insufficient samples. Experiments show significant performance improvement in terms of both accuracy and efficiency over SOTA methods.
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