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Graph-based anomaly detection is pivotal in diverse security applications, such as fraud detection in transaction networks and intrusion detection for network traffic. Standard approaches, including Graph Neural Networks (GNNs), often struggle to generalize across shifting data distributions. For instance, we observe that a real-world eBay transaction dataset revealed an over 50% decline in fraud detection accuracy when adding data from only a single new day to the graph due to data distribution shifts. This highlights a critical vulnerability in purely data-driven approaches. Meanwhile, real-world domain knowledge, such as "simultaneous transactions in two locations are suspicious," is more stable and a common existing component of real-world detection strategies. To explicitly integrate such knowledge into data-driven models such as GCNs, we propose KnowGraph, which integrates domain knowledge with data-driven learning for enhanced graph-based anomaly detection. KnowGraph comprises two principal components: (1) a statistical learning component that utilizes a main model for the overarching detection task, augmented by multiple specialized knowledge models that predict domain-specific semantic entities; (2) a reasoning component that employs probabilistic graphical models to execute logical inferences based on model outputs, encoding domain knowledge through weighted first-order logic formulas. In addition, KnowGraph has leveraged the Predictability-Computability-Stability (PCS) framework for veridical data science to estimate and mitigate prediction uncertainties. Empirically, KnowGraph has been rigorously evaluated on two significant real-world scenarios: collusion detection in the online marketplace eBay and intrusion detection within enterprise networks. Extensive experiments on these large-scale real-world datasets show that KnowGraph consistently outperforms state-of-the-art baselines in both transductive and inductive settings, achieving substantial gains in average precision when generalizing to completely unseen test graphs. Further ablation studies demonstrate the effectiveness of the proposed reasoning component in improving detection performance, especially under extreme class imbalance. These results highlight the potential of integrating domain knowledge into data-driven models for high-stakes, graph-based security applications. 

Machine learning (ML) robustness and domain generalization are fundamentally correlated: they essentially concern data distribution shifts under adversarial and natural settings, respectively. On one hand, recent studies show that more robust (adversarially trained) models are more generalizable. On the other hand, there is a lack of theoretical understanding of their fundamental connections. In this paper, we explore the relationship between regularization and domain transferability considering different factors such as norm regularization and data augmentations (DA). We propose a general theoretical framework proving that factors involving the model function class regularization are sufficient conditions for relative domain transferability. Our analysis implies that “robustness" is neither necessary nor sufficient for transferability; rather, regularization is a more fundamental perspective for understanding domain transferability. We then discuss popular DA protocols (including adversarial training) and show when they can be viewed as the function class regularization under certain conditions and therefore improve generalization. We conduct extensive experiments to verify our theoretical findings and show several counterexamples where robustness and generalization are negatively correlated on different datasets. 

As machine learning (ML) systems become pervasive, safeguarding their security is critical. However, recently it has been demonstrated that motivated adversaries are able to mislead ML systems by perturbing test data using semantic transformations. While there exists a rich body of research providing provable robustness guarantees for ML models against ℓp norm bounded adversarial perturbations, guarantees against semantic perturbations remain largely underexplored. In this paper, we provide TSS -- a unified framework for certifying ML robustness against general adversarial semantic transformations. First, depending on the properties of each transformation, we divide common transformations into two categories, namely resolvable (e.g., Gaussian blur) and differentially resolvable (e.g., rotation) transformations. For the former, we propose transformation-specific randomized smoothing strategies and obtain strong robustness certification. The latter category covers transformations that involve interpolation errors, and we propose a novel approach based on stratified sampling to certify the robustness. Our framework TSS leverages these certification strategies and combines with consistency-enhanced training to provide rigorous certification of robustness. We conduct extensive experiments on over ten types of challenging semantic transformations and show that TSS significantly outperforms the state of the art. Moreover, to the best of our knowledge, TSS is the first approach that achieves nontrivial certified robustness on the large-scale ImageNet dataset. For instance, our framework achieves 30.4% certified robust accuracy against rotation attack (within ±30∘) on ImageNet. Moreover, to consider a broader range of transformations, we show TSS is also robust against adaptive attacks and unforeseen image corruptions such as CIFAR-10-C and ImageNet-C.