ADA-GAD: Anomaly-Denoised Autoencoders for Graph Anomaly Detection

Graph anomaly detection is crucial for identifying nodes that deviate from regular behavior within graphs, benefiting various domains such as fraud detection and social network. Although existing reconstruction-based methods have achieved considerable success, they may face the \textit{Anomaly Overfitting} and \textit{Homophily Trap} problems caused by the abnormal patterns in the graph, breaking the assumption that normal nodes are often better reconstructed than abnormal ones. Our observations indicate that models trained on graphs with fewer anomalies exhibit higher detection performance. Based on this insight, we introduce a novel two-stage framework called Anomaly-Denoised Autoencoders for Graph Anomaly Detection (ADA-GAD). In the first stage, we design a learning-free anomaly-denoised augmentation method to generate graphs with reduced anomaly levels. We pretrain graph autoencoders on these augmented graphs at multiple levels, which enables the graph autoencoders to capture normal patterns. In the next stage, the decoders are retrained for detection on the original graph, benefiting from the multi-level representations learned in the previous stage. Meanwhile, we propose the node anomaly distribution regularization to further alleviate \textit{Anomaly Overfitting}. We validate the effectiveness of our approach through extensive experiments on both synthetic and real-world datasets.

A Unified Generalization Analysis of Re-Weighting and Logit-Adjustment for Imbalanced Learning

Real-world datasets are typically imbalanced in the sense that only a few classes have numerous samples, while many classes are associated with only a few samples. As a result, a na\"ive ERM learning process will be biased towards the majority classes, making it difficult to generalize to the minority classes. To address this issue, one simple but effective approach is to modify the loss function to emphasize the learning on minority classes, such as re-weighting the losses or adjusting the logits via class-dependent terms. However, existing generalization analysis of such losses is still coarse-grained and fragmented, failing to explain some empirical results. To bridge this gap, we propose a novel technique named data-dependent contraction to capture how these modified losses handle different classes. On top of this technique, a fine-grained generalization bound is established for imbalanced learning, which helps reveal the mystery of re-weighting and logit-adjustment in a unified manner. Furthermore, a principled learning algorithm is developed based on the theoretical insights. Finally, the empirical results on benchmark datasets not only validate the theoretical results but also demonstrate the effectiveness of the proposed method.

Optimizing Partial Area Under the Top-k Curve: Theory and Practice

Top-k error has become a popular metric for large-scale classification benchmarks due to the inevitable semantic ambiguity among classes. Existing literature on top-k optimization generally focuses on the optimization method of the top-k objective, while ignoring the limitations of the metric itself. In this paper, we point out that the top-k objective lacks enough discrimination such that the induced predictions may give a totally irrelevant label a top rank. To fix this issue, we develop a novel metric named partial Area Under the top-k Curve (AUTKC). Theoretical analysis shows that AUTKC has a better discrimination ability, and its Bayes optimal score function could give a correct top-K ranking with respect to the conditional probability. This shows that AUTKC does not allow irrelevant labels to appear in the top list. Furthermore, we present an empirical surrogate risk minimization framework to optimize the proposed metric. Theoretically, we present (1) a sufficient condition for Fisher consistency of the Bayes optimal score function; (2) a generalization upper bound which is insensitive to the number of classes under a simple hyperparameter setting. Finally, the experimental results on four benchmark datasets validate the effectiveness of our proposed framework.