Data imputation is crucial for addressing challenges posed by missing values in multivariate time series data across various fields, such as healthcare, traffic, and economics, and has garnered significant attention. Among various methods, diffusion model-based approaches show notable performance improvements. However, existing methods often cause disharmonious boundaries between missing and known regions and overlook long-range dependencies in missing data estimation, leading to suboptimal results. To address these issues, we propose a Diffusion-based time Series Data Imputation (DSDI) framework. We develop a weight-reducing injection strategy that incorporates the predicted values of missing points with reducing weights into the reverse diffusion process to mitigate boundary inconsistencies. Further, we introduce a multi-scale S4-based U-Net, which combines hierarchical information from different levels via multi-resolution integration to capture long-term dependencies. Experimental results demonstrate that our model outperforms existing imputation methods.

Graph-level anomaly detection is significant in diverse domains. To improve detection performance, counterfactual graphs have been exploited to benefit the generalization capacity by learning causal relations. Most existing studies directly introduce perturbations (e.g., flipping edges) to generate counterfactual graphs, which are prone to alter the semantics of generated examples and make them off the data manifold, resulting in sub-optimal performance. To address these issues, we propose a novel approach, Motif-consistent Counterfactuals with Adversarial Refinement (MotifCAR), for graph-level anomaly detection. The model combines the motif of one graph, the core subgraph containing the identification (category) information, and the contextual subgraph (non-motif) of another graph to produce a raw counterfactual graph. However, the produced raw graph might be distorted and cannot satisfy the important counterfactual properties: Realism, Validity, Proximity and Sparsity. Towards that, we present a Generative Adversarial Network (GAN)-based graph optimizer to refine the raw counterfactual graphs. It adopts the discriminator to guide the generator to generate graphs close to realistic data, i.e., meet the property Realism. Further, we design the motif consistency to force the motif of the generated graphs to be consistent with the realistic graphs, meeting the property Validity. Also, we devise the contextual loss and connection loss to control the contextual subgraph and the newly added links to meet the properties Proximity and Sparsity. As a result, the model can generate high-quality counterfactual graphs. Experiments demonstrate the superiority of MotifCAR.

A critical aspect of Graph Neural Networks (GNNs) is to enhance the node representations by aggregating node neighborhood information. However, when detecting anomalies, the representations of abnormal nodes are prone to be averaged by normal neighbors, making the learned anomaly representations less distinguishable. To tackle this issue, we propose CAGAD -- an unsupervised Counterfactual data Augmentation method for Graph Anomaly Detection -- which introduces a graph pointer neural network as the heterophilic node detector to identify potential anomalies whose neighborhoods are normal-node-dominant. For each identified potential anomaly, we design a graph-specific diffusion model to translate a part of its neighbors, which are probably normal, into anomalous ones. At last, we involve these translated neighbors in GNN neighborhood aggregation to produce counterfactual representations of anomalies. Through aggregating the translated anomalous neighbors, counterfactual representations become more distinguishable and further advocate detection performance. The experimental results on four datasets demonstrate that CAGAD significantly outperforms strong baselines, with an average improvement of 2.35% on F1, 2.53% on AUC-ROC, and 2.79% on AUC-PR.