Many real-world datasets including stock prices or disease records are represented as regular or irregular tensors across multiple domains.How can we accurately capture patterns from both irregular and regular tensors in a newly emerging domain by leveraging existing ones from multiple domains?This problem is crucial for applications such as identifying patterns of new diseases using data from existing ones. A main challenge is that the new target tensors contain limited information due to their recent emergence. Previously, PARAFAC2- and PARAFAC-based methods have been widely used to find patterns in irregular and regular tensors, respectively, through decomposing them into latent factors. However, they cannot effectively transfer knowledge from previously known tensors to the new one. In this work, we propose a fast and accurate domain adaptation method for tensor decomposition. We proposeMeta-P2for irregular tensors andMeta-Pfor regular tensors. BothMeta-P2andMeta-Plearn general and easily-adaptable information– - referred to as the meta factor—from multiple source domains. Using this meta factor, they efficiently identify patterns in a new target tensor. Extensive experiments on real-world datasets show thatMeta-P2andMeta-Pachieve the state-of-the-art performance across various downstream tasks, including missing value prediction and anomaly detection.

Given an edge-incomplete graph, how can we accurately find its missing links? The problem aims to discover the missing relations between entities when their relationships are represented as a graph. Edge-incomplete graphs are prevalent in real-world due to practical limitations, such as not checking all users when adding friends in a social network. Addressing the problem is crucial for various tasks, including recommending friends in social networks and finding references in citation networks. However, previous approaches rely heavily on the given edge-incomplete (observed) graph, making it challenging to consider the missing (unobserved) links. In this paper, we propose PULL, an accurate link prediction method based on the positive-unlabeled (PU) learning. PULL treats the observed edges in the training graph as positive examples, and the unconnected node pairs as unlabeled ones. PULL effectively prevents the link predictor from blindly trusting the observed graph by proposing latent variables for every edge, and leveraging the expected graph structure with respect to these variables. Extensive experiments on real- world datasets show that PULL consistently outperforms the baselines for predicting links in edge-incomplete graphs.

How can we accurately predict the signs of unseen links in partially observed signed graphs? Signed graphs are widely used to represent complex relationships in areas such as social and biological networks. Although prior methods enhance representation learning by extending Graph Neural Networks with social theories, they rely on the unrealistic assumption that all link signs are known. In practice, however, link signs are often only partially labeled due to the high cost or difficulty of obtaining ground-truth annotations. For example, in the Bitcoin transaction network, only a subset of interactions can be labeled as trusted or untrusted, while many remain unlabeled. In this work, we propose PIGLET (PROBABILISTIC MESSAGE PASSING FOR SEMI-SUPERVISED LINK SIGN PREDICTION), a novel approach for accurate link sign prediction on signed graphs with partially observed sign labels. The main idea is to probabilistically interpret unlabeled links as both positive and negative based on a soft-labeling strategy, allowing information to be propagated through both types of edges. To mitigate the effect of uncertain predictions, we use confidence-based weights to downplay unreliable edges. PIGLET balances the importance of edges with relation-aware attention scores as well. PIGLET establishes a theoretical connection between the ExpectationMaximization (EM) algorithm and its iterative refinement of node embeddings and soft labels. Extensive experiments show that PIGLET consistently outperforms existing methods on realworld datasets under semi-supervised setting.

Given an irregular tensor from a newly emerging domain, how can we quickly and accurately capture its patterns utilizing existing irregular tensors in multiple domains? The problem is of great importance for various tasks such as finding patterns of a new disease using pre-existing diseases data. This is challenging as new target tensors have limited information due to their recent emergence. Thus, carefully utilizing the existing source tensors for analyzing the target tensor is helpful. PARAFAC2 decomposition is a strong tool for finding the patterns of irregular tensors, and the patterns are used in many applications such as missing value prediction and anomaly detection. However, previous PARAFAC2-based works cannot adaptably handle newly emerging target tensors utilizing the source tensors.