Dynamic graphs are common in many applications to conveniently model heterogeneous data integrated from multiple sources. We study the monitoring of predictive events in dynamic graphs. Treating the problem as a continuous multi-label classification, we use deep metric learning to manage the embedding space and to create spherical codes where each codeword is an embedding vector representing a cluster of data state embeddings with the same results of the predictive events. By continuously training data embeddings from a dynamic graph neural network (DGNN) model and a code generator together, our method, called SCode, achieves significantly better accuracy than DGNN baselines. Moreover, SCode is also about twice as fast as the DGNN baselines, owing to its efficient matching between data state embedding and codewords for multiple events together. Finally, our training sample complexity analysis also sheds light on the generalizability of the online learning.

We observe the need for continuous, online training of dynamic graph neural network (DGNN) models while at the same time using them to answer continuous predictive queries as data streams in. This implies significant training-time and memory costs. Along with the DGNN model learning, we simultaneously learn a weight/priority distribution over the nodes via a randomized online algorithm. In turn, the DGNN is continuously trained/learned by sampling nodes from the learned distribution and performing the chosen nodes' partitions of training work. We also devise a novel graph Kernel Density Estimation technique to smooth the distribution and improve the learning quality. Our experiments show that continuous online learning is much needed for graph streams and our approach significantly improves the standard DGNN models-to achieve the same accuracy, the training time ranges from several times to two orders of magnitude shorter, and the maximum memory consumption is several times to 20 times smaller.

We study a novel problem of continuously predicting a number of user-subscribed continuous analytics targets (CATs) in dynamic networks. Our architecture includes any dynamic graph neural network model as the back end applied over the network data, and per CAT front end models that return results with their confidence to users. We devise a data filtering algorithm that feeds a provably optimal subset of data in the embedding space from back end model to front end models. Secondly, to ensure fairness in terms of query result accuracy for different CATs and users, we propose a fairness metric and a fairness-aware training scheduling algorithm, along with accuracy guarantees on fairness estimation. Our experiments over five real-world datasets show that our proposed solution is effective, efficient, fair, extensible, and adaptive.

Heterogeneous graph streams are very common in the applications today. Although representation learning has advantages in prediction accuracy, it is inherently deficient in the abilities to interpret or to reason well. It has long been realized as far back as in 1990 by Marvin Minsky that connectionist networks and symbolic rules should co-exist in a system and overcome the deficiencies of each other. The goal of this paper is to show that it is feasible to simultaneously and efficiently perform representation learning (for connectionist networks) and rule learning spontaneously out of the same online training process for graph streams. We devise such a system called RL$^2$, and show, both analytically and empirically, that it is highly efficient and responsive for graph streams, and produces good results for both representation learning and rule learning in terms of prediction accuracy and returning top-quality rules for interpretation and building dynamic Bayesian networks.