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Dynamic graphs are rife with higher-order interactions, such as co-authorshiprelationships and protein-protein interactions in biological networks, thatnaturally arise between more than two nodes at once. In spite of the ubiquitouspresence of such higher-order interactions, limited attention has been paid tothe higher-order counterpart of the popular pairwise link prediction problem.Existing higher-order structure prediction methods are mostly based onheuristic feature extraction procedures, which work well in practice but lacktheoretical guarantees. Such heuristics are primarily focused on predictinglinks in a static snapshot of the graph. Moreover, these heuristic-basedmethods fail to effectively utilize and benefit from the knowledge of latentsubstructures already present within the higher-order structures. In thispaper, we overcome these obstacles by capturing higher-order interactionssuccinctly as \textit{simplices}, model their neighborhood by face-vectors, anddevelop a nonparametric kernel estimator for simplices that views the evolvinggraph from the perspective of a time process (i.e., a sequence of graphsnapshots). Our method substantially outperforms several baseline higher-orderprediction methods. As a theoretical achievement, we prove the consistency andasymptotic normality in terms of the Wasserstein distance of our estimatorusing Stein's method.

Understanding Higher-order Structures in Evolving Graphs: A Simplicial Complex based Kernel Estimation Approach