  Dynamic graphs are rife with higher-order interactions, such as co-authorship
relationships and protein-protein interactions in biological networks, that
naturally arise between more than two nodes at once. In spite of the ubiquitous
presence of such higher-order interactions, limited attention has been paid to
the higher-order counterpart of the popular pairwise link prediction problem.
Existing higher-order structure prediction methods are mostly based on
heuristic feature extraction procedures, which work well in practice but lack
theoretical guarantees. Such heuristics are primarily focused on predicting
links in a static snapshot of the graph. Moreover, these heuristic-based
methods fail to effectively utilize and benefit from the knowledge of latent
substructures already present within the higher-order structures. In this
paper, we overcome these obstacles by capturing higher-order interactions
succinctly as \textit{simplices}, model their neighborhood by face-vectors, and
develop a nonparametric kernel estimator for simplices that views the evolving
graph from the perspective of a time process (i.e., a sequence of graph
snapshots). Our method substantially outperforms several baseline higher-order
prediction methods. As a theoretical achievement, we prove the consistency and
asymptotic normality in terms of the Wasserstein distance of our estimator
using Stein's method.
