2021/02/06 by Manohar Kaul, Kaul, Manohar, Masaaki Imaizumi +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Bioinformatics and Genomic Networks #Complex Network Analysis Techniques #Computer science #Estimator #FOS: Computer and information sciences #Graph #Heuristic #Heuristics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical optimization #Mathematics #Pairwise comparison #Theoretical computer science #Topological and Geometric Data Analysis #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2102.03609
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/02/06 · openalex publication_date 2021/02/06 · arxiv updated 2021/02/09 · openalex created_date 2021/02/15 · openalex updated_date 2026/07/28
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 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.