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High-order interaction events are common in real-world applications. Learningembeddings that encode the complex relationships of the participants from theseevents is of great importance in knowledge mining and predictive tasks. Despitethe success of existing approaches, e.g. Poisson tensor factorization, theyignore the sparse structure underlying the data, namely the occurredinteractions are far less than the possible interactions among all theparticipants. In this paper, we propose Nonparametric Embeddings of SparseHigh-order interaction events (NESH). We hybridize a sparse hypergraph (tensor)process and a matrix Gaussian process to capture both the asymptotic structuralsparsity within the interactions and nonlinear temporal relationships betweenthe participants. We prove strong asymptotic bounds (including both a lower andan upper bound) of the sparsity ratio, which reveals the asymptotic propertiesof the sampled structure. We use batch-normalization, stick-breakingconstruction, and sparse variational GP approximations to develop an efficient,scalable model inference algorithm. We demonstrate the advantage of ourapproach in several real-world applications.

Nonparametric Embeddings of Sparse High-Order Interaction Events