Nonparametric Embeddings of Sparse High-Order Interaction Events

TL;DR

This paper introduces NESH, a nonparametric embedding method for sparse high-order interaction events that captures structural sparsity and nonlinear temporal relationships, with proven asymptotic bounds and scalable inference.

Contribution

The paper proposes a novel nonparametric embedding model combining hypergraph processes and Gaussian processes, addressing sparsity and nonlinear dynamics in high-order interactions.

Findings

Proven asymptotic bounds on sparsity ratio.

Efficient scalable inference algorithm.

Improved performance in real-world applications.

Abstract

High-order interaction events are common in real-world applications. Learning embeddings that encode the complex relationships of the participants from these events is of great importance in knowledge mining and predictive tasks. Despite the success of existing approaches, e.g. Poisson tensor factorization, they ignore the sparse structure underlying the data, namely the occurred interactions are far less than the possible interactions among all the participants. In this paper, we propose Nonparametric Embeddings of Sparse High-order interaction events (NESH). We hybridize a sparse hypergraph (tensor) process and a matrix Gaussian process to capture both the asymptotic structural sparsity within the interactions and nonlinear temporal relationships between the participants. We prove strong asymptotic bounds (including both a lower and an upper bound) of the sparsity ratio, which reveals the asymptotic properties of the sampled structure. We use batch-normalization, stick-breaking construction, and sparse variational GP approximations to develop an efficient, scalable model inference algorithm. We demonstrate the advantage of our approach in several real-world applications.