Nonparametric Embeddings of Sparse High-Order Interaction Events
Nonparametric Embeddings of Sparse High-Order Interaction Events
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DOI：
10.48550/arxiv.2207.03639
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Z. Wang;Yiming Xu;Conor Tillinghast;Shibo Li;A. Narayan;Shandian Zhe
中科院分区：
文献类型：
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作者：
Z. Wang;Yiming Xu;Conor Tillinghast;Shibo Li;A. Narayan;Shandian Zhe
高阶交互事件在现实应用中很常见。学习嵌入对这些事件中参与者的复杂关系进行编码，对于知识挖掘和预测任务非常重要。尽管现有方法取得了成功，例如泊松张量分解，他们忽略了数据背后的稀疏结构，即发生的交互远远小于所有参与者之间可能的交互。在本文中，我们提出了稀疏高阶交互事件的非参数嵌入（NESH）。我们将稀疏超图（张量）过程和矩阵高斯过程混合起来，以捕获交互中的渐近结构稀疏性和参与者之间的非线性时间关系。我们证明了稀疏比的强渐近界（包括下界和上限），这揭示了采样结构的渐近特性。我们使用批量归一化、破棒构造和稀疏变分 GP 近似来开发高效、可扩展的模型推理算法。我们在几个实际应用中展示了我们的方法的优势。
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.