超图表示学习中的超边随机效应

中文摘要 AI 辅助

超图记录了实体之间的多向交互。从观察到的多向交互背后的组合结构中提取信息是许多现实世界问题中的核心任务。现有方法面临若干局限性。首先，许多针对超图的深度架构并未明确利用潜在的低秩结构，这可能会牺牲学习表示中的简约性和可解释性。其次，许多基于低秩的方法作用于张量表示，这通常要求超边具有均匀大小，从而限制了它们对具有非均匀超边大小的一般超图的适用性。第三，许多方法忽略了超边往往源于异构机制这一事实。例如，医疗症状可能共同出现在患有非常不同病症的患者档案中，这种异质性应被纳入学习过程。在本工作中，我们开发了一个使用超边随机效应的超图表示学习通用框架，同时利用超图中的低秩结构。所提出的框架适应超边形成中的潜在异质性，同时保留实体交互模式。我们建立了模型参数的可辨识性以及该框架下表示级恢复的理论保证。该框架允许对超边随机效应进行灵活设定；在本文中，我们研究了三种选择：类别型、高斯混合型和基于得分的效应，并开发了相应的估计算法。通过模拟研究，我们证明了所提方法在恢复潜在结构和捕获异构交互模式方面的有效性。对真实世界超图数据集的实证研究进一步说明了我们方法的实际效用。

英文摘要

Hypergraphs record multi-way interactions among entities. Extracting information from the combinatorial structure underlying observed multi-way interactions is a central task in many real-world problems. Existing methods face several limitations. First, many deep architectures for hypergraphs do not explicitly exploit the potential low-rank structure, which can sacrifice parsimony and interpretability in the learned representations. Second, many low-rank-based methods operate on tensor representations, which typically require hyperlinks to have uniform sizes and thus limit their applicability to general hypergraphs with non-uniform hyperlink sizes. Third, many methods ignore the fact that hyperlinks often arise from heterogeneous mechanisms. For example, medical symptoms may co-occur in the profiles of patients with very different conditions, and such heterogeneity should be incorporated into the learning process. In this work, we develop a general framework for hypergraph representation learning using hyperlink random effects while exploiting the low-rank structure in hypergraphs. The proposed framework accommodates latent heterogeneity in hyperlink formation while preserving entity interaction patterns. We establish identifiability of the model parameters and theoretical guarantees of representation-level recovery under this framework. The framework allows flexible specifications for the hyperlink random effects; in this paper, we study three choices: categorical, Gaussian mixture, and score-based effects, and develop corresponding estimation algorithms. Through simulation studies, we demonstrate the effectiveness of the proposed method in recovering latent structure and capturing heterogeneous interaction patterns. Empirical studies on real-world hypergraph datasets further illustrate the practical utility of our approach.

发表机构

• Harvard University（哈佛大学）
• University of California, Davis（加州大学戴维斯分校）
• University of Michigan（密歇根大学）

机构由 AI 辅助整理，请以论文原文为准。