提出高效且理论严谨的变分方法，提升二部网络节点流行度建模精度。
Variational Estimators for Node Popularity Models
- 基于变分期望最大化框架，实现对节点流行度模型的快速估计。
- 在多种二部与无向网络中，估计精度显著优于现有算法。
- 适用于真实网络数据，兼具理论保障与实际鲁棒性，适合网络分析研究者。
节点流行度是刻画现实世界网络连接异质性的重要因素，尤其在二部网络中，不同分区的节点可能呈现不同的流行度模式，由此催生了双路节点流行度模型（TNPM）。现有方法如两阶段分段余弦（TSDC）算法虽具可扩展性，但在准确性和跨网络适用性上存在局限。本文提出一种计算高效且理论严谨的变分期望最大化（VEM）框架用于TNPM。我们建立了所提变分估计器在二部网络中社区分配标签的一致性。通过大量模拟实验表明，该方法在多种二部及无向网络中均实现更优的估计精度。最后，在真实世界二部与无向网络上的评估进一步验证了其有效性与鲁棒性。
原文摘要 · Abstract (English)
Node popularity is recognized as a key factor in modeling real-world networks, capturing heterogeneity in connectivity across communities. This concept is equally important in bipartite networks, where nodes in different partitions may exhibit varying popularity patterns, motivating models such as the Two-Way Node Popularity Model (TNPM). Existing methods, such as the Two-Stage Divided Cosine (TSDC) algorithm, provide a scalable estimation approach but may have limitations in terms of accuracy or applicability across different types of networks. In this paper, we develop a computationally efficient and theoretically justified variational expectation-maximization (VEM) framework for the TNPM. We establish label consistency for the estimated community assignments produced by the proposed variational estimator in bipartite networks. Through extensive simulation studies, we show that our method achieves superior estimation accuracy across a range of bipartite as well as undirected networks compared to existing algorithms. Finally, we evaluate our method on real-world bipartite and undirected networks, further demonstrating its practical effectiveness and robustness.
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