彙總關係資料下未知網絡連結重建：貝葉斯潛在曲面建模與懲罰迴歸法探討

Abstract

精確的網絡資料對於經濟學、金融、社會學、流行病學及電腦科學等領域皆至關重要。然而，現實限制常使研究者無法取得完整的鄰接矩陣，只能仰賴部分或彙總資訊。彙總型關係資料（Aggregated Relational Data, ARD）為常見形式，受訪者僅需回報與具特定屬性節點的連結數，而非完整列出所有聯絡對象。 本論文比較並延伸兩種從 ARD 重建網絡的核心方法：貝氏潛曲面模型（Bayesian Latent Surface Model, BLSM）與懲罰式迴歸（Frequentist Penalized Regression）。研究內容涵蓋可識別性、一致性、對報告誤差的穩健處理、大規模資料推斷，以及潛在的隱私保護應用。貝氏方法將節點嵌入高維球面空間，以幾何距離刻畫連結傾向；懲罰式迴歸則利用高維最佳化結構整合協變數，具良好擴展性。模擬實驗探討特徵設計、測量誤差與樣本規模之交互作用，並以（類）實證資料展示方法於金融風險管理、社群推薦與疫情追蹤等領域的應用潛力。 結果顯示，儘管 ARD 資訊較粗，仍保留大量網絡結構訊息，能支撐規模化且準確的推斷。本研究亦提出自適應特徵收集、幾何—懲罰混合方法及審慎資料共享策略，以兼顧理論嚴謹與實務價值。

Accurate network data matter across economics, finance, sociology, epidemiology, and computer science, yet complete adjacency matrices are rarely available. Researchers therefore rely on partial or aggregated information. Aggregated Relational Data (ARD) summarizes the number of ties to attribute-defined groups rather than enumerating all links. This dissertation compares and extends two approaches for reconstructing networks from ARD: a Bayesian Latent Surface Model (BLSM) and frequentist penalized regression. We study identifiability, robustness to misreporting, scalability, and privacy. BLSM places nodes on a hypersphere so that link likelihoods depend on geometric distance; penalized regression recasts unobserved edges as a high-dimensional optimization that integrates covariates and scales efficiently. Simulations examine the roles of trait design, measurement error, and sample size, and applications with real or quasi-real data—interbank risk, social recommendation, and epidemic contact tracing—demonstrate practical utility. Results show that, despite its coarseness, ARD preserves sufficient structure for accurate, scalable inference. The work proposes adaptive trait collection, hybrid geometry–penalty models, and privacy-aware data-sharing strategies that balance theoretical guarantees with practical deployment.