网络拓扑影响结构学习效果，超线性结构最难识别。
Benchmarking Constraint-Based Bayesian Structure Learning Algorithms: Role of Network Topology
- 固定节点数、边数和样本量，比较不同拓扑下的学习性能。
- 三种算法在超线性拓扑下敏感度显著下降，降幅达统计显著水平。
- 适合研究因果推断或算法评估的学者参考，尤其关注网络结构影响。
从多变量横截面数据建模现实实体间的关联，有助于揭示系统内各要素的协同作用。约束型贝叶斯结构学习（BSL）算法将这些关联建模为有向无环图（DAG）。以往基准测试主要关注维度（节点数）与样本量对性能的影响。本研究强调网络拓扑在基准测试中的关键作用：在固定节点数（48,64）、边数、样本量（2^10）及噪声强度（σ=3,6）的前提下，考察子线性、线性和超线性拓扑下三种主流约束型BSL算法（Peter-Clarke、Grow-Shrink、Incremental Association Markov Blanket）的表现。在线性和非线性模型中，三类算法在从子线性到超线性拓扑时，敏感度均出现统计显著（α=0.05）下降。结果表明，网络拓扑是制约约束型BSL算法性能的重要因素，应纳入基准测试设计考量。
原文摘要 · Abstract (English)
Modeling the associations between real world entities from their multivariate cross-sectional profiles can provide cues into the concerted working of these entities as a system. Several techniques have been proposed for deciphering these associations including constraint-based Bayesian structure learning (BSL) algorithms that model them as directed acyclic graphs. Benchmarking these algorithms have typically focused on assessing the variation in performance measures such as sensitivity as a function of the dimensionality represented by the number of nodes in the DAG, and sample size. The present study elucidates the importance of network topology in benchmarking exercises. More specifically, it investigates variations in sensitivity across distinct network topologies while constraining the nodes, edges, and sample-size to be identical, eliminating these as potential confounders. Sensitivity of three popular constraint-based BSL algorithms (Peter-Clarke, Grow-Shrink, Incremental Association Markov Blanket) in learning the network structure from multivariate cross-sectional profiles sampled from network models with sub-linear, linear, and super-linear DAG topologies generated using preferential attachment is investigated. Results across linear and nonlinear models revealed statistically significant $(α=0.05)$ decrease in sensitivity estimates from sub-linear to super-linear topology constitutively across the three algorithms. These results are demonstrated on networks with nodes $(N_{nods}=48,64)$, noise strengths $(σ=3,6)$ and sample size $(N = 2^{10})$. The findings elucidate the importance of accommodating the network topology in constraint-based BSL benchmarking exercises.
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