发表机构
King Juan Carlos University; Delft University of Technology（胡安·卡洛斯国王大学; 代尔夫特理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于节点信号观测的精确贝叶斯跟踪器，用于动态网络拓扑，利用快速沃尔什-哈达玛变换降低计算复杂度，并通过期望最大化学习转移概率，在合成和真实数据上验证了优越性能。
AI 中文摘要
跟踪网络拓扑的时间演化是社交网络、流行病学和传感器系统等领域的一个基本挑战。本文利用节点信号观测，为无权重有向图开发了一种精确的贝叶斯跟踪器。该框架在每个时间步生成网络状态的完整后验概率分布，自然地实现了不确定性量化、预测和基于原则的决策。我们将网络动态建模为布尔超立方体上的马尔可夫过程，其中边根据翻转概率独立转移。为了高效计算，我们将预测步骤转化为二元卷积，并利用快速沃尔什-哈达玛变换将计算成本从$\mathcal{O} (4^k)$降低到$\mathcal{O} (k 2^k)$，其中$k$是最大节点度。当网络转移概率未知时，我们开发了一个期望最大化框架，从观测信号中学习这些概率。在合成数据集和六个真实世界数据集上的综合实验验证了所提出的方法，并展示了其相对于最先进和经典基线方法的优越跟踪精度、更快的拓扑变化恢复速度以及有意义的不确定性估计。
英文摘要
Tracking the temporal evolution of network topologies is a fundamental challenge in social networks, epidemiology, and sensor systems, among others. This paper develops an exact Bayesian tracker for unweighted, directed graphs using nodal signal observations. This framework yields the full posterior probability distribution over network states at each time step, naturally enabling uncertainty quantification, prediction, and principled decision-making. We model the network dynamics as a Markov process on the Boolean hypercube, where edges transition independently according to a flip probability. For efficient computation, we cast the prediction step as a dyadic convolution, and leverage the Fast Walsh-Hadamard Transform to reduce the computational cost from $\mathcal{O} (4^k)$ to $\mathcal{O} (k 2^k)$, where $k$ is the maximum node degree. When the network transition probabilities are unknown, we develop an Expectation-Maximization framework to learn them from the observed signals. Comprehensive experiments on synthetic and six real-world datasets validate the proposed method and demonstrate its superior tracking accuracy, faster recovery from topological changes, and meaningful uncertainty estimates compared to state-of-the-art and classical baselines.
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