Given a sequence of random (directed and weighted) graphs, we address the problem of online monitoring and detection of changes in the underlying data distribution. Our idea is to endow sequential change-point detection (CPD) techniques with a graph representation learning substrate based on the versatile Random Dot Product Graph (RDPG) model. We consider efficient, online updates of a judicious monitoring function, which quantifies the discrepancy between the streaming graph observations and the nominal RDPG. This reference distribution is inferred via spectral embeddings of the first few graphs in the sequence. We characterize the distribution of this running statistic to select thresholds that guarantee error-rate control, and under simplifying approximations we offer insights on the algorithm’s detection resolution and delay. The end result is a lightweight online CPD algorithm, that is also explainable by virtue of the well-appreciated interpretability of RDPG embeddings. This is in stark contrast with most existing graph CPD approaches, which either rely on extensive computation, or they store and process the entire observed time series. An apparent limitation of the RDPG model is its suitability for undirected and unweighted graphs only, a gap we aim to close here to broaden the scope of the CPD framework. Unlike previous proposals, our non-parametric RDPG model for weighted graphs does not require a priori specification of the weights’ distribution to perform inference and estimation. This network modeling contribution is of independent interest beyond CPD. We offer an open-source implementation of the novel online CPD algorithm for weighted and direct graphs, whose effectiveness and efficiency are demonstrated via (reproducible) synthetic and real network data experiments.

中文翻译：

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加权和有向随机点积图的在线变点检测


给定一系列随机（有向和加权）图，我们解决了在线监控和检测底层数据分布变化的问题。我们的想法是为顺序变化点检测（CPD）技术提供基于通用随机点积图（RDPG）模型的图表示学习基底。我们考虑对明智的监控功能进行高效、在线更新，该功能量化流图观测值与名义 RDPG 之间的差异。该参考分布是通过序列中前几张图的谱嵌入推断出来的。我们描述了该运行统计数据的分布，以选择保证错误率控制的阈值，并在简化近似下，我们提供了有关算法检测分辨率和延迟的见解。最终结果是一个轻量级的在线 CPD 算法，该算法也可以通过 RDPG 嵌入广受好评的可解释性来解释。这与大多数现有的图 CPD 方法形成鲜明对比，这些方法要么依赖于大量计算，要么存储和处理整个观察到的时间序列。 RDPG 模型的一个明显限制是它仅适用于无向图和未加权图，我们的目标是缩小这一差距以扩大 CPD 框架的范围。与之前的提议不同，我们的加权图非参数 RDPG 模型不需要先验指定权重分布来执行推理和估计。这种网络建模贡献具有超越 CPD 的独立意义。 我们为加权图和直接图提供了新颖的在线 CPD 算法的开源实现，其有效性和效率通过（可重现的）合成和真实网络数据实验得到了证明。