加权有向随机点积图的在线变点检测
Online Change Point Detection for Weighted and Directed Random Dot Product Graphs
摘要：
给定一个随机（有向和加权）图序列，我们解决了在线监测和检测底层数据分布变化的问题。我们的想法是赋予顺序变点检测（CPD）技术与图形表示学习基板的基础上，通用的随机点积图（RDPG）模型。我们认为有效的，在线更新的明智的监测功能，量化的流图观测和标称RDPG之间的差异。该参考分布通过序列中前几个图的谱嵌入来推断。我们的特征分布的运行统计选择阈值，保证错误率控制，并在简化的近似下，我们提供的算法的检测分辨率和延迟的见解。最终的结果是一个轻量级的在线CPD算法，这也是可以解释的RDPG嵌入的良好理解的可解释性。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的计算，要么存储和处理整个观察到的时间序列。RDPG模型的一个明显的局限性是它只适用于无向和无权图，我们的目标是在这里缩小差距，扩大CPD框架的范围。与以前的建议，我们的非参数RDPG模型的加权图不需要先验规范的权重的分布进行推断和估计。这种网络建模的贡献是独立的利益超越CPD。我们提供了一个开源的实现的新的在线CPD算法的加权和直接的图形，其有效性和效率证明通过（可重复的）合成和真实的网络数据实验。
英文摘要：
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.
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