论文标题
AZ-WHITESS测试：在时空图上对不相关噪声的测试
AZ-whiteness test: a test for uncorrelated noise on spatio-temporal graphs
论文作者
论文摘要
我们介绍了图形的第一个白度测试，即与动态图的节点相关的多变量时间序列的白度测试。该统计检验旨在在近距离观察结果之间找到串行依赖性，以及给定基础图的相邻观测值之间的空间依赖性。提出的测试是系统识别文献中传统测试的时空扩展，并在涉及图信号的类似但更通用的应用程序场景中找到应用。 AZ-Test具有多功能性，可以使基础图具有动态性，拓扑和节点集的变化并加权，因此可以考虑到不同强度的连接，就像在许多应用程序场景中一样，例如运输网络和传感器网格。已知渐近分布（随着图表的数量或时间观测的增加）是已知的，并且不假定分布的数据相同。我们验证了对合成和现实世界问题的测试的实用值，并通过分析附加到图形流的预测残差来展示如何使用测试来评估时空预测模型的质量。
We present the first whiteness test for graphs, i.e., a whiteness test for multivariate time series associated with the nodes of a dynamic graph. The statistical test aims at finding serial dependencies among close-in-time observations, as well as spatial dependencies among neighboring observations given the underlying graph. The proposed test is a spatio-temporal extension of traditional tests from the system identification literature and finds applications in similar, yet more general, application scenarios involving graph signals. The AZ-test is versatile, allowing the underlying graph to be dynamic, changing in topology and set of nodes, and weighted, thus accounting for connections of different strength, as is the case in many application scenarios like transportation networks and sensor grids. The asymptotic distribution -- as the number of graph edges or temporal observations increases -- is known, and does not assume identically distributed data. We validate the practical value of the test on both synthetic and real-world problems, and show how the test can be employed to assess the quality of spatio-temporal forecasting models by analyzing the prediction residuals appended to the graphs stream.
