多通道二进制和计数数据离线变点检测的精确检验及其在网络中的应用
Exact Tests for Offline Changepoint Detection in Multichannel Binary and Count Data with Application to Networks
摘要：
我们考虑离线检测一个单一的二进制和计数时间序列的变点。我们比较精确的累积和（AUUM）和似然比（LR）统计的基础上，和一个新的建议，结合精确的双样本条件检验与多重校正，对标准的渐近检验的基础上的布朗桥近似AUUM统计。我们从经验上看到，在驱动渐近检验的正态近似不值得信赖的情况下，精确检验要强大得多：（i）小样本设置;（ii）稀疏参数设置;（iii）边界附近有变点的时间序列。我们还考虑了多通道版本的问题，其中通道可以有不同的变点。通过控制错误发现率（FDR），我们可以同时检测多个通道中的变化。这种“本地”的方法被证明是更有利的多变量的全球测试方法时，变点的通道的数量远远小于通道的总数。作为一个自然的应用，我们考虑网络值时间序列，并使用我们的方法（a）边缘作为二进制通道和（b）节点度或其他局部子图统计作为计数通道。局部测试方法被认为是更翔实的比全球网络变点算法。
英文摘要：
We consider offline detection of a single changepoint in binary and count time-series. We compare exact tests based on the cumulative sum (CUSUM) and the likelihood ratio (LR) statistics, and a new proposal that combines exact two-sample conditional tests with multiplicity correction, against standard asymptotic tests based on the Brownian bridge approximation to the CUSUM statistic. We see empirically that the exact tests are much more powerful in situations where normal approximations driving asymptotic tests are not trustworthy: (i) small sample settings; (ii) sparse parametric settings; (iii) time-series with changepoint near the boundary. We also consider a multichannel version of the problem, where channels can have different changepoints. Controlling the False Discovery Rate (FDR), we simultaneously detect changes in multiple channels. This "local" approach is shown to be more advantageous than multivariate global testing approaches when the number of channels with changepoints is much smaller than the total number of channels. As a natural application, we consider network-valued time-series and use our approach with (a) edges as binary channels and (b) node-degrees or other local subgraph statistics as count channels. The local testing approach is seen to be much more informative than global network changepoint algorithms.
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