论文标题
多通道二进制中的离线更改点检测的精确测试，并将数据计入应用于网络的数据
Exact Tests for Offline Changepoint Detection in Multichannel Binary and Count Data with Application to Networks
论文作者
论文摘要
我们考虑在线检测二进制的单个变更点并计算时间序列。我们比较了基于累积总和（CUSUM）和似然比（LR）统计数据的精确测试，以及一个新的建议，将精确的两样本条件测试与多重性校正结合的新建议与基于布朗尼桥的标准渐近测试相结合，基于布朗桥的标准测试。从经验上我们看到，在驱动渐近测试的正常近似值的情况下，确切的测试更强大，不值得信赖：（i）小样本设置； （ii）稀疏参数设置； （iii）在边界附近具有变更点的时间序列。 我们还考虑了该问题的多通道版本，其中频道可以具有不同的更改点。控制错误的发现率（FDR），我们同时检测多个通道的变化。当具有变更点的通道数量远小于通道总数时，这种“本地”方法比多元全局测试方法更有优势。 作为一种自然应用，我们将网络值的时间序列考虑，并将我们的方法与（a）边缘用作二进制通道，以及（b）节点 - 数字或其他本地子图统计量作为计数通道。本地测试方法比全球网络变更点算法更具信息性。
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.
