Exact tests for offline changepoint detection in multichannel binary and count data with application to networks

Abstract

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 compare these exact tests against their bootstrap-based variants which do not have exact type I error control guarantees. Further, we 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.

Keywords:

• Conditional tests
• permutation tests and bootstrap-based tests
• CUSUM statistic
• global vs. local testing
• multiple testing

Mathematics subject classifications:

• 62F03
• 62M99

View correction statement:

Correction

Acknowledgments

We thank the referees for their thoughtful comments which led to an improved version of this manuscript.

Data availability statement

The US senate rollcall dataset is available in [30] and the MIT reality mining data is available in [32]. We constructed the corresponding network-valued time-series using the above mentioned publicly available datasets. The constructed network time-series that support the findings of this study are available from the corresponding author upon request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article was originally published with errors, which have now been corrected in the online version. Please see Correction (https://doi.org/10.1080/00949655.2023.2235788)

Additional information

Funding

The research of Shyamal K. De is supported by grant MTR/2017/000503 under the MATRICS scheme provided by Science and Engineering Research Board, Government of India. Soumendu Sundar Mukherjee is supported by an INSPIRE Faculty Fellowship from the Department of Science and Technology, Government of India.