High-dimensional, multiscale online changepoint detection

• 成果类型: Article
• 署名作者: Chen, Yudong; Wang, Tengyao; Samworth, Richard J.
• 署名单位: University of Cambridge; University of London; London School Economics & Political Science; University of London; University College London
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12447
• 发表日期: 2022
• 页码: 234-266
• 关键词: change-point estimation; SPARSE; sums

摘要

We introduce a new method for high-dimensional, online changepoint detection in settings where a p-variate Gaussian data stream may undergo a change in mean. The procedure works by performing likelihood ratio tests against simple alternatives of different scales in each coordinate, and then aggregating test statistics across scales and coordinates. The algorithm is online in the sense that both its storage requirements and worstcase computational complexity per new observation are independent of the number of previous observations; in practice, it may even be significantly faster than this. We prove that the patience, or average run length under the null, of our procedure is at least at the desired nominal level, and provide guarantees on its response delay under the alternative that depend on the sparsity of the vector of mean change. Simulations confirm the practical effectiveness of our proposal, which is implemented in the R package ocd, and we also demonstrate its utility on a seismology data set.