Online multivariate changepoint detection: leveraging links with computational geometry

• 成果类型: Article; Early Access
• 署名作者: Pishchagina, Liudmila; Romano, Gaetano; Fearnhead, Paul; Runge, Vincent; Rigaill, Guillem
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Lancaster University; Universite Paris Saclay; INRAE; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Universite Paris Saclay; AgroParisTech; INRAE
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf046
• 发表日期: 2025
• 关键词: convex-hull; binary segmentation; algorithm; points; number

摘要

The increasing volume of data streams poses significant computational challenges for detecting changepoints online. Likelihood-based methods are effective, but a naive sequential implementation becomes impractical online due to high computational costs. We develop an online algorithm that exactly calculates the likelihood ratio test for a single changepoint in p-dimensional data streams by leveraging a fascinating connection with computational geometry. This connection straightforwardly allows us to exactly recover sparse likelihood ratio statistics: that is assuming only a subset of the dimensions are changing. Our algorithm is straightforward, fast, and apparently quasi-linear. A dyadic variant of our algorithm is provably quasi-linear, being O(nlog(n)(p+1)) for n data points and p less than 3, but slower in practice. These algorithms are computationally impractical when p is larger than 5, and we provide an approximate algorithm suitable for such p which is O(nplog(n)(p+1)), for some user-specified (p) over tilde <= 5. We derive statistical guarantees for the proposed procedures in the Gaussian case, and confirm the good computational and statistical performance, and usefulness, of the algorithms on both empirical data and NBA data.