Online Multivariate Changepoint Detection : Leveraging Links With Computational Geometry

Pishchagina, Liudmila and Romano, Gaetano and Fearnhead, Paul and Runge, Vincent and Rigaill, Guillem (2025) Online Multivariate Changepoint Detection : Leveraging Links With Computational Geometry. Journal of the Royal Statistical Society: Series B (Statistical Methodology). ISSN 1369-7412 (In Press)

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Abstract

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 $\mathcal{O}(n\log(n)^{p+1})$ 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 $\mathcal{O}(np\log(n)^{\tilde{p}+1}), $ for some user-specified $\tilde{p} \leq 5$. 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.

Item Type:
Journal Article
Journal or Publication Title:
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Uncontrolled Keywords:
Research Output Funding/yes_externally_funded
Subjects:
?? stat.coyes - externally fundedstatistics and probabilitystatistics, probability and uncertainty ??
ID Code:
209818
Deposited By:
Deposited On:
14 Nov 2023 12:45
Refereed?:
Yes
Published?:
In Press
Last Modified:
12 Sep 2025 03:20