Online Multivariate Changepoint Detection : Leveraging Links With Computational Geometry

Pishchagina, Liudmila and Romano, Gaetano and Fearnhead, Paul and Runge, Vincent and Rigaill, Guillem (2023) Online Multivariate Changepoint Detection : Leveraging Links With Computational Geometry. Other. Arxiv.

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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 their straightforward implementation becomes impractical online. We develop two online algorithms that exactly calculate the likelihood ratio test for a single changepoint in p-dimensional data streams by leveraging fascinating connections with computational geometry. Our first algorithm is straightforward and empirically quasi-linear. The second is more complex but provably quasi-linear: $\mathcal{O}(n\log(n)^{p+1})$ for $n$ data points. Through simulations, we illustrate, that they are fast and allow us to process millions of points within a matter of minutes up to $p=5$.