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: O(nlog(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.Comment: 31 pages,15 figure