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 $p=5$.

翻译：随着数据流量的不断增加，在线检测变点面临显著的计算挑战。基于似然的方法虽有效，但其直接实现在在线场景中变得不切实际。我们开发了两种在线算法，通过利用与计算几何的迷人联系，精确计算p维数据流中单个变点的似然比检验。第一种算法简单且经验上接近线性。第二种算法更为复杂，但可证明为准线性：对于n个数据点，其复杂度为$\mathcal{O}(n\log(n)^{p+1})$。通过模拟，我们表明这些算法速度快，能够在数分钟内处理多达p=5的百万级数据点。