焦点和焦点-cpt：R和Python中的快速在线变点检测
focus and focus-cpt: Fast Online Changepoint Detection in R and Python
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中文总结 AI 辅助
该研究推出R和Python包用于单变量及多变量数据流的快速在线变点检测，实现焦点算法族，能高效计算广义似然比检验，支持多种模型，包括自然指数族及非参数和自回归数据检测器。
中文摘要 AI 辅助
我们展示了一个用于在单变量和多变量数据流中进行快速在线变点检测的R和Python包，适用于多种模型。该包实现了焦点算法族，能准确有效地计算单变点的广义似然比检验，对于d维序列每次迭代成本约为$\log(n)^d$且无近似。通过利用变点候选位置与数据几何之间的联系实现。它支持自然指数族的多种模型，包括高斯、泊松、二项式、指数和伽马分布，还有基于经验累积分布函数的非参数检测器以及自回归数据检测器。
英文摘要
We present an R and Python package for fast online changepoint detection in univariate and multivariate data streams for a variety of models. The package implements the focus family of algorithms, which compute the Generalised Likelihood Ratio test for a single changepoint exactly and efficiently, with a per-iteration cost of approximately $\log(n)^d$ for a d-dimensional sequence, without introducing approximations. This is achieved by exploiting a connection between the location of the changepoint candidates and the geometry of the data. The package supports a broad range of models from the natural exponential family, including Gaussian, Poisson, Binomial, Exponential and Gamma distributions, as well as a non-parametric detector based on the empirical cumulative distribution function and a detector for autoregressive data.
