focus and focus-cpt: Fast Online Changepoint Detection in R and Python

2026-07-22

AI Summary

This work addresses the problem of efficient online change-point detection in both univariate and multivariate data streams by introducing a novel method grounded in the Focus algorithm family. Leveraging the generalized likelihood ratio test, the approach enables exact detection of a single change point without requiring approximations. By exploiting the relationship between candidate change-point locations and the geometric structure of the data, it achieves a computational complexity of approximately $\log(n)^d$ per iteration. Notably, this is the first method to support exponential-family models, nonparametric settings, and autoregressive data under no approximation assumptions, integrating natural exponential-family modeling, empirical cumulative distribution functions, and geometric optimization techniques. The accompanying R/Python software package substantially enhances the efficiency and applicability of change-point detection in high-dimensional streaming data.

Abstract

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.

Problem

• online changepoint detection
• data streams
• univariate
• multivariate
• Generalised Likelihood Ratio test

Innovation

• online changepoint detection
• Generalised Likelihood Ratio test
• FOCUS algorithm
• computational efficiency
• multivariate data streams