Fast Change Point Detection via Sequential Gradient Descent

Implements fast change point detection algorithm based on the paper "Sequential Gradient Descent and Quasi-Newton's Method for Change-Point Analysis" by Xianyang Zhang, Trisha Dawn < https://proceedings.mlr.press/v206/zhang23b.html>. The algorithm is based on dynamic programming with pruning and sequential gradient descent. See Li and Zhang (2026) for details.

Fast Change Point Detection

Overview

The fastcpd (fast change point detection) is a fast implmentation of change point detection methods in R/Python.

Documentation

R documentation: fastcpd.xingchi.li
Python documentation: fastcpd.xingchi.li/python

Installation

R

# install.packages("pak")
pak::pak("doccstat/fastcpd")
# or install from CRAN
install.packages("fastcpd")

Python WIP

# python -m ensurepip --upgrade
pip install .
# or install from PyPI
pip install fastcpd

Usage

R

set.seed(1)
n <- 1000
x <- rep(0, n + 3)
for (i in 1:600) {
  x[i + 3] <- 0.6 * x[i + 2] - 0.2 * x[i + 1] + 0.1 * x[i] + rnorm(1, 0, 3)
}
for (i in 601:1000) {
  x[i + 3] <- 0.3 * x[i + 2] + 0.4 * x[i + 1] + 0.2 * x[i] + rnorm(1, 0, 3)
}
result <- fastcpd::fastcpd.ar(x[3 + seq_len(n)], 3, r.progress = FALSE)
summary(result)
#> 
#> Call:
#> fastcpd::fastcpd.ar(data = x[3 + seq_len(n)], order = 3, r.progress = FALSE)
#> 
#> Change points:
#> 614 
#> 
#> Cost values:
#> 2754.116 2038.945 
#> 
#> Parameters:
#>     segment 1 segment 2
#> 1  0.57120256 0.2371809
#> 2 -0.20985108 0.4031244
#> 3  0.08221978 0.2290323
plot(result)

Python WIP

import fastcpd.segmentation
from numpy import concatenate
from numpy.random import normal, multivariate_normal
covariance_mat = [[100, 0, 0], [0, 100, 0], [0, 0, 100]]
data = concatenate((multivariate_normal([0, 0, 0], covariance_mat, 300),
                    multivariate_normal([50, 50, 50], covariance_mat, 400),
                    multivariate_normal([2, 2, 2], covariance_mat, 300)))
fastcpd.segmentation.mean(data)

import fastcpd.variance_estimation
fastcpd.variance_estimation.mean(data)

Comparison

library(microbenchmark)
set.seed(1)
n <- 5 * 10^6
mean_data <- c(rnorm(n / 2, 0, 1), rnorm(n / 2, 50, 1))
ggplot2::autoplot(microbenchmark(
  not = not::not(mean_data, contrast = "pcwsConstMean"),
  changepoint = changepoint::cpt.mean(mean_data, method = "PELT"),
  jointseg = jointseg::jointSeg(mean_data, K = 12),
  fpop = fpop::Fpop(mean_data, 2 * log(n)),
  mosum = mosum::mosum(c(mean_data), G = 40),
  fastcpd = fastcpd::fastcpd.mean(mean_data, r.progress = FALSE, cp_only = TRUE, variance_estimation = 1),
  times = 10
))

library(microbenchmark)
set.seed(1)
n <- 10^8
mean_data <- c(rnorm(n / 2, 0, 1), rnorm(n / 2, 50, 1))
system.time(fastcpd::fastcpd.mean(mean_data, r.progress = FALSE, cp_only = TRUE, variance_estimation = 1))
#>    user  system elapsed 
#>   9.866   4.932  14.831
system.time(mosum::mosum(c(mean_data), G = 40))
#>    user  system elapsed 
#>   9.229   6.694  15.936
system.time(fpop::Fpop(mean_data, 2 * log(n)))
#>    user  system elapsed 
#>  44.848   2.346  47.220
system.time(changepoint::cpt.mean(mean_data, method = "PELT"))
#>     user   system  elapsed 
#>  468.840  956.814 1479.480
ggplot2::autoplot(microbenchmark(
  changepoint = changepoint::cpt.mean(mean_data, method = "PELT"),
  fpop = fpop::Fpop(mean_data, 2 * log(n)),
  mosum = mosum::mosum(c(mean_data), G = 40),
  fastcpd = fastcpd::fastcpd.mean(mean_data, r.progress = FALSE, cp_only = TRUE, variance_estimation = 1),
  times = 10
))

Cheatsheet

References

FAQ

Should I install suggested packages?

The suggested packages are not required for the main functionality of the package. They are only required for the vignettes. If you want to learn more about the package comparison and other vignettes, you could either check out vignettes on CRAN or pkgdown generated documentation.

I countered problems related to gfortran on Mac OSX or Linux!

The package should be able to install on Mac and any Linux distribution without any problems if all the dependencies are installed. However, if you encountered problems related to gfortran, it might be because RcppArmadillo is not installed previously. Try Mac OSX stackoverflow solution or Linux stackover solution if you have trouble installing RcppArmadillo.

We welcome contributions from everyone. Please follow the instructions below to make contributions.

Fork the repo.
Create a new branch from main branch.
Make changes and commit them.
1. Please follow the Google’s R style guide for naming variables and functions.
2. If you are adding a new family of models with new cost functions with corresponding gradient and Hessian, please add them to src/fastcpd_class_cost.cc with proper example and tests in vignettes/gallery.Rmd and tests/testthat/test-gallery.R.
3. Add the family name to src/fastcpd_constants.h.
4. [Recommended] Add a new wrapper function in R/fastcpd_wrappers.R for the new family of models and move the examples to the new wrapper function as roxygen examples.
5. Add the new wrapper function to the corresponding section in _pkgdown.yml.
Push the changes to your fork.
Create a pull request.
Make sure the pull request does not create new warnings or errors in devtools::check().