Fast Change Point Detection via Sequential Gradient Descent • fastcpd

Overview

The fastcpd (fast change point detection) is a fast implmentation of change point detection methods in R. The fastcpd package is designed to find change points in a fast manner. It is easy to install and extensible to all kinds of change point problems with a user specified cost function apart from the built-in cost functions.

To learn more behind the algorithms:

Installation

install.packages(
  "fastcpd",
  repos = c("https://doccstat.r-universe.dev", "https://cloud.r-project.org")
)

Development version

pak::pak("doccstat/fastcpd")
devtools::install_github("doccstat/fastcpd")

With mamba or conda (available soon)

# conda-forge is a fork from CRAN and may not be up-to-date

# Use mamba
mamba install r-fastcpd
# Use conda
conda install -c conda-forge r-fastcpd

Usage

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)

Note

r.progress = FALSE is used to suppress the progress bar. Users are expected to see the progress bar when running the code by default.

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(
  fastcpd = fastcpd::fastcpd.mean(mean_data, r.progress = FALSE, cp_only = TRUE, variance_estimation = 1),
  changepoint = changepoint::cpt.mean(mean_data, method = "PELT"),
  fpop = fpop::Fpop(mean_data, 2 * log(n)),
  gfpop = gfpop::gfpop(
    data = mean_data,
    mygraph = gfpop::graph(
      penalty = 2 * log(length(mean_data)) * gfpop::sdDiff(mean_data) ^ 2,
      type = "updown"
    ),
    type = "mean"
  ),
  jointseg = jointseg::jointSeg(mean_data, K = 12),
  mosum = mosum::mosum(c(mean_data), G = 40),
  not = not::not(mean_data, contrast = "pcwsConstMean"),
  wbs = wbs::wbs(mean_data)
))
#> Warning in microbenchmark(fastcpd = fastcpd::fastcpd.mean(mean_data, r.progress
#> = FALSE, : less accurate nanosecond times to avoid potential integer overflows

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 
#>  11.753   9.150  26.455 
system.time(changepoint::cpt.mean(mean_data, method = "PELT"))
#>    user  system elapsed 
#>  32.342   9.681  66.056 
system.time(fpop::Fpop(mean_data, 2 * log(n)))
#>    user  system elapsed 
#>  35.926   5.231  58.269 
system.time(mosum::mosum(c(mean_data), G = 40))
#>    user  system elapsed 
#>   5.518  11.516  38.368 
ggplot2::autoplot(microbenchmark(
  fastcpd = fastcpd::fastcpd.mean(mean_data, r.progress = FALSE, cp_only = TRUE, variance_estimation = 1),
  changepoint = changepoint::cpt.mean(mean_data, method = "PELT"),
  fpop = fpop::Fpop(mean_data, 2 * log(n)),
  mosum = mosum::mosum(c(mean_data), G = 40),
  times = 10
))
#> Warning in microbenchmark(fastcpd = fastcpd::fastcpd.mean(mean_data, r.progress
#> = FALSE, : less accurate nanosecond times to avoid potential integer overflows

Some packages are not included in the microbenchmark comparison due to either memory constraints or long running time.

# Device: Mac mini (M1, 2020)
# Memory: 8 GB
system.time(CptNonPar::np.mojo(mean_data, G = floor(length(mean_data) / 6)))
#> Error: vector memory limit of 16.0 Gb reached, see mem.maxVSize()
#> Timing stopped at: 0.061 0.026 0.092
system.time(ecp::e.divisive(matrix(mean_data)))
#> Error: vector memory limit of 16.0 Gb reached, see mem.maxVSize()
#> Timing stopped at: 0.076 0.044 0.241
system.time(strucchange::breakpoints(y ~ 1, data = data.frame(y = mean_data)))
#> Timing stopped at: 265.1 145.8 832.5
system.time(breakfast::breakfast(mean_data))
#> Timing stopped at: 45.9 89.21 562.3

Cheatsheet

Function references

Main function
- fastcpd
Wrapper functions
- Time series
  - AR(p): fastcpd_ar
  - ARIMA(p, d, q): fastcpd_arima
  - ARMA(p, q): fastcpd_arma
  - GARCH(p, q): fastcpd_garch
  - VAR(p): fastcpd_var
  - General time series: fastcpd_ts
- Unlabeled data
  - Mean change: fastcpd_mean
  - Variance change: fastcpd_variance
  - Mean and/or variance change: fastcpd_meanvariance
- Regression data
  - Logistic regression: fastcpd_binomial
  - Penalized linear regression: fastcpd_lasso
  - Linear regression: fastcpd_lm
  - Poisson regression: fastcpd_poisson
Utility functions
- Variance estimation
  - Variance estimation in ARMA models: variance_arma
  - Variance estimation in linear models: variance_lm
  - Variance estimation in mean change models: variance_mean
  - Variance estimation in median change models: variance_median
Class methods
- Plot: plot
- Print: print
- Show: show
- Summary: summary
Data
- Bitcoin Market Price (USD): bitcoin
- Occupancy Detection Data Set: occupancy
- Transcription Profiling of 57 Human Bladder Carcinoma Samples: transcriptome
- UK Seatbelts Data: uk_seatbelts
- Well-log Dataset from Numerical Bayesian Methods Applied to Signal Processing: well_log
Main class
- fastcpd

R Shiny App

Available soon: rshiny.fastcpd.xingchi.li

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().

Encountered a bug or unintended behavior?

File a ticket at GitHub Issues.
Contact the authors specified in DESCRIPTION.

fastcpd: Fast Change Point Detection in R