crossvalidationCP-package {crossvalidationCP}

Cross-validation for change-point regression

Description

Implements the cross-validation methodology from Pein and Shah (2021). The approach can be customised by providing cross-validation criteria, estimators for the change-point locations and local parameters, and freely chosen folds. Pre-implemented estimators and criteria are available. It also includes our own implementation of the COPPS procedure Zou et al. (2020). By default, 5-fold cross-validation with ordered folds, absolute error loss, and least squares estimation for estimating the change-point locations is used.

Details

The main function is crossvalidationCP. It selects among a list of parameters the one with the smallest cross-validation criterion for a given method. The user can freely choose the folds, the local estimator and the criterion. Several pre-implemented estimators and criteria are available. Estimators have to allow a list of parameters at the same time. One can use convertSingleParam to convert a function allowing only a single parameter to a function that allows a list of parameters.

A ssimpler, but more limited access is given by the functions VfoldCV, COPPS, CV1 and CVmod. VfoldCV performs V-fold cross-validation, where the tuning parameter is directly the number of change-points. COPPS implements the COPPS procedure Zou et al. (2020), i.e. 2-fold cross-validation with Order-Preserved Sample-Splitting and the tuning parameter being again the number of change-points. CV1 and CVmod do the same, but with absolute error loss and the modified quadratic error loss, see (15) and (16) in Pein and Shah (2021), instead of quadratic error loss.

Note that COPPS can be problematic when larger changes occur at odd locations. For a detailed discussion, why standard quadratic error loss can lead to misestimation, see Section 2 in Pein and Shah (2021). By default, we recommend to use absolute error loss and 5-fold cross-validation as offered by VfoldCV.

So far only univariate data is supported, but support for multivariate data is planned.

References

Pein, F., and Shah, R. D. (2021) Cross-validation for change-point regression: pitfalls and solutions. arXiv:2112.03220.

Zou, C., Wang, G., and Li, R. (2020) Consistent selection of the number of change-points via sample-splitting. The Annals of Statistics, 48(1), 413–439.

See Also

crossvalidationCP, estimators, criteria, convertSingleParam, VfoldCV, COPPS, CV1, CVmod

Examples

# call with default parameters:
# 5-fold cross-validation with absolute error loss, least squares estimation,
# and possible parameters being 0 to 5 change-points
Y <- rnorm(100)
(ret <- crossvalidationCP(Y = Y))
# a simpler, but more limited access to it is offered by VfoldCV()
identical(VfoldCV(Y = Y), ret)

# more interesting data and more detailed output
set.seed(1L)
Y <- c(rnorm(50), rnorm(50, 5), rnorm(50), rnorm(50, 5))
VfoldCV(Y = Y, output = "detailed")
# finds the correct change-points at 50, 100, 150
# (plus the start and end points 0 and 200)

# reducing the maximal number of change-points to 2
VfoldCV(Y = Y, Kmax = 2)

# crossvalidationCP is more flexible and allows a list of parameters
# here only 1 or 2 change-points are allowed
crossvalidationCP(Y = Y, param = as.list(1:2))

# reducing the number of folds to 3
ret <- VfoldCV(Y = Y, V = 3L, output = "detailed")
# the same but with explicitly specified folds
identical(crossvalidationCP(Y = Y, folds = list(seq(1, 200, 3), seq(2, 200, 3), seq(3, 200, 3)),
                            output = "detailed"), ret)
                            
# 2-fold cross-validation with Order-Preserved Sample-Splitting
ret <- crossvalidationCP(Y = Y, folds = "COPPS", output = "detailed")

# a simpler access to it is offered by CV1()
identical(CV1(Y = Y, output = "detailed"), ret)

# different criterion: quadratic error loss
ret <- crossvalidationCP(Y = Y, folds = "COPPS", output = "detailed", criterion = criterionL2loss)

# same as COPPS procedure; as offered by COPPS()
identical(COPPS(Y = Y, output = "detailed"), ret)

# COPPS potentially fails to provide a good selection when large changes occur at odd locations
# Example 1 in (Pein and Shah, 2021), see Section 2.2 in this paper for more details
set.seed(1)
exampleY <- rnorm(102, c(rep(10, 46), rep(0, 5), rep(30, 51)))
# misses one change-point
crossvalidationCP(Y = exampleY, folds = "COPPS", criterion = criterionL2loss) 

# correct number of change-points when modified criterion (or absolute error loss) is used
(ret <- crossvalidationCP(Y = exampleY, folds = "COPPS", criterion = criterionMod)) 

# a simpler access to it is offered by CVmod() 
identical(CVmod(Y = exampleY), ret)

# manually given criterion; identical to criterionL1loss()
testCriterion <- function(testset, estset, value = NULL, ...) {
  if (!is.null(value)) {
    return(sum(abs(testset - value)))
  }
  
  sum(abs(testset - mean(estset)))
}
identical(crossvalidationCP(Y = Y, criterion = testCriterion, output = "detailed"),
          crossvalidationCP(Y = Y, output = "detailed"))

# PELT as a local estimator instead of least squares estimation
# param must contain parameters that are acceptable for the given estimator
crossvalidationCP(Y = Y, estimator = pelt, output = "detailed",
                  param = list("SIC", "MBIC", 3 * log(length(Y))))

# argument minseglen of pelt specified in ...
crossvalidationCP(Y = Y, estimator = pelt, output = "detailed",
                  param = list("SIC", "MBIC", 3 * log(length(Y))), minseglen = 60)