Package 'cpss' reference manual

Title:	Change-Point Detection by Sample-Splitting Methods
Description:	Implements multiple change searching algorithms for a variety of frequently considered parametric change-point models. In particular, it integrates a criterion proposed by Zou, Wang and Li (2020) <doi:10.1214/19-AOS1814> to select the number of change-points in a data-driven fashion. Moreover, it also provides interfaces for user-customized change-point models with one's own cost function and parameter estimation routine. It is easy to get started with the cpss.* set of functions by accessing their documentation pages (e.g., ?cpss).
Authors:	Guanghui Wang [aut, cre], Changliang Zou [aut]
Maintainer:	Guanghui Wang <[email protected]>
License:	GPL (>= 3)
Version:	0.0.3
Built:	2024-11-16 06:45:49 UTC
Source:	CRAN

Generic functions and methods: algo

Description

Generic functions and methods: algo

Usage

algo(x)

algo(x) <- value

## S4 method for signature 'cpss'
algo(x)

## S4 replacement method for signature 'cpss'
algo(x) <- value
algo(x)

algo(x) <- value

## S4 method for signature 'cpss'
algo(x)

## S4 replacement method for signature 'cpss'
algo(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x

Generic functions and methods: algo_param_dim

Description

Generic functions and methods: algo_param_dim

Usage

algo_param_dim(x)

algo_param_dim(x) <- value

## S4 method for signature 'cpss'
algo_param_dim(x)

## S4 replacement method for signature 'cpss'
algo_param_dim(x) <- value
algo_param_dim(x)

algo_param_dim(x) <- value

## S4 method for signature 'cpss'
algo_param_dim(x)

## S4 replacement method for signature 'cpss'
algo_param_dim(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x

coef method

Description

coef method

Usage

## S4 method for signature 'cpss'
coef(object)
## S4 method for signature 'cpss'
coef(object)

Arguments

`object`	object from cpss
`cpss`	cpss class

Generic functions and methods: cps

Description

Generic functions and methods: cps

Usage

cps(x)

cps(x) <- value

## S4 method for signature 'cpss'
cps(x)

## S4 replacement method for signature 'cpss'
cps(x) <- value
cps(x)

cps(x) <- value

## S4 method for signature 'cpss'
cps(x)

## S4 replacement method for signature 'cpss'
cps(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x

cpss: Change-Point Detection by Sample-Splitting Methods

Description

Implements multiple change searching algorithms for a variety of frequently considered parametric change-point models. In particular, it integrates a criterion proposed by Zou, Wang and Li (2020) doi:10.1214/19-AOS1814 to select the number of change-points in a data-driven fashion. Moreover, it also provides interfaces for user-customized change-point models with one's own cost function and parameter estimation routine.

Getting started

Easy to get started with the cpss.* set of functions by accessing their documentation pages
library(cpss)
?cpss.mean
?cpss.var
?cpss.meanvar
?cpss.glm
?cpss.lm
?cpss.em
?cpss.custom

cpss: an S4 class which collects data and information required for further change-point analyses and summaries

Description

cpss: an S4 class which collects data and information required for further change-point analyses and summaries

Slots

dat: ANY.
mdl: character.
algo: character.
algo_param_dim: numeric.
SC: character.
ncps: integer.
pelt_pen: numeric.
cps: numeric.
params: list.
S_vals: numeric.
SC_vals: matrix.
call: list.
update_inputs: list.

Detecting changes in uers-customized models

Description

Detecting changes in uers-customized models

Usage

cpss.custom(
  dataset,
  n,
  g_subdat,
  g_param,
  g_cost,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2,
  model = NULL,
  g_smry = NULL,
  easy_cost = NULL,
  param.opt = NULL
)
cpss.custom(
  dataset,
  n,
  g_subdat,
  g_param,
  g_cost,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2,
  model = NULL,
  g_smry = NULL,
  easy_cost = NULL,
  param.opt = NULL
)

Arguments

`dataset`	an `ANY` object that could be a vector, matrix, tensor, list, etc.
`n`	an integer indicating the sample size of the data `dataset`.
`g_subdat`	a customized R function of two arguments `dat` and `indices`, which extracts a subset of data `dat` according to a collection of time indices `indices`. The returned object inherits the class from that of `dataset`. The argument `dat` inherits the class from that of `dataset`, and the argument `indices` is a logical vector with `TRUE`s indicating extracted indices.
`g_param`	a customized R function of two arguments `dat` (cf. `dat` of `g\_subdat`) and `param.opt` (cf. `param.opt` of `cpss.custom`), which returns estimated parameters based on the data segment `dat`. It could return a numeric value, vector, matrix, list, etc.
`g_cost`	a customized R function of two arguments `dat` (cf. `dat` of `g\_subdat`) and `param`, which returns a numeric value of the associated cost for data segment `dat` with parameters `param`. The argument `param` inherits the class from that of the returned object of `g\_param`.
`algorithm`	a character string specifying the change-point searching algorithm, one of the following choices: "SN" (segment neighborhood), "BS" (binary segmentation), "WBS" (wild binary segmentation) and "PELT" (pruned exact linear time) algorithms.
`dist_min`	an integer specifying minimum searching distance (length of feasible segments).
`ncps_max`	an integer specifying an upper bound of the number of true change-points.
`pelt_pen_val`	a numeric vector specifying candidate values of the penalty only if `algorithm = "PELT"`.
`pelt_K`	a numeric value for pruning adjustment only if `algorithm = "PELT"`. It is usually taken to be 0 if the negative log-likelihood is used as a cost, see Killick et al. (2012).
`wbs_nintervals`	an integer specifying the number of random intervals drawn only if `algorithm = "WBS"`, see Fryzlewicz (2014).
`criterion`	a character string specifying the model selection criterion, "CV" ("cross-validation") or "MS" ("multiple-splitting").
`times`	an integer specifying how many times of sample-splitting should be performed; It should be 2 if `criterion = "CV"`.
`model`	a character string indicating the considered change model.
`g_smry`	a customized R function of two arguments `dataset` (cf. `dataset` of `cpss.custom`) and `param.opt` (cf. `param.opt` of `cpss.custom`), which calculates the summary statistics that will be used for cost evaluation. The returned object is a list.
`easy_cost`	a customized R function of three arguments `data_smry`, `s` and `e`, which evaluates the value of the cost for a date segment form observed time point $s$ to $e$. The argument `data_smry` inherits the class from that of the returned object of `g_smry`.
`param.opt`	an `ANY` object specifying additional constant parameters needed for parameter estimation or cost evaluation beyond unknown parameters.

Value

cpss.custom returns an object of an S4 class, called "cpss", which collects data and information required for further change-point analyses and summaries.

dat: data set
mdl: considered change-point model
algo: change-point searching algorithm
algo_param_dim: user-specified upper bound of the number of true change-points if algorithm = "SN"/"BS"/"WBS", or user-specified candidate values of the penalty only if algorithm = "PELT"
SC: model selection criterion
ncps: estimated number of change-points
pelt_pen: selected value of the penalty only if algorithm = "PELT"
cps: a vector of estimated locations of change-points
params: a list object, each member is a list containing estimated parameters in the associated data segment
S_vals: a numeric vector of candidate model dimensions in terms of a sequence of numbers of change-points or values of the penalty
SC_vals: a numeric matrix, each column records the values of the criterion based on the validation data split under the corresponding model dimension (S_vals), and each row represents a splitting at each time

References

Killick, R., Fearnhead, P., and Eckley, I. A. (2012). Optimal Detection of Changepoints With a Linear Computational Cost. Journal of the American Statistical Association, 107(500): 1590–1598.

Fryzlewicz, P. (2014). Wild binary segmentation for multiple change-point detection. The Annals of Statistics, 42(6): 2243–2281.

Examples


library("cpss")
g_subdat_l1 <- function(dat, indices) {
  dat[indices]
}
g_param_l1 <- function(dat, param.opt = NULL) {
  return(median(dat))
}
g_cost_l1 <- function(dat, param) {
  return(sum(abs(dat - param)))
}
res <- cpss.custom(
  dataset = well, n = length(well),
  g_subdat = g_subdat_l1, g_param = g_param_l1, g_cost = g_cost_l1,
  ncps_max = 11
)
summary(res)
plot(well)
abline(v = res@cps, col = "red")

library("cpss")
g_subdat_l1 <- function(dat, indices) {
  dat[indices]
}
g_param_l1 <- function(dat, param.opt = NULL) {
  return(median(dat))
}
g_cost_l1 <- function(dat, param) {
  return(sum(abs(dat - param)))
}
res <- cpss.custom(
  dataset = well, n = length(well),
  g_subdat = g_subdat_l1, g_param = g_param_l1, g_cost = g_cost_l1,
  ncps_max = 11
)
summary(res)
plot(well)
abline(v = res@cps, col = "red")

Detecting changes in exponential family

Description

Detecting changes in exponential family

Usage

cpss.em(
  dataset,
  family,
  size = NULL,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2
)
cpss.em(
  dataset,
  family,
  size = NULL,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2
)

Arguments

`dataset`	a numeric matrix of dimension $n\times d$ , where each row represents an observation and each column stands for a variable. A numeric vector is also acceptable for univariate observations.
`family`	a character string specifying the underlying distribution. In the current version, detecting changes in binomial ("`binom`"), multinomial ("`multinom`"), Poisson ("`pois`"), exponential ("`exp`"), geometric ("`geom`"), Dirichlet ("`diri`"), gamma ("`gamma`"), beta ("`beta`"), chi-square ("`chisq`") and inverse gaussian ("`invgauss`") distributions are supported.
`size`	an integer indicating the number of trials only if `family = "binom"` or `family = "multinom"`.
`algorithm`	a character string specifying the change-point searching algorithm, one of the following choices: "SN" (segment neighborhood), "BS" (binary segmentation), "WBS" (wild binary segmentation) and "PELT" (pruned exact linear time) algorithms.
`dist_min`	an integer specifying minimum searching distance (length of feasible segments).
`ncps_max`	an integer specifying an upper bound of the number of true change-points.
`pelt_pen_val`	a numeric vector specifying candidate values of the penalty only if `algorithm = "PELT"`.
`pelt_K`	a numeric value for pruning adjustment only if `algorithm = "PELT"`. It is usually taken to be 0 if the negative log-likelihood is used as a cost, see Killick et al. (2012).
`wbs_nintervals`	an integer specifying the number of random intervals drawn only if `algorithm = "WBS"`, see Fryzlewicz (2014).
`criterion`	a character string specifying the model selection criterion, "CV" ("cross-validation") or "MS" ("multiple-splitting").
`times`	an integer specifying how many times of sample-splitting should be performed; It should be 2 if `criterion = "CV"`.

Value

cpss.em returns an object of an S4 class, called "cpss", which collects data and information required for further change-point analyses and summaries. See cpss.custom.

References

Killick, R., Fearnhead, P., and Eckley, I. A. (2012). Optimal Detection of Changepoints With a Linear Computational Cost. Journal of the American Statistical Association, 107(500):1590–1598.

Fryzlewicz, P. (2014). Wild binary segmentation for multiple change-point detection. The Annals of Statistics, 42(6): 2243–2281.

Examples

library("cpss")
set.seed(666)
n <- 1000
tau <- c(100, 300, 700, 900)
tau_ext <- c(0, tau, n)
theta <- c(1, 0.2, 1, 0.2, 1)
seg_len <- diff(c(0, tau, n))
y <- unlist(lapply(seq(1, length(tau) + 1), function(k) {
  rexp(seg_len[k], theta[k])
}))
res <- cpss.em(
  y, family = "exp", algorithm = "WBS", ncps_max = 10,
  criterion = "MS", times = 10
)
cps(res)
# [1] 100 299 705 901
library("cpss")
set.seed(666)
n <- 1000
tau <- c(100, 300, 700, 900)
tau_ext <- c(0, tau, n)
theta <- c(1, 0.2, 1, 0.2, 1)
seg_len <- diff(c(0, tau, n))
y <- unlist(lapply(seq(1, length(tau) + 1), function(k) {
  rexp(seg_len[k], theta[k])
}))
res <- cpss.em(
  y, family = "exp", algorithm = "WBS", ncps_max = 10,
  criterion = "MS", times = 10
)
cps(res)
# [1] 100 299 705 901

Detecting changes in GLMs

Description

Detecting changes in GLMs

Usage

cpss.glm(
  formula,
  family,
  data = NULL,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2
)
cpss.glm(
  formula,
  family,
  data = NULL,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2
)

Arguments

`formula`	a `formula` object specifying the GLM with change-points.
`family`	a description of the error distribution and link function to be used in the model, which can be a character string naming a family function or a family function.
`data`	an optional data frame containing the variables in the model.
`algorithm`	a character string specifying the change-point searching algorithm, one of the following choices: "SN" (segment neighborhood), "BS" (binary segmentation), "WBS" (wild binary segmentation) and "PELT" (pruned exact linear time) algorithms.
`dist_min`	an integer specifying minimum searching distance (length of feasible segments).
`ncps_max`	an integer specifying an upper bound of the number of true change-points.
`pelt_pen_val`	a numeric vector specifying candidate values of the penalty only if `algorithm = "PELT"`.
`pelt_K`	a numeric value for pruning adjustment only if `algorithm = "PELT"`. It is usually taken to be 0 if the negative log-likelihood is used as a cost, see Killick et al. (2012).
`wbs_nintervals`	an integer specifying the number of random intervals drawn only if `algorithm = "WBS"`, see Fryzlewicz (2014).
`criterion`	a character string specifying the model selection criterion, "CV" ("cross-validation") or "MS" ("multiple-splitting").
`times`	an integer specifying how many times of sample-splitting should be performed; It should be 2 if `criterion = "CV"`.

Value

cpss.glm returns an object of an S4 class, called "cpss", which collects data and information required for further change-point analyses and summaries. See cpss.custom.

References

Killick, R., Fearnhead, P., and Eckley, I. A. (2012). Optimal Detection of Changepoints With a Linear Computational Cost. Journal of the American Statistical Association, 107(500):1590–1598.

Fryzlewicz, P. (2014). Wild binary segmentation for multiple change-point detection. The Annals of Statistics, 42(6): 2243–2281.

Examples

library("cpss")
set.seed(666)
n <- 200
size <- rpois(n, 20 - 1) + 1
tau <- c(75, 100, 175)
tau_ext <- c(0, tau, n)
be <- list(c(0, 0.5), c(0, -0.5), c(0.5, -0.5), c(-0.5, -0.5))
seg_len <- diff(c(0, tau, n))
x <- rnorm(n)
eta <- lapply(seq(1, length(tau) + 1), function(k) {
  be[[k]][1] + be[[k]][2] * x[(tau_ext[k] + 1):tau_ext[k + 1]]
})
eta <- do.call(c, eta)
p <- 1 / (1 + exp(-eta))
y <- rbinom(n, size = size, prob = p)

pelt_pen_val <- (log(n))^seq(0.5, 2, by = 0.1)
res <- cpss.glm(
  formula = cbind(y, size - y) ~ x, family = binomial(),
  algorithm = "PELT", pelt_pen_val = pelt_pen_val, ncps_max = 10
)
summary(res)
# 75  105  175
coef(res)
# [1,] 0.02540872  0.08389551  0.5284425 -0.4980768
# [2,] 0.57222684 -0.45430385 -0.5203319 -0.4581678

library("cpss")
set.seed(666)
n <- 200
size <- rpois(n, 20 - 1) + 1
tau <- c(75, 100, 175)
tau_ext <- c(0, tau, n)
be <- list(c(0, 0.5), c(0, -0.5), c(0.5, -0.5), c(-0.5, -0.5))
seg_len <- diff(c(0, tau, n))
x <- rnorm(n)
eta <- lapply(seq(1, length(tau) + 1), function(k) {
  be[[k]][1] + be[[k]][2] * x[(tau_ext[k] + 1):tau_ext[k + 1]]
})
eta <- do.call(c, eta)
p <- 1 / (1 + exp(-eta))
y <- rbinom(n, size = size, prob = p)

pelt_pen_val <- (log(n))^seq(0.5, 2, by = 0.1)
res <- cpss.glm(
  formula = cbind(y, size - y) ~ x, family = binomial(),
  algorithm = "PELT", pelt_pen_val = pelt_pen_val, ncps_max = 10
)
summary(res)
# 75  105  175
coef(res)
# [1,] 0.02540872  0.08389551  0.5284425 -0.4980768
# [2,] 0.57222684 -0.45430385 -0.5203319 -0.4581678

Detecting changes in linear models

Description

Detecting changes in linear models

Usage

cpss.lm(
  formula,
  data = NULL,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2
)
cpss.lm(
  formula,
  data = NULL,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2
)

Arguments

`formula`	a `formula` object specifying the GLM with change-points.
`data`	an optional data frame containing the variables in the model.
`algorithm`	a character string specifying the change-point searching algorithm, one of the following choices: "SN" (segment neighborhood), "BS" (binary segmentation), "WBS" (wild binary segmentation) and "PELT" (pruned exact linear time) algorithms.
`dist_min`	an integer specifying minimum searching distance (length of feasible segments).
`ncps_max`	an integer specifying an upper bound of the number of true change-points.
`pelt_pen_val`	a numeric vector specifying candidate values of the penalty only if `algorithm = "PELT"`.
`pelt_K`	a numeric value for pruning adjustment only if `algorithm = "PELT"`. It is usually taken to be 0 if the negative log-likelihood is used as a cost, see Killick et al. (2012).
`wbs_nintervals`	an integer specifying the number of random intervals drawn only if `algorithm = "WBS"`, see Fryzlewicz (2014).
`criterion`	a character string specifying the model selection criterion, "CV" ("cross-validation") or "MS" ("multiple-splitting").
`times`	an integer specifying how many times of sample-splitting should be performed; It should be 2 if `criterion = "CV"`.

Value

cpss.lm returns an object of an S4 class, called "cpss", which collects data and information required for further change-point analyses and summaries. See cpss.custom.

References

Killick, R., Fearnhead, P., and Eckley, I. A. (2012). Optimal Detection of Changepoints With a Linear Computational Cost. Journal of the American Statistical Association, 107(500):1590–1598.

Fryzlewicz, P. (2014). Wild binary segmentation for multiple change-point detection. The Annals of Statistics, 42(6): 2243–2281.

Examples

library("cpss")
set.seed(666)
n <- 400
tau <- c(80, 200, 300)
tau_ext <- c(0, tau, n)
be <- list(c(0, 1), c(1, 0.5), c(0, 1), c(-1, 0.5))
seg_len <- diff(c(0, tau, n))
x <- rnorm(n)
mu <- lapply(seq(1, length(tau) + 1), function(k) {
  be[[k]][1] + be[[k]][2] * x[(tau_ext[k] + 1):tau_ext[k + 1]]
})
mu <- do.call(c, mu)
sig <- unlist(lapply(seq(1, length(tau) + 1), function(k) {
  rep(be[[k]][2], seg_len[k])
}))
y <- rnorm(n, mu, sig)
res <- cpss.lm(
  formula = y ~ x,
  algorithm = "BS", ncps_max = 10
)
summary(res)
# 80  202  291
coef(res)
# $coef
#             [,1]      [,2]        [,3]       [,4]
# [1,] -0.00188792 1.0457718 -0.03963209 -0.9444813
# [2,]  0.91061557 0.6291965  1.20694409  0.4410036
#
# $sigma
# [1] 0.8732233 0.4753216 0.9566516 0.4782329
library("cpss")
set.seed(666)
n <- 400
tau <- c(80, 200, 300)
tau_ext <- c(0, tau, n)
be <- list(c(0, 1), c(1, 0.5), c(0, 1), c(-1, 0.5))
seg_len <- diff(c(0, tau, n))
x <- rnorm(n)
mu <- lapply(seq(1, length(tau) + 1), function(k) {
  be[[k]][1] + be[[k]][2] * x[(tau_ext[k] + 1):tau_ext[k + 1]]
})
mu <- do.call(c, mu)
sig <- unlist(lapply(seq(1, length(tau) + 1), function(k) {
  rep(be[[k]][2], seg_len[k])
}))
y <- rnorm(n, mu, sig)
res <- cpss.lm(
  formula = y ~ x,
  algorithm = "BS", ncps_max = 10
)
summary(res)
# 80  202  291
coef(res)
# $coef
#             [,1]      [,2]        [,3]       [,4]
# [1,] -0.00188792 1.0457718 -0.03963209 -0.9444813
# [2,]  0.91061557 0.6291965  1.20694409  0.4410036
#
# $sigma
# [1] 0.8732233 0.4753216 0.9566516 0.4782329

Detecting changes in mean

Description

Detecting changes in mean

Usage

cpss.mean(
  dataset,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2,
  Sigma = NULL
)
cpss.mean(
  dataset,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2,
  Sigma = NULL
)

Arguments

`dataset`	a numeric matrix of dimension $n\times d$ , where each row represents an observation and each column stands for a variable. A numeric vector is also acceptable for univariate observations.
`algorithm`	a character string specifying the change-point searching algorithm, one of the following choices: "SN" (segment neighborhood), "BS" (binary segmentation), "WBS" (wild binary segmentation) and "PELT" (pruned exact linear time) algorithms.
`dist_min`	an integer specifying minimum searching distance (length of feasible segments).
`ncps_max`	an integer specifying an upper bound of the number of true change-points.
`pelt_pen_val`	a numeric vector specifying candidate values of the penalty only if `algorithm = "PELT"`.
`pelt_K`	a numeric value for pruning adjustment only if `algorithm = "PELT"`. It is usually taken to be 0 if the negative log-likelihood is used as a cost, see Killick et al. (2012).
`wbs_nintervals`	an integer specifying the number of random intervals drawn only if `algorithm = "WBS"`, see Fryzlewicz (2014).
`criterion`	a character string specifying the model selection criterion, "CV" ("cross-validation") or "MS" ("multiple-splitting").
`times`	an integer specifying how many times of sample-splitting should be performed; It should be 2 if `criterion = "CV"`.
`Sigma`	if a numeric matrix (or constant) is supplied, it will be taken as the value of the common covariance (or variance). By default it is `NULL`, and the covariance is estimated by $\widehat{\Sigma} = \frac{1}{2(n-1)}\sum_{i=1}^{n-1} (Y_i-Y_{i+1})(Y_i-Y_{i+1})';$

Value

cpss.mean returns an object of an S4 class, called "cpss", which collects data and information required for further change-point analyses and summaries. See cpss.custom.

References

Killick, R., Fearnhead, P., and Eckley, I. A. (2012). Optimal Detection of Changepoints With a Linear Computational Cost. Journal of the American Statistical Association, 107(500): 1590–1598. Fryzlewicz, P. (2014). Wild binary segmentation for multiple change-point detection. The Annals of Statistics, 42(6): 2243–2281.

Examples

library("cpss")
set.seed(666)
n <- 2048
tau <- c(205, 267, 308, 472, 512, 820, 902, 1332, 1557, 1598, 1659)
seg_len <- diff(c(0, tau, n))
mu <- rep(c(0, 14.64, -3.66, 7.32, -7.32, 10.98, -4.39, 3.29, 19.03, 7.68, 15.37, 0), seg_len)
ep <- 7 * rnorm(n)
y <- mu + ep

res <- cpss.mean(y, algorithm = "SN", ncps_max = 20)
summary(res)
# 205  267  307  471  512  820  897  1332  1557  1601  1659
plot(res, type = "scatter")
plot(res, type = "path")
out <- update(res, dim_update = 12)
out@cps
# 205  267  307  471  512  820  897 1332 1557 1601 1659 1769
# coef(out)

library("cpss")
set.seed(666)
n <- 2048
tau <- c(205, 267, 308, 472, 512, 820, 902, 1332, 1557, 1598, 1659)
seg_len <- diff(c(0, tau, n))
mu <- rep(c(0, 14.64, -3.66, 7.32, -7.32, 10.98, -4.39, 3.29, 19.03, 7.68, 15.37, 0), seg_len)
ep <- 7 * rnorm(n)
y <- mu + ep

res <- cpss.mean(y, algorithm = "SN", ncps_max = 20)
summary(res)
# 205  267  307  471  512  820  897  1332  1557  1601  1659
plot(res, type = "scatter")
plot(res, type = "path")
out <- update(res, dim_update = 12)
out@cps
# 205  267  307  471  512  820  897 1332 1557 1601 1659 1769
# coef(out)

Detecting changes in mean and (co)variance

Description

Detecting changes in mean and (co)variance

Usage

cpss.meanvar(
  dataset,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2
)
cpss.meanvar(
  dataset,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2
)

Arguments

`dataset`	a numeric matrix of dimension $n\times d$ , where each row represents an observation and each column stands for a variable. A numeric vector is also acceptable for univariate observations.
`algorithm`	a character string specifying the change-point searching algorithm, one of the following choices: "SN" (segment neighborhood), "BS" (binary segmentation), "WBS" (wild binary segmentation) and "PELT" (pruned exact linear time) algorithms.
`dist_min`	an integer specifying minimum searching distance (length of feasible segments).
`ncps_max`	an integer specifying an upper bound of the number of true change-points.
`pelt_pen_val`	a numeric vector specifying candidate values of the penalty only if `algorithm = "PELT"`.
`pelt_K`	a numeric value for pruning adjustment only if `algorithm = "PELT"`. It is usually taken to be 0 if the negative log-likelihood is used as a cost, see Killick et al. (2012).
`wbs_nintervals`	an integer specifying the number of random intervals drawn only if `algorithm = "WBS"`, see Fryzlewicz (2014).
`criterion`	a character string specifying the model selection criterion, "CV" ("cross-validation") or "MS" ("multiple-splitting").
`times`	an integer specifying how many times of sample-splitting should be performed; It should be 2 if `criterion = "CV"`.

Value

cpss.meanvar returns an object of an S4 class, called "cpss", which collects data and information required for further change-point analyses and summaries. See cpss.custom.

References

Killick, R., Fearnhead, P., and Eckley, I. A. (2012). Optimal Detection of Changepoints With a Linear Computational Cost. Journal of the American Statistical Association, 107(500):1590–1598. Fryzlewicz, P. (2014). Wild binary segmentation for multiple change-point detection. The Annals of Statistics, 42(6): 2243–2281.

Examples

library("cpss")
if (!requireNamespace("MASS", quietly = TRUE)) {
  stop("Please install the package \"MASS\".")
}
set.seed(666)
n <- 1000
tau <- c(200, 400, 600, 800)
mu <- list(rep(0, 2), rep(1, 2), rep(1, 2), rep(0, 2), rep(0, 2))
Sigma <- list(diag(2), diag(2), matrix(c(1,-1,-1, 4), 2), matrix(c(1, 0.5, 0.5, 1), 2), diag(2))
seg_len <- diff(c(0, tau, n))
y <- lapply(seq(1, length(tau) + 1), function(k) {
  MASS::mvrnorm(n = seg_len[k], mu = mu[[k]], Sigma = Sigma[[k]])
})
y <- do.call(rbind, y)
res <- cpss.meanvar(y, algorithm = "BS", dist_min = 20)
cps(res)
# [1] 211 402 598 804
plot(res, type = "coef")
library("cpss")
if (!requireNamespace("MASS", quietly = TRUE)) {
  stop("Please install the package \"MASS\".")
}
set.seed(666)
n <- 1000
tau <- c(200, 400, 600, 800)
mu <- list(rep(0, 2), rep(1, 2), rep(1, 2), rep(0, 2), rep(0, 2))
Sigma <- list(diag(2), diag(2), matrix(c(1,-1,-1, 4), 2), matrix(c(1, 0.5, 0.5, 1), 2), diag(2))
seg_len <- diff(c(0, tau, n))
y <- lapply(seq(1, length(tau) + 1), function(k) {
  MASS::mvrnorm(n = seg_len[k], mu = mu[[k]], Sigma = Sigma[[k]])
})
y <- do.call(rbind, y)
res <- cpss.meanvar(y, algorithm = "BS", dist_min = 20)
cps(res)
# [1] 211 402 598 804
plot(res, type = "coef")

Detecting changes in (co)variance

Description

Detecting changes in (co)variance

Usage

cpss.var(
  dataset,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2,
  mu = NULL
)
cpss.var(
  dataset,
  algorithm = "BS",
  dist_min = floor(log(n)),
  ncps_max = ceiling(n^0.4),
  pelt_pen_val = NULL,
  pelt_K = 0,
  wbs_nintervals = 500,
  criterion = "CV",
  times = 2,
  mu = NULL
)

Arguments

`dataset`	a numeric matrix of dimension $n\times d$ , where each row represents an observation and each column stands for a variable. A numeric vector is also acceptable for univariate observations.
`algorithm`	a character string specifying the change-point searching algorithm, one of the following choices: "SN" (segment neighborhood), "BS" (binary segmentation), "WBS" (wild binary segmentation) and "PELT" (pruned exact linear time) algorithms.
`dist_min`	an integer specifying minimum searching distance (length of feasible segments).
`ncps_max`	an integer specifying an upper bound of the number of true change-points.
`pelt_pen_val`	a numeric vector specifying candidate values of the penalty only if `algorithm = "PELT"`.
`pelt_K`	a numeric value for pruning adjustment only if `algorithm = "PELT"`. It is usually taken to be 0 if the negative log-likelihood is used as a cost, see Killick et al. (2012).
`wbs_nintervals`	an integer specifying the number of random intervals drawn only if `algorithm = "WBS"`, see Fryzlewicz (2014).
`criterion`	a character string specifying the model selection criterion, "CV" ("cross-validation") or "MS" ("multiple-splitting").
`times`	an integer specifying how many times of sample-splitting should be performed; It should be 2 if `criterion = "CV"`.
`mu`	If a numeric vector or constant is supplied, it will be taken as the value of the common mean. By default it is `NULL`, and the mean is estimated by the sample mean.

Value

cpss.var returns an object of an S4 class, called "cpss", which collects data and information required for further change-point analyses and summaries. See cpss.custom.

References

Examples

library("cpss")
if (!requireNamespace("MASS", quietly = TRUE)) {
  stop("Please install the package \"MASS\".")
}
set.seed(666)
n <- 1000
tau <- c(200, 500, 750)
mu <- list(rep(0, 2), rep(0, 2), rep(0, 2), rep(0, 2))
Sigma <- list(diag(2), matrix(c(1, 0, 0, 4), 2), matrix(c(1, -0.5, -0.5, 4), 2), diag(2))
seg_len <- diff(c(0, tau, n))
y <- lapply(seq(1, length(tau) + 1), function(k) {
  MASS::mvrnorm(n = seg_len[k], mu = mu[[k]], Sigma = Sigma[[k]])
})
y <- do.call(rbind, y)
res <- cpss.var(y, algorithm = "BS", dist_min = 20)
cps(res)
# [1] 215 515 751
library("cpss")
if (!requireNamespace("MASS", quietly = TRUE)) {
  stop("Please install the package \"MASS\".")
}
set.seed(666)
n <- 1000
tau <- c(200, 500, 750)
mu <- list(rep(0, 2), rep(0, 2), rep(0, 2), rep(0, 2))
Sigma <- list(diag(2), matrix(c(1, 0, 0, 4), 2), matrix(c(1, -0.5, -0.5, 4), 2), diag(2))
seg_len <- diff(c(0, tau, n))
y <- lapply(seq(1, length(tau) + 1), function(k) {
  MASS::mvrnorm(n = seg_len[k], mu = mu[[k]], Sigma = Sigma[[k]])
})
y <- do.call(rbind, y)
res <- cpss.var(y, algorithm = "BS", dist_min = 20)
cps(res)
# [1] 215 515 751

Generic functions and methods: dat

Description

Generic functions and methods: dat

Usage

dat(x)

dat(x) <- value

## S4 method for signature 'cpss'
dat(x)

## S4 replacement method for signature 'cpss'
dat(x) <- value
dat(x)

dat(x) <- value

## S4 method for signature 'cpss'
dat(x)

## S4 replacement method for signature 'cpss'
dat(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x
`cpss`	cpss class

Generic functions and methods: mdl

Description

Generic functions and methods: mdl

Usage

mdl(x)

mdl(x) <- value

## S4 method for signature 'cpss'
mdl(x)

## S4 replacement method for signature 'cpss'
mdl(x) <- value
mdl(x)

mdl(x) <- value

## S4 method for signature 'cpss'
mdl(x)

## S4 replacement method for signature 'cpss'
mdl(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x

Generic functions and methods: ncps

Description

Generic functions and methods: ncps

Usage

ncps(x)

ncps(x) <- value

## S4 method for signature 'cpss'
ncps(x)

## S4 replacement method for signature 'cpss'
ncps(x) <- value
ncps(x)

ncps(x) <- value

## S4 method for signature 'cpss'
ncps(x)

## S4 replacement method for signature 'cpss'
ncps(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x

Generic functions and methods: params

Description

Generic functions and methods: params

Usage

params(x)

params(x) <- value

## S4 method for signature 'cpss'
params(x)

## S4 replacement method for signature 'cpss'
params(x) <- value
params(x)

params(x) <- value

## S4 method for signature 'cpss'
params(x)

## S4 replacement method for signature 'cpss'
params(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x

Generic functions and methods: pelt_pen

Description

Generic functions and methods: pelt_pen

Usage

pelt_pen(x)

pelt_pen(x) <- value

## S4 method for signature 'cpss'
pelt_pen(x)

## S4 replacement method for signature 'cpss'
pelt_pen(x) <- value
pelt_pen(x)

pelt_pen(x) <- value

## S4 method for signature 'cpss'
pelt_pen(x)

## S4 replacement method for signature 'cpss'
pelt_pen(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x

plot method

Description

plot method

Usage

## S4 method for signature 'cpss'
plot(obj, type, x = c(), y = c(), ...)
## S4 method for signature 'cpss'
plot(obj, type, x = c(), y = c(), ...)

Arguments

`obj`	object from cpss
`type`	type of visualization
`x`	x
`y`	y
`...`	...
`cpss`	cpss class

Generic functions and methods: S_vals

Description

Generic functions and methods: S_vals

Usage

S_vals(x)

S_vals(x) <- value

## S4 method for signature 'cpss'
S_vals(x)

## S4 replacement method for signature 'cpss'
S_vals(x) <- value
S_vals(x)

S_vals(x) <- value

## S4 method for signature 'cpss'
S_vals(x)

## S4 replacement method for signature 'cpss'
S_vals(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x

Generic functions and methods: SC

Description

Generic functions and methods: SC

Usage

SC(x)

SC(x) <- value

## S4 method for signature 'cpss'
SC(x)

## S4 replacement method for signature 'cpss'
SC(x) <- value
SC(x)

SC(x) <- value

## S4 method for signature 'cpss'
SC(x)

## S4 replacement method for signature 'cpss'
SC(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x

Generic functions and methods: SC_vals

Description

Generic functions and methods: SC_vals

Usage

SC_vals(x)

SC_vals(x) <- value

## S4 method for signature 'cpss'
SC_vals(x)

## S4 replacement method for signature 'cpss'
SC_vals(x) <- value
SC_vals(x)

SC_vals(x) <- value

## S4 method for signature 'cpss'
SC_vals(x)

## S4 replacement method for signature 'cpss'
SC_vals(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x

summary method

Description

summary method

Usage

## S4 method for signature 'cpss'
summary(object)
## S4 method for signature 'cpss'
summary(object)

Arguments

`object`	object from cpss
`cpss`	cpss class

Generic functions and methods: update_inputs

Description

Generic functions and methods: update_inputs

Usage

update_inputs(x)

update_inputs(x) <- value

## S4 method for signature 'cpss'
update_inputs(x)

## S4 replacement method for signature 'cpss'
update_inputs(x) <- value
update_inputs(x)

update_inputs(x) <- value

## S4 method for signature 'cpss'
update_inputs(x)

## S4 replacement method for signature 'cpss'
update_inputs(x) <- value

Arguments

`x`	object from cpss
`value`	value assigned to x

update method

Description

update method

Usage

## S4 method for signature 'cpss'
update(object, dim_update)
## S4 method for signature 'cpss'
update(object, dim_update)

Arguments

`object`	object from cpss
`dim_update`	model dimension to update
`cpss`	cpss class

Well-log data

Description

Measurements of the nuclear magnetic response of underground rocks.

Usage

well
well

Format

A vector of 4,050 measurements:

well: Measurements.

Source

doi:10.1111/1467-9868.00421

Package 'cpss'

Help Index

Generic functions and methods: algo

Description

Usage

Arguments

Generic functions and methods: algo_param_dim

Description

Usage

Arguments

coef method

Description

Usage

Arguments

Generic functions and methods: cps

Description

Usage

Arguments

cpss: Change-Point Detection by Sample-Splitting Methods

Description

Getting started

cpss: an S4 class which collects data and information required for further change-point analyses and summaries

Description

Slots

Detecting changes in uers-customized models

Description

Usage

Arguments

Value

References

Examples

Detecting changes in exponential family

Description

Usage

Arguments

Value

References

See Also

Examples

Detecting changes in GLMs

Description

Usage

Arguments

Value

References

See Also

Examples

Detecting changes in linear models

Description

Usage

Arguments

Value

References

See Also

Examples

Detecting changes in mean

Description

Usage

Arguments

Value

References

See Also

Examples

Detecting changes in mean and (co)variance

Description

Usage

Arguments

Value

References

See Also

Examples

Detecting changes in (co)variance

Description

Usage

Arguments

Value

References

See Also

Examples

Generic functions and methods: dat