| Type: | Package |
| Title: | A Collection of Change-Point Detection Methods |
| Version: | 1.1.0 |
| Date: | 2022-08-25 |
| Maintainer: | Haotian Xu <haotian.xu@uclouvain.be> |
| Description: | Performs a series of offline and/or online change-point detection algorithms for 1) univariate mean: <doi:10.1214/20-EJS1710>, <doi:10.48550/arXiv.2006.03283>; 2) univariate polynomials: <doi:10.1214/21-EJS1963>; 3) univariate and multivariate nonparametric settings: <doi:10.1214/21-EJS1809>, <doi:10.1109/TIT.2021.3130330>; 4) high-dimensional covariances: <doi:10.3150/20-BEJ1249>; 5) high-dimensional networks with and without missing values: <doi:10.1214/20-AOS1953>, <doi:10.48550/arXiv.2101.05477>, <doi:10.48550/arXiv.2110.06450>; 6) high-dimensional linear regression models: <doi:10.48550/arXiv.2010.10410>, <doi:10.48550/arXiv.2207.12453>; 7) high-dimensional vector autoregressive models: <doi:10.48550/arXiv.1909.06359>; 8) high-dimensional self exciting point processes: <doi:10.48550/arXiv.2006.03572>; 9) dependent dynamic nonparametric random dot product graphs: <doi:10.48550/arXiv.1911.07494>; 10) univariate mean against adversarial attacks: <doi:10.48550/arXiv.2105.10417>. |
| Depends: | R (≥ 3.5.0) |
| Imports: | stats, gglasso, glmnet, ks, MASS, data.tree, Rcpp |
| Suggests: | knitr, abind, DiagrammeR, rmarkdown |
| LinkingTo: | Rcpp, RcppArmadillo |
| License: | GPL (≥ 3) |
| RoxygenNote: | 7.2.1 |
| Encoding: | UTF-8 |
| URL: | https://github.com/HaotianXu/changepoints |
| VignetteBuilder: | knitr |
| NeedsCompilation: | yes |
| Packaged: | 2022-08-25 15:59:18 UTC; haotianxu |
| Author: | Haotian Xu [aut, cre], Oscar Padilla [aut], Daren Wang [aut], Mengchu Li [aut], Qin Wen [ctb] |
| Repository: | CRAN |
| Date/Publication: | 2022-09-04 14:30:08 UTC |
changepoints-package: A Collections of Change-Point Detection Methods
Description
Performs a series of offline and/or online change-point detection algorithms for 1) univariate mean; 2) univariate polynomials; 3) univariate and multivariate nonparametric settings; 4) high-dimensional covariances; 5) high-dimensional networks with and without missing values; 6) high-dimensional linear regression models; 7) high-dimensional vector autoregressive models; 8) high-dimensional self exciting point processes; 9) dependent dynamic nonparametric random dot product graphs; 10) univariate mean against adversarial attacks. For more informations, see Wang et al. (2020) <arXiv:1810.09498>; Yu et al. (2020) <arXiv:2006.03283>; Yu and Chatterjee (2020) <arXiv:2007.09910>; Padilla et al. (2021) <arXiv:1905.10019>; Padilla et al. (2019) <arXiv:1910.13289>; Wang et al. (2021) <arXiv:1712.09912>; Wang et al. (2018) <arXiv:1809.09602>; Padilla et al. (2019) <arXiv:1911.07494>; Yu et al. (2021) <arXiv:2101.05477>; Rinaldo et al. (2020) <arXiv:2010.10410>; Wang et al. (2019) <arXiv:1909.06359>; Wang et al. (2020) <arXiv:2006.03572>; Dubey et al. (2021) <arXiv:2110.06450>; Li and Yu (2021) <arXiv:2105.10417>.
Adversarially robust univariate mean change point detection.
Description
Perform the adversarially robust change point detection method.
Usage
ARC(y, h, block_num = 1, epsilon, gaussian = TRUE)
Arguments
y |
A |
h |
An |
block_num |
An |
epsilon |
A |
gaussian |
A |
Value
An numeric vector of estimated change point locations
Author(s)
Mengchu Li
References
Li and Yu (2021) <arXiv:2105.10417>.
Examples
### simulate data with contamination
obs_num = 1000
D = 2
noise = 0.1 # proportion of contamination
mu0 = 0
mu1 = 1
sd =1
idmixture = rbinom(obs_num/D, 1, 1-noise)
dat = NULL
for (j in 1:D){
for (i in 1:(obs_num/(2*D))){
if (idmixture[i] == 1){
dat = c(dat,rnorm(1,mu0,sd))
}
else{
dat = c(dat,rnorm(1,mu1/(2*noise),0))
}
}
for (i in (obs_num/(2*D)+1):(obs_num/D)){
if (idmixture[i] == 1){
dat = c(dat,rnorm(1,mu1,sd))
}
else{
dat = c(dat,rnorm(1,mu1/(2*noise)-(1-noise)*mu1/noise,0))
}
}
}
plot(dat)
### perform ARC
ARC(dat,h = 120, epsilon = 0.1)
Backward detection with a robust bootstrap change point test using U-statistics for univariate mean change.
Description
Perform the backward detection method with a robust bootstrap change point test using U-statistics on univariate data.
Usage
BD_U(y, M, B = 100, inter = NULL, inter_ini = TRUE)
Arguments
y |
A |
M |
An |
B |
An |
inter |
A nuisance parameter. |
inter_ini |
A nuisance parameter. |
Value
An numeric vector of estimated change point locations.
Author(s)
Mengchu Li
References
Yu and Chen (2019) <arXiv:1904.03372>.
Binary Segmentation for covariance change points detection through Operator Norm.
Description
Perform binary segmentation for covariance change points detection through Operator Norm.
Usage
BS.cov(X, s, e, level = 0)
Arguments
X |
A |
s |
A |
e |
A |
level |
A parameter for tracking the level at which a change point is detected. Should be fixed as 0. |
Value
An object of class "BS", which is a list with the structure:
S: A vector of estimated changepoints (sorted in strictly increasing order).
Dval: A vector of values of CUSUM statistic based on KS distance.
Level: A vector representing the levels at which each change point is detected.
Parent: A matrix with the starting indices on the first row and the ending indices on the second row.
Author(s)
Haotian Xu
References
Wang, Yu and Rinaldo (2021) <doi:10.3150/20-BEJ1249>.
See Also
thresholdBS for obtain change points estimation.
Examples
p = 10
A1 = gen.cov.mat(p, 1, "equal")
A2 = gen.cov.mat(p, 2, "diagonal")
A3 = gen.cov.mat(p, 3, "power")
X = cbind(t(MASS::mvrnorm(100, mu = rep(0, p), A1)),
t(MASS::mvrnorm(150, mu = rep(0, p), A2)),
t(MASS::mvrnorm(200, mu = rep(0, p), A3)))
temp = BS.cov(X, 1, 450)
thresholdBS(temp, 10)
Standard binary segmentation for univariate nonparametric change points detection.
Description
Perform standard binary segmentation for univariate nonparametric change points detection.
Usage
BS.uni.nonpar(Y, s, e, N, delta, level = 0)
Arguments
Y |
A |
s |
A |
e |
A |
N |
A |
delta |
A positive |
level |
Should be fixed as 0. |
Value
An object of class "BS", which is a list with the following structure:
S |
A vector of estimated change points (sorted in strictly increasing order). |
Dval |
A vector of values of CUSUM statistic based on KS distance. |
Level |
A vector representing the levels at which each change point is detected. |
Parent |
A matrix with the starting indices on the first row and the ending indices on the second row. |
Author(s)
Oscar Hernan Madrid Padilla & Haotian Xu
References
Padilla, Yu, Wang and Rinaldo (2021) <doi:10.1214/21-EJS1809>.
See Also
thresholdBS for obtaining change points estimation, tuneBSuninonpar for a tuning version.
Examples
Y = t(as.matrix(c(rnorm(100, 0, 1), rnorm(100, 0, 10), rnorm(100, 0, 40))))
N = rep(1, 300)
temp = BS.uni.nonpar(Y, 1, 300, N, 5)
plot.ts(t(Y))
points(x = tail(temp$S[order(temp$Dval)],4), y = Y[,tail(temp$S[order(temp$Dval)],4)], col = "red")
Standard binary segmentation for univariate mean change points detection.
Description
Perform standard binary segmentation for univariate mean change points detection.
Usage
BS.univar(y, s, e, delta = 2, level = 0)
Arguments
y |
A |
s |
A |
e |
A |
delta |
A positive |
level |
Should be fixed as 0. |
Value
An object of class "BS", which is a list with the following structure:
S |
A vector of estimated change point locations (sorted in strictly increasing order). |
Dval |
A vector of values of CUSUM statistic. |
Level |
A vector representing the levels at which each change point is detected. |
Parent |
A matrix with the starting indices on the first row and the ending indices on the second row. |
Author(s)
Haotian Xu
References
Wang, Yu and Rinaldo (2020) <doi:10.1214/20-EJS1710>.
See Also
thresholdBS for obtaining change points estimation, tuneBSunivar for a tuning version.
Examples
set.seed(0)
cpt_true = c(20, 50, 170)
y = rnorm(300) + c(rep(0,20),rep(2,30),rep(0,120),rep(2,130))
temp = BS.univar(y, 1, length(y), delta = 5)
plot.ts(y)
points(x = tail(temp$S[order(temp$Dval)],4),
y = y[tail(temp$S[order(temp$Dval)],4)], col = "red")
BS_result = thresholdBS(temp, tau = 4)
BS_result
print(BS_result$BS_tree, "value")
print(BS_result$BS_tree_trimmed, "value")
cpt_hat = sort(BS_result$cpt_hat[,1]) # the threshold tau is specified to be 4
Hausdorff.dist(cpt_hat, cpt_true)
cpt_LR = local.refine.univar(cpt_hat, y)
Hausdorff.dist(cpt_LR, cpt_true)
Confidence interval construction of change points for regression settings with change points.
Description
Construct element-wise confidence interval for change points.
Usage
CI.regression(
cpt_init,
cpt_LR,
beta_hat,
y,
X,
w = 0.9,
B = 1000,
M,
alpha_vec,
rounding = TRUE
)
Arguments
cpt_init |
An |
cpt_LR |
An |
beta_hat |
A |
y |
A |
X |
A |
w |
A |
B |
An |
M |
An |
alpha_vec |
An |
rounding |
A |
Value
An length(cpt_init)-2-length(alpha_vec) array of confidence intervals.
Author(s)
Haotian Xu
References
Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.
Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.
Examples
d0 = 5
p = 10
n = 200
cpt_true = c(70, 140)
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)
lambda_set = c(0.1, 0.5, 1, 2)
zeta_set = c(10, 15, 20)
temp = CV.search.DPDU.regression(y = data$y, X = data$X, lambda_set, zeta_set)
temp$test_error # test error result
# find the indices of lambda_set and zeta_set which minimizes the test error
min_idx = as.vector(arrayInd(which.min(temp$test_error), dim(temp$test_error)))
lambda_set[min_idx[2]]
zeta_set[min_idx[1]]
cpt_init = unlist(temp$cpt_hat[min_idx[1], min_idx[2]])
beta_hat = matrix(unlist(temp$beta_hat[min_idx[1], min_idx[2]]), ncol = length(cpt_init)+1)
cpt_LR = local.refine.DPDU.regression(cpt_init, beta_hat, data$y, data$X, w = 0.9)
alpha_vec = c(0.01, 0.05, 0.1)
CI.regression(cpt_init, cpt_LR, beta_hat, data$y, data$X, w = 0.9, B = 1000, M = n, alpha_vec)
Grid search based on Cross-Validation of all tuning parameters (gamma, lambda and zeta) for regression.
Description
Perform grid search based on Cross-Validation of all tuning parameters (gamma, lambda and zeta)
Usage
CV.search.DP.LR.regression(
y,
X,
gamma_set,
lambda_set,
zeta_set,
delta,
eps = 0.001
)
Arguments
y |
A |
X |
A |
gamma_set |
A |
lambda_set |
A |
zeta_set |
A |
delta |
A strictly positive |
eps |
A |
Value
A list with the following structure:
cpt_hat |
A list of vector of estimated changepoints (sorted in strictly increasing order) |
K_hat |
A list of scalar of number of estimated changepoints |
test_error |
A list of vector of testing errors (each row corresponding to each gamma, and each column corresponding to each lambda) |
train_error |
A list of vector of training errors |
Author(s)
Daren Wang & Haotian Xu
References
Rinaldo, Wang, Wen, Willett and Yu (2020) <arxiv:2010.10410>
Examples
set.seed(123)
d0 = 8
p = 15
n = 100
cpt_true = c(30, 70)
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)
gamma_set = c(0.01, 0.1)
lambda_set = c(0.01, 0.1)
temp = CV.search.DP.regression(y = data$y, X = data$X, gamma_set, lambda_set, delta = 2)
temp$test_error # test error result
# find the indices of gamma_set and lambda_set which minimizes the test error
min_idx = as.vector(arrayInd(which.min(temp$test_error), dim(temp$test_error)))
gamma_set[min_idx[1]]
lambda_set[min_idx[2]]
cpt_init = unlist(temp$cpt_hat[min_idx[1], min_idx[2]])
zeta_set = c(0.1, 1)
temp_zeta = CV.search.DP.LR.regression(data$y, data$X, gamma_set[min_idx[1]],
lambda_set[min_idx[2]], zeta_set, delta = 2, eps = 0.001)
min_zeta_idx = which.min(unlist(temp_zeta$test_error))
cpt_LR = local.refine.regression(cpt_init, data$y, X = data$X, zeta = zeta_set[min_zeta_idx])
Hausdorff.dist(cpt_init, cpt_true)
Hausdorff.dist(cpt_LR, cpt_true)
Grid search based on cross-validation of dynamic programming for VAR change points detection via l_0 penalty.
Description
Perform grid search based on cross-validation of dynamic programming for VAR change points detection.
Usage
CV.search.DP.VAR1(DATA, gamma_set, lambda_set, delta, eps = 0.001)
Arguments
DATA |
A |
gamma_set |
A |
lambda_set |
A |
delta |
A strictly |
eps |
A |
Value
A list with the following structure:
cpt_hat |
A list of vector of estimated change points |
K_hat |
A list of scalar of number of estimated change points |
test_error |
A list of vector of testing errors (each row corresponding to each gamma, and each column corresponding to each lambda) |
train_error |
A list of vector of training errors |
Author(s)
Daren Wang & Haotian Xu
References
Wang, Yu, Rinaldo and Willett (2019) <arxiv:1909.06359>
Examples
set.seed(123)
p = 10
sigma = 1
n = 20
v1 = 2*(seq(1,p,1)%%2) - 1
v2 = -v1
AA = matrix(0, nrow = p, ncol = p-2)
A1 = cbind(v1,v2,AA)*0.1
A2 = cbind(v2,v1,AA)*0.1
A3 = A1
cpt_true = c(40, 80)
data = simu.VAR1(sigma, p, 2*n+1, A1)
data = cbind(data, simu.VAR1(sigma, p, 2*n, A2, vzero=c(data[,ncol(data)])))
data = cbind(data, simu.VAR1(sigma, p, 2*n, A3, vzero=c(data[,ncol(data)])))
gamma_set = c(0.1, 0.5, 1)
lambda_set = c(0.1, 1, 3.2)
temp = CV.search.DP.VAR1(data, gamma_set, lambda_set, delta = 5)
temp$test_error # test error result
# find the indices of gamma.set and lambda.set which minimizes the test error
min_idx = as.vector(arrayInd(which.min(temp$test_error), dim(temp$test_error)))
cpt_init = unlist(temp$cpt_hat[min_idx[1], min_idx[2]])
Hausdorff.dist(cpt_init, cpt_true)
Grid search for dynamic programming to select the tuning parameter through Cross-Validation.
Description
Perform grid search for dynamic programming to select the tuning parameter through Cross-Validation.
Usage
CV.search.DP.poly(y, r, gamma_set, delta)
Arguments
y |
A |
r |
An |
gamma_set |
A |
delta |
A positive |
Value
A list with the following structure:
cpt_hat |
A list of vector of estimated change points locations (sorted in strictly increasing order) |
K_hat |
A list of scalar of number of estimated change points |
test_error |
A list of vector of testing errors |
train_error |
A list of vector of training errors |
Author(s)
Haotian Xu
References
Yu and Chatterjee (2020) <arXiv:2007.09910>
Examples
set.seed(0)
cpt_true = c(20, 50, 170)
y = rnorm(300) + c(rep(0,20),rep(2,30),rep(0,120),rep(2,130))
plot.ts(y)
gamma_set = 3:9
DP_result = CV.search.DP.poly(y, r = 2, gamma_set, delta = 5)
min_idx = which.min(DP_result$test_error)
cpt_init = unlist(DP_result$cpt_hat[min_idx])
local.refine.poly(cpt_init, y, r = 2, delta_lr = 5)
Grid search based on cross-validation of dynamic programming for regression change points localisation with l_0 penalisation.
Description
Perform grid search to select tuning parameters gamma (for l_0 penalty of DP) and lambda (for lasso penalty) based on cross-validation.
Usage
CV.search.DP.regression(y, X, gamma_set, lambda_set, delta, eps = 0.001)
Arguments
y |
A |
X |
A |
gamma_set |
A |
lambda_set |
A |
delta |
A strictly positive |
eps |
A |
Value
A list with the following structure:
cpt_hat |
A list of vector of estimated change points |
K_hat |
A list of scalar of number of estimated change points |
test_error |
A list of vector of testing errors (each row corresponding to each gamma, and each column corresponding to each lambda) |
train_error |
A list of vector of training errors |
Author(s)
Daren Wang
References
Rinaldo, Wang, Wen, Willett and Yu (2020) <arxiv:2010.10410>
Examples
d0 = 10
p = 20
n = 100
cpt_true = c(30, 70)
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)
gamma_set = c(0.01, 0.1, 1)
lambda_set = c(0.01, 0.1, 1, 3)
temp = CV.search.DP.regression(y = data$y, X = data$X, gamma_set, lambda_set, delta = 2)
temp$test_error # test error result
# find the indices of gamma_set and lambda_set which minimizes the test error
min_idx = as.vector(arrayInd(which.min(temp$test_error), dim(temp$test_error)))
gamma_set[min_idx[1]]
lambda_set[min_idx[2]]
cpt_init = unlist(temp$cpt_hat[min_idx[1], min_idx[2]])
Grid search for dynamic programming to select the tuning parameter through Cross-Validation.
Description
Perform grid search for dynamic programming to select the tuning parameter through Cross-Validation.
Usage
CV.search.DP.univar(y, gamma_set, delta)
Arguments
y |
A |
gamma_set |
A |
delta |
A positive |
Value
A list with the following structure:
cpt_hat |
A list of vector of estimated change points (sorted in strictly increasing order). |
K_hat |
A list of scalar of number of estimated change points. |
test_error |
A list of vector of testing errors. |
train_error |
A list of vector of training errors. |
Author(s)
Daren Wang & Haotian Xu
References
Wang, Yu and Rinaldo (2020) <doi:10.1214/20-EJS1710>
Examples
set.seed(0)
cpt_true = c(20, 50, 170)
y = rnorm(300) + c(rep(0,20),rep(2,30),rep(0,120),rep(2,130))
gamma_set = 1:5
DP_result = CV.search.DP.univar(y, gamma_set, delta = 5)
min_idx = which.min(DP_result$test_error)
cpt_hat = unlist(DP_result$cpt_hat[min_idx])
Hausdorff.dist(cpt_hat, cpt_true)
Grid search based on cross-validation of dynamic programming for regression change points localisation with l_0 penalisation.
Description
Perform grid search to select tuning parameters gamma (for l_0 penalty of DP) and lambda (for lasso penalty) based on cross-validation.
Usage
CV.search.DPDU.regression(y, X, lambda_set, zeta_set, eps = 0.001)
Arguments
y |
A |
X |
A |
lambda_set |
A |
zeta_set |
An |
eps |
A |
Value
A list with the following structure:
cpt_hat |
A list of vectors of estimated change points |
K_hat |
A list of scalars of number of estimated change points |
test_error |
A matrix of testing errors (each row corresponding to each gamma, and each column corresponding to each lambda) |
train_error |
A matrix of training errors |
beta_hat |
A list of matrices of estimated regression coefficients |
Author(s)
Haotian Xu
References
Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.
Examples
d0 = 5
p = 30
n = 200
cpt_true = 100
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)
lambda_set = c(0.01, 0.1, 1, 2)
zeta_set = c(10, 15, 20)
temp = CV.search.DPDU.regression(y = data$y, X = data$X, lambda_set, zeta_set)
temp$test_error # test error result
# find the indices of lambda_set and zeta_set which minimizes the test error
min_idx = as.vector(arrayInd(which.min(temp$test_error), dim(temp$test_error)))
lambda_set[min_idx[2]]
zeta_set[min_idx[1]]
cpt_init = unlist(temp$cpt_hat[min_idx[1], min_idx[2]])
beta_hat = matrix(unlist(temp$beta_hat[min_idx[1], min_idx[2]]), ncol = length(cpt_init)+1)
Dynamic programming for SEPP change points detection through l_0 penalty.
Description
Perform dynamic programming for SEPP change points detection.
Usage
DP.SEPP(DATA, gamma, lambda, delta, delta2, intercept, threshold)
Arguments
DATA |
A |
gamma |
A |
lambda |
A |
delta |
An |
delta2 |
An |
intercept |
A |
threshold |
A |
Value
An object of class "DP", which is a list with the following structure:
partition |
A vector of the best partition. |
cpt |
A vector of change points estimation. |
Author(s)
Daren Wang & Haotian Xu
References
Wang, D., Yu, Y., & Willett, R. (2020). Detecting Abrupt Changes in High-Dimensional Self-Exciting Poisson Processes. arXiv preprint arXiv:2006.03572.
Examples
p = 8 # dimension
n = 15
s = 3 # s is sparsity
factor = 0.2 # large factor gives exact recovery
threshold = 4 # thresholding makes the process stable
intercept = 1/2 # intercept of the model. Assume to be known as in the existing literature
A1 = A2 = A3 = matrix(0, p, p)
diag(A1[,-1]) = 1
diag(A1) = 1
diag(A1[-1,]) = -1
A1 = A1*factor
A1[(s+1):p, (s+1):p] = 0
diag(A2[,-1]) = 1
diag(A2) = -1
diag(A2[-1,]) = 1
A2 = A2*factor
A2[(s+1):p, (s+1):p] = 0
data1 = simu.SEPP(intercept, n, A1, threshold, vzero = NULL)
data2 = simu.SEPP(intercept, n, A2, threshold, vzero = data1[,n])
data = cbind(data1, data2)
gamma = 0.1
delta = 0.5*n
delta2 = 1.5*n
intercept = 1/2
threshold = 6
DP_result = DP.SEPP(data, gamma = gamma, lambda = 0.03, delta, delta2, intercept, threshold)
cpt_hat = DP_result$cpt
Dynamic programming for VAR1 change points detection through l_0 penalty.
Description
Perform dynamic programming for VAR1 change points detection through l_0 penalty.
Usage
DP.VAR1(X_futu, X_curr, gamma, lambda, delta, eps = 0.001)
Arguments
X_futu |
A |
X_curr |
A |
gamma |
A |
lambda |
A |
delta |
A strictly |
eps |
A |
Value
An object of class "DP", which is a list with the following structure:
partition |
A vector of the best partition. |
cpt |
A vector of change points estimation. |
Author(s)
Daren Wang & Haotian Xu
References
Wang, Yu, Rinaldo and Willett (2019) <arxiv:1909.06359>
Examples
p = 10
sigma = 1
n = 20
v1 = 2*(seq(1,p,1)%%2) - 1
v2 = -v1
AA = matrix(0, nrow = p, ncol = p-2)
A1 = cbind(v1,v2,AA)*0.1
A2 = cbind(v2,v1,AA)*0.1
A3 = A1
data = simu.VAR1(sigma, p, 2*n+1, A1)
data = cbind(data, simu.VAR1(sigma, p, 2*n, A2, vzero=c(data[,ncol(data)])))
data = cbind(data, simu.VAR1(sigma, p, 2*n, A3, vzero=c(data[,ncol(data)])))
N = ncol(data)
X_curr = data[,1:(N-1)]
X_futu = data[,2:N]
DP_result = DP.VAR1(X_futu, X_curr, gamma = 1, lambda = 1, delta = 5)
DP_result$cpt
Dynamic programming algorithm for univariate polynomials change points detection.
Description
Perform dynamic programming algorithm for univariate polynomials change points detection.
Usage
DP.poly(y, r, gamma, delta)
Arguments
y |
A |
r |
An |
gamma |
A |
delta |
A strictly |
Value
A list with the following structure:
An object of class "DP", which is a list with the following structure:
partition |
A vector of the best partition. |
yhat |
A vector of mean estimation for corresponding to the best partition. |
cpt |
A vector of change points estimation. |
Author(s)
Haotian Xu
References
Yu and Chatterjee (2020) <arXiv:2007.09910>
Examples
set.seed(0)
cpt_true = c(20, 50, 170)
y = rnorm(300) + c(rep(0,20),rep(2,30),rep(0,120),rep(2,130))
plot.ts(y)
temp = DP.poly(y, r = 2, gamma = 15, delta = 5)
temp$cpt
Dynamic programming algorithm for regression change points localisation with l_0 penalisation.
Description
Perform dynamic programming algorithm for regression change points localisation.
Usage
DP.regression(y, X, gamma, lambda, delta, eps = 0.001)
Arguments
y |
A |
X |
A |
gamma |
A positive |
lambda |
A positive |
delta |
A positive |
eps |
A |
Value
An object of class "DP", which is a list with the following structure:
partition |
A vector of the best partition. |
cpt |
A vector of change points estimation. |
Author(s)
Daren Wang & Haotian Xu
References
Rinaldo, Wang, Wen, Willett and Yu (2020) <arxiv:2010.10410>
Examples
d0 = 10
p = 20
n = 100
cpt_true = c(30, 70)
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)
temp = DP.regression(y = data$y, X = data$X, gamma = 2, lambda = 1, delta = 5)
cpt_hat = temp$cpt
Dynamic programming for univariate mean change points detection through l_0 penalty.
Description
Perform dynamic programming for univariate mean change points detection.
Usage
DP.univar(y, gamma, delta)
Arguments
y |
A |
gamma |
A |
delta |
A positive |
Value
An object of class "DP", which is a list with the following structure:
partition |
A vector of the best partition. |
yhat |
A vector of mean estimation for corresponding to the best partition. |
cpt |
A vector of change points estimation. |
Author(s)
Haotian Xu
References
Wang, Yu and Rinaldo (2020) <doi:10.1214/20-EJS1710>
Examples
set.seed(123)
cpt_true = c(20, 50, 170)
y = rnorm(300) + c(rep(0,20),rep(1,30),rep(0,120),rep(1,130))
DP_result = DP.univar(y, gamma = 5, delta = 5)
cpt_hat = DP_result$cpt
Hausdorff.dist(cpt_hat, cpt_true)
Dynamic programming with dynamic update algorithm for regression change points localisation with l_0 penalisation.
Description
Perform DPDU algorithm for regression change points localisation.
Usage
DPDU.regression(y, X, lambda, zeta, eps = 0.001)
Arguments
y |
A |
X |
A |
lambda |
A positive |
zeta |
A positive |
eps |
A |
Value
An object of class "DP", which is a list with the following structure:
partition |
A vector of the best partition. |
cpt |
A vector of change points estimation. |
Author(s)
Haotian Xu
References
Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.
Examples
d0 = 10
p = 20
n = 100
cpt_true = c(30, 70)
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)
temp = DPDU.regression(y = data$y, X = data$X, lambda = 1, zeta = 20)
cpt_hat = temp$cpt
Bidirectional Hausdorff distance.
Description
Compute the bidirectional Hausdorff distance between two sets.
Usage
Hausdorff.dist(vec1, vec2)
Arguments
vec1 |
A |
vec2 |
A |
Value
An integer scalar of bidirectional Hausdorff distance.
Author(s)
Daren Wang
Examples
vec1 = sample.int(1000, size = 50)
vec2 = sample.int(2000, size = 100)
Hausdorff.dist(vec1, vec2)
Long-run variance estimation for regression settings with change points.
Description
Estimating long-run variance for regression settings with change points.
Usage
LRV.regression(cpt_init, beta_hat, y, X, w = 0.9, block_size)
Arguments
cpt_init |
An |
beta_hat |
A |
y |
A |
X |
A |
w |
A |
block_size |
An |
Value
A vector of long-run variance estimators associated with all local refined intervals.
Author(s)
Haotian Xu
References
Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.
Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.
Examples
d0 = 5
p = 10
n = 200
cpt_true = c(70, 140)
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)
lambda_set = c(0.1, 0.5, 1, 2)
zeta_set = c(10, 15, 20)
temp = CV.search.DPDU.regression(y = data$y, X = data$X, lambda_set, zeta_set)
temp$test_error # test error result
# find the indices of lambda_set and zeta_set which minimizes the test error
min_idx = as.vector(arrayInd(which.min(temp$test_error), dim(temp$test_error)))
lambda_set[min_idx[2]]
zeta_set[min_idx[1]]
cpt_init = unlist(temp$cpt_hat[min_idx[1], min_idx[2]])
beta_hat = matrix(unlist(temp$beta_hat[min_idx[1], min_idx[2]]), ncol = length(cpt_init)+1)
interval_refine = trim_interval(n, cpt_init)
# choose S
block_size = ceiling(sqrt(min(floor(interval_refine[,2]) - ceiling(interval_refine[,1])))/2)
LRV_est = LRV.regression(cpt_init, beta_hat, data$y, data$X, w = 0.9, block_size)
Generate random intervals for WBS.
Description
Generate random intervals for WBS.
Usage
WBS.intervals(M, lower = 1, upper)
Arguments
M |
A positive |
lower |
A positive |
upper |
A positive |
Value
A list with the following structure:
Alpha |
A M-dim vector representing the starting indices of random intervals |
Beta |
A M-dim vector representing the ending indices of random intervals |
Author(s)
Oscar Hernan Madrid Padilla
Examples
WBS.intervals(120, lower = 1, upper = 300)
Wild binary segmentation for multivariate nonparametric change points detection.
Description
Perform wild binary segmentation for multivariate nonparametric change points detection.
Usage
WBS.multi.nonpar(Y, W, s, e, Alpha, Beta, h, delta, level = 0)
Arguments
Y |
A |
W |
A copy of the matrix Y, it can be Y itself. |
s |
A |
e |
A |
Alpha |
A |
Beta |
A |
h |
A |
delta |
A |
level |
Should be fixed as 0. |
Value
An object of class "BS", which is a list with the following structure:
S |
A vector of estimated change points (sorted in strictly increasing order). |
Dval |
A vector of values of CUSUM statistic based on KS distance. |
Level |
A vector representing the levels at which each change point is detected. |
Parent |
A matrix with the starting indices on the first row and the ending indices on the second row. |
Author(s)
Oscar Hernan Madrid Padilla & Haotian Xu
References
Padilla, Yu, Wang and Rinaldo (2019) <arxiv:1910.13289>.
See Also
thresholdBS for obtain change points estimation, tuneBSmultinonpar for a tuning version.
Examples
n = 70
v = c(floor(n/3), 2*floor(n/3)) # location of change points
p = 4
Y = matrix(0, p, n) # matrix for data
mu0 = rep(0, p) # mean of the data
mu1 = rep(0, p)
mu1[1:floor(p/2)] = 2
Sigma0 = diag(p) #Covariance matrices of the data
Sigma1 = diag(p)*2
# Generate data
for(t in 1:n){
if(t < v[1] || t > v[2]){
Y[,t] = MASS::mvrnorm(n = 1, mu0, Sigma0)
}
if(t >= v[1] && t < v[2]){
Y[,t] = MASS::mvrnorm(n = 1, mu1, Sigma1)
}
}## close for generate data
M = 10
intervals = WBS.intervals(M = M, lower = 1, upper = ncol(Y)) #Random intervals
K_max = 30
h = 5*(K_max*log(n)/n)^{1/p} # bandwith
temp = WBS.multi.nonpar(Y, Y, 1, ncol(Y), intervals$Alpha, intervals$Beta, h, delta = 10)
result = thresholdBS(temp, median(temp$Dval))
Wild binary segmentation for network change points detection.
Description
Perform wild binary segmentation for network change points detection.
Usage
WBS.network(data_mat1, data_mat2, s, e, Alpha, Beta, delta, level = 0)
Arguments
data_mat1 |
A |
data_mat2 |
An independent copy of data_mat1. |
s |
A |
e |
A |
Alpha |
A |
Beta |
A |
delta |
A positive |
level |
Should be fixed as 0. |
Value
An object of class "BS", which is a list with the following structure:
S |
A vector of estimated change points (sorted in strictly increasing order). |
Dval |
A vector of values of CUSUM statistic based on KS distance. |
Level |
A vector representing the levels at which each change point is detected. |
Parent |
A matrix with the starting indices on the first row and the ending indices on the second row. |
Author(s)
Daren Wang & Haotian Xu
References
Wang, Yu and Rinaldo (2018) <arxiv:1809.09602>.
See Also
thresholdBS for obtaining change points estimation.
Examples
p = 15 # number of nodes
rho = 0.5 # sparsity parameter
block_num = 3 # number of groups for SBM
n = 100 # sample size for each segment
# connectivity matrix for the first and the third segments
conn1_mat = rho * matrix(c(0.6,1,0.6,1,0.6,0.5,0.6,0.5,0.6), nrow = 3)
# connectivity matrix for the second segment
conn2_mat = rho * matrix(c(0.6,0.5,0.6,0.5,0.6,1,0.6,1,0.6), nrow = 3)
set.seed(1)
can_vec = sample(1:p, replace = FALSE) # randomly assign nodes into groups
sbm1 = simu.SBM(conn1_mat, can_vec, n, symm = TRUE, self = TRUE)
sbm2 = simu.SBM(conn2_mat, can_vec, n, symm = TRUE, self = TRUE)
data_mat = cbind(sbm1$obs_mat, sbm2$obs_mat)
data_mat1 = data_mat[,seq(1,ncol(data_mat),2)]
data_mat2 = data_mat[,seq(2,ncol(data_mat),2)]
M = 10
intervals = WBS.intervals(M = M, lower = 1, upper = ncol(data_mat1))
temp = WBS.network(data_mat1, data_mat2, 1, ncol(data_mat1),
intervals$Alpha, intervals$Beta, delta = 5)
rho_hat = quantile(rowMeans(data_mat), 0.95)
tau = p*rho_hat*(log(n))^2/20 # default threshold given in the paper
cpt_init = unlist(thresholdBS(temp, tau)$cpt_hat[,1])
cpt_refined = local.refine.network(cpt_init, data_mat1, data_mat2,
self = TRUE, tau2 = p*rho_hat/3, tau3 = Inf)
cpt_WBS = 2*cpt_init
cpt_refined = 2*cpt_refined
Wild binary segmentation for dependent dynamic random dot product graph models.
Description
Perform wild binary segmentation for dependent dynamic random dot product graph models.
Usage
WBS.nonpar.RDPG(data_mat, lowerdiag = FALSE, d, Alpha, Beta, delta)
Arguments
data_mat |
A |
lowerdiag |
A |
d |
A |
Alpha |
A |
Beta |
A |
delta |
A positive |
Value
An object of class "BS", which is a list with the following structure:
S |
A vector of estimated change point locations (sorted in strictly increasing order). |
Dval |
A vector of values of CUSUM statistic. |
Level |
A vector representing the levels at which each change point is detected. |
Parent |
A matrix with the starting indices on the first row and the ending indices on the second row. |
Author(s)
Oscar Hernan Madrid Padilla, Haotian Xu
References
Padilla, Yu and Priebe (2019) <arxiv:1911.07494>.
See Also
thresholdBS for obtaining change points estimation, tuneBSnonparRDPG for a tuning version.
Examples
### generate data
p = 20 # number of nodes
n = 50 # sample size for each segment
lat_dim_num = 5 # number of latent dimensions
set.seed(1)
x_mat = matrix(runif(p*lat_dim_num), nrow = p, ncol = lat_dim_num)
x_tilde_mat = matrix(runif(p*lat_dim_num), nrow = p, ncol = lat_dim_num)
y_mat = rbind(x_tilde_mat[1:floor(p/4),], x_mat[(floor(p/4)+1):p,])
rdpg1 = simu.RDPG(x_mat, n, symm = TRUE, self = FALSE)
rdpg2 = simu.RDPG(y_mat, n, symm = TRUE, self = FALSE)
data1_mat = rdpg1$obs_mat
data2_mat = rdpg2$obs_mat
data_mat = cbind(data1_mat, data2_mat)
### detect change points
M = 30 # number of random intervals for WBS
d = 10 # parameter for scaled PCA algorithm
delta = 5
intervals = WBS.intervals(M = M, lower = 1, upper = ncol(data_mat))
WBS_result = WBS.nonpar.RDPG(data_mat, lowerdiag = TRUE, d,
Alpha = intervals$Alpha, Beta = intervals$Beta, delta)
Wild binary segmentation for univariate nonparametric change points detection.
Description
Perform wild binary segmentation for univariate nonparametric change points detection.
Usage
WBS.uni.nonpar(Y, s, e, Alpha, Beta, N, delta, level = 0)
Arguments
Y |
A |
s |
A |
e |
A |
Alpha |
A |
Beta |
A |
N |
A |
delta |
A positive |
level |
Should be fixed as 0. |
Value
A list with the following structure:
S |
A vector of estimated change points (sorted in strictly increasing order) |
Dval |
A vector of values of CUSUM statistic based on KS distance |
Level |
A vector representing the levels at which each change point is detected |
Parent |
A matrix with the starting indices on the first row and the ending indices on the second row |
Author(s)
Oscar Hernan Madrid Padilla, Haotian Xu
References
Padilla, Yu, Wang and Rinaldo (2021) <doi:10.1214/21-EJS1809>.
See Also
thresholdBS for obtaining change points estimation, tuneBSuninonpar for a tuning version.
Examples
Y = t(as.matrix(c(rnorm(100, 0, 1), rnorm(100, 0, 10), rnorm(100, 0, 40))))
N = rep(1, 300)
M = 20
intervals = WBS.intervals(M = M, lower = 1, upper = ncol(Y))
temp = WBS.uni.nonpar(Y, 1, 300, intervals$Alpha, intervals$Beta, N, 5)
plot.ts(t(Y))
points(x = tail(temp$S[order(temp$Dval)], 4), y = Y[,tail(temp$S[order(temp$Dval)],4)], col = "red")
thresholdBS(temp, 2)
Robust wild binary segmentation for univariate mean change points detection.
Description
Perform a robust version of the wild binary segmentation method using Huber loss.
Usage
WBS.uni.rob(y, s, e, Alpha, Beta, K = 1.345, delta, level = 0)
Arguments
y |
A |
s |
A |
e |
A |
Alpha |
An |
Beta |
An |
K |
A |
delta |
A positive |
level |
Should be fixed as 0. |
Value
An object of class "BS", which is a list with the following structure:
S |
A vector of estimated change points (sorted in strictly increasing order). |
Dval |
A vector of values of CUSUM statistic based on KS distance. |
Level |
A vector representing the levels at which each change point is detected. |
Parent |
A matrix with the starting indices on the first row and the ending indices on the second row. |
Author(s)
Mengchu Li & Haotian Xu
References
Fearnhead & Rigaill (2019) <doi:10.1080/01621459.2017.1385466>.
See Also
thresholdBS for obtaining change points estimation.
Wild binary segmentation for univariate mean change points detection.
Description
Perform wild binary segmentation for univariate mean change points detection.
Usage
WBS.univar(y, s, e, Alpha, Beta, delta = 2, level = 0)
Arguments
y |
A |
s |
A |
e |
A |
Alpha |
A |
Beta |
A |
delta |
A positive |
level |
Should be fixed as 0. |
Value
An object of class "BS", which is a list with the following structure:
S |
A vector of estimated change point locations (sorted in strictly increasing order). |
Dval |
A vector of values of CUSUM statistic. |
Level |
A vector representing the levels at which each change point is detected. |
Parent |
A matrix with the starting indices on the first row and the ending indices on the second row. |
Author(s)
Haotian Xu
References
Wang, Yu and Rinaldo (2020) <doi:10.1214/20-EJS1710>.
See Also
thresholdBS for obtaining change points estimation, tuneBSunivar for a tuning version.
Examples
set.seed(0)
cpt_true = c(20, 50, 170)
y = rnorm(300) + c(rep(0,20),rep(2,30),rep(0,120),rep(2,130))
intervals = WBS.intervals(M = 300, lower = 1, upper = length(y))
temp = WBS.univar(y, 1, length(y), intervals$Alpha, intervals$Beta, delta = 5)
plot.ts(y)
points(x = tail(temp$S[order(temp$Dval)],4),
y = y[tail(temp$S[order(temp$Dval)],4)], col = "red")
WBS_result = thresholdBS(temp, tau = 4)
print(WBS_result$BS_tree, "value")
plot(WBS_result$BS_tree)
print(WBS_result$BS_tree_trimmed, "value")
plot(WBS_result$BS_tree_trimmed)
cpt_hat = sort(WBS_result$cpt_hat[,1]) # the threshold tau is specified to be 4
Hausdorff.dist(cpt_hat, cpt_true)
cpt_LR = local.refine.univar(cpt_hat, y)
Hausdorff.dist(cpt_LR, cpt_true)
Wild binary segmentation for covariance change points detection through Independent Projection.
Description
Perform wild binary segmentation for covariance change points detection through Independent Projection
Usage
WBSIP.cov(X, X_prime, s, e, Alpha, Beta, delta, level = 0)
Arguments
X |
A |
X_prime |
A |
s |
A |
e |
A |
Alpha |
A |
Beta |
A |
delta |
A positive |
level |
A parameter for tracking the level at which a change point is detected. Should be fixed as 0. |
Value
An object of class "BS", which is a list with the following structure:
S |
A vector of estimated change points (sorted in strictly increasing order) |
Dval |
A vector of values of CUSUM statistic based on KS distance |
Level |
A vector representing the levels at which each change point is detected |
Parent |
A matrix with the starting indices on the first row and the ending indices on the second row |
Author(s)
Haotian Xu
References
Wang, Yu and Rinaldo (2021) <doi:10.3150/20-BEJ1249>.
See Also
thresholdBS for obtain change points estimation.
Examples
p = 10
A1 = gen.cov.mat(p, 1, "equal")
A2 = gen.cov.mat(p, 3, "power")
A3 = A1
set.seed(1234)
X = cbind(t(MASS::mvrnorm(50, mu = rep(0, p), A1)),
t(MASS::mvrnorm(50, mu = rep(0, p), A2)),
t(MASS::mvrnorm(50, mu = rep(0, p), A3)))
X_prime = cbind(t(MASS::mvrnorm(50, mu = rep(0, p), A1)),
t(MASS::mvrnorm(50, mu = rep(0, p), A2)),
t(MASS::mvrnorm(50, mu = rep(0, p), A3)))
intervals = WBS.intervals(M = 120, lower = 1, upper = dim(X)[2])
temp = WBSIP.cov(X, X_prime, 1, dim(X)[2], intervals$Alpha, intervals$Beta, delta = 5)
tau = sqrt(p*log(ncol(X)))*1.5
sort(thresholdBS(temp, tau)$cpt_hat[,1])
Automatic adversarially robust univariate mean change point detection.
Description
Perform the adversarially robust change point detection method with automatic selection of the contamination proportion epsilon when treating the inliner distributions as Gaussian.
Usage
aARC(y, t_dat, guess_true = 0.05, h, block_num = 1)
Arguments
y |
A |
t_dat |
A |
guess_true |
A |
h |
An |
block_num |
An |
Value
An numeric vector of estimated change point locations.
Author(s)
Mengchu Li
References
Li and Yu (2021) <arXiv:2105.10417>.
Examples
#' ### simulate data with contamination
obs_num = 1000
D = 2
noise = 0.1 # proportion of contamination
mu0 = 0
mu1 = 1
sd =1
idmixture = rbinom(obs_num/D, 1, 1-noise)
dat = NULL
for (j in 1:D){
for (i in 1:(obs_num/(2*D))){
if (idmixture[i] == 1){
dat = c(dat,rnorm(1,mu0,sd))
}
else{
dat = c(dat,rnorm(1,mu1/(2*noise),0))
}
}
for (i in (obs_num/(2*D)+1):(obs_num/D)){
if (idmixture[i] == 1){
dat = c(dat,rnorm(1,mu1,sd))
}
else{
dat = c(dat,rnorm(1,mu1/(2*noise)-(1-noise)*mu1/noise,0))
}
}
}
plot(dat)
### perform aARC
aARC(dat, dat[1:200], h = 120)
Calibrate step for online change point detection for network data with missing values.
Description
Calibrate step for online change point detection for network data by controlling the false alarm rate at level alpha.
Usage
calibrate.online.network.missing(
train_miss_list,
train_eta_list,
threshold_len,
alpha_grid,
permu_num,
pi_lb_hat,
pi_ub_hat,
rho_hat,
rank_hat,
C_lambda = 2/3,
delta = 5
)
Arguments
train_miss_list |
A |
train_eta_list |
A |
threshold_len |
An |
alpha_grid |
A |
permu_num |
An |
pi_lb_hat |
A |
pi_ub_hat |
A |
rho_hat |
A |
rank_hat |
An |
C_lambda |
A |
delta |
An |
Value
A list with the following structure:
C_lambda |
The absolute constant |
rho_hat |
the (estimated) sparsity parameter |
rank_hat |
the (estimated) rank of underlying graphon matrix |
pi_lb_hat |
the (estimated) lower bound of the missing probability |
pi_ub_hat |
the (estimated) upper bound of the missing probability |
thresholds_array |
A |
Author(s)
Haotian Xu
References
Dubey, Xu and Yu (2021) <arxiv:2110.06450>
See Also
online.network.missing for detecting online change point.
Examples
p = 6 # number of nodes
rho = 0.5 # sparsity parameter
block_num = 3 # number of groups for SBM
train_obs_num = 150 # sample size for each segment
conn1_mat = rho * matrix(c(0.6,1,0.6,1,0.6,0.5,0.6,0.5,0.6), nrow = 3) # connectivity matrix
set.seed(1)
can_vec = sample(1:p, replace = FALSE) # randomly assign nodes into groups
sbm = simu.SBM(conn1_mat, can_vec, train_obs_num, symm = TRUE, self = TRUE)
train_mat = sbm$obs_mat
train_list = lapply(1:ncol(train_mat), function(t) lowertri2mat(train_mat[,t], p, diag = TRUE))
pi_mat = matrix(0.9, p, p)
train_eta_list = lapply(1:length(train_list), function(t) gen.missing(pi_mat, symm = TRUE))
train_miss_list = lapply(1:length(train_list), function(t) train_eta_list[[t]] * train_list[[t]])
pi_lb_hat = quantile(Reduce("+", train_eta_list)/train_obs_num, 0.05) # estimator of pi_lb
pi_ub_hat = quantile(Reduce("+", train_eta_list)/train_obs_num, 0.95) # estimator of pi_ub
C_lambda = 2/3
lambda = lambda.network.missing(1, length(train_miss_list), length(train_miss_list), 0.05,
rho = 0.509, pi_ub = pi_ub_hat, p, C_lambda)
graphon_miss_impute = softImpute.network.missing(train_miss_list, train_eta_list, lambda, 1)
graphon_miss_hat = graphon_miss_impute$u %*% diag(as.numeric(graphon_miss_impute$d)) %*%
t(graphon_miss_impute$v)
rho_hat = quantile(graphon_miss_hat, 0.95)
rank_hat = sum(graphon_miss_impute$d != 0)
alpha_grid = c(0.05)
permu_num = 10
threshold_len = 30
temp = calibrate.online.network.missing(train_miss_list, train_eta_list, threshold_len, alpha_grid,
permu_num, pi_lb_hat, pi_ub_hat, rho_hat, rank_hat, C_lambda, delta = 5)
Generate population covariance matrix with dimension p.
Description
Generate population covariance matrix with dimension p.
Usage
gen.cov.mat(p, sigma2, type)
Arguments
p |
A |
sigma2 |
A positive |
type |
Specify the type of a covariance matrix: Diagonal structure ("diagonal"); Equal correlation structure ("equal"); Power decay structure ("power"). |
Value
A numeric p-by-p matrix.
Author(s)
Haotian Xu
Examples
gen.cov.mat(p = 5, sigma2 = 1, type = "diagonal")
Function to generate a matrix with values 0 or 1, where 0 indicating the entry is missing
Description
Function to generate a matrix with values 0 or 1, where 0 indicating the entry is missing
Usage
gen.missing(pi_mat, symm = TRUE)
Arguments
pi_mat |
A |
symm |
A |
Value
A numeric p x p matrix.
Author(s)
Haotian Xu
Examples
p = 5
pi_mat = matrix(0.9, p, p)
eta_mat = gen.missing(pi_mat, symm = TRUE)
Generate univariate data from piecewise polynomials of degree at most r.
Description
Generate univariate data from piecewise polynomials (currently, only the linear, quadratic functions and cubic functions are considered).
Usage
gen.piece.poly(init_coef_vec, cpt_vec, kappa_mat, n, sigma)
Arguments
init_coef_vec |
A (r+1)-dim |
cpt_vec |
A K-dim |
kappa_mat |
A (r+1)xK |
n |
An |
sigma |
A |
Value
A vector of data generated from piecewise polynomials.
Author(s)
Haotian Xu
References
Yu and Chatterjee (2020) <arXiv:2007.09910>.
Examples
r = 2
init_coef_vec = c(-2, 2, 9)
cpt_true = c(100, 200)
n = 300
sigma = 1
kappa_mat = cbind(c(3, 9, -27), c(-3, 9, -27))
plot.ts(gen.piece.poly(init_coef_vec, cpt_true, kappa_mat, n, sigma), ylab = "y")
Mean function of piecewise polynomials.
Description
Compute mean function of piecewise polynomials (currently, only the linear, quadratic functions and cubic functions are considered).
Usage
gen.piece.poly.noiseless(init_coef_vec, cpt_vec, kappa_mat, n)
Arguments
init_coef_vec |
A |
cpt_vec |
An |
kappa_mat |
A |
n |
An |
Value
A vector of mean function of piecewise polynomials.
Author(s)
Haotian Xu
References
Yu and Chatterjee (2020) <arXiv:2007.09910>
Examples
r = 2
init_coef_vec = c(-2, 2, 9)
cpt_true = c(100, 200)
n = 300
kappa_mat = cbind(c(3, 9, -27), c(-3, 9, -27))
plot.ts(gen.piece.poly.noiseless(init_coef_vec, cpt_true, kappa_mat, n),
ylab = "Values of piecewise polynomials")
Element-wise adaptive Huber mean estimator.
Description
Computes the element-wise adaptive Huber mean estimator.
Usage
huber_mean(x, tau)
Arguments
x |
A |
tau |
A |
Value
A numeric scalar corresponding to the adaptive Huber mean estimator.
Author(s)
Haotian Xu
Examples
set.seed(123)
y = rnorm(100)
mean(y)
huber_mean(y, 1.345)
Function to compute the default thresholding parameter for leading singular value in the soft-impute algorithm.
Description
Function to compute the default thresholding parameter for leading singular value in the soft-impute algorithm.
Usage
lambda.network.missing(s, e, t, alpha, rho, pi_ub, p, C_lambda)
Arguments
s |
An |
e |
An |
t |
An |
alpha |
A |
rho |
A |
pi_ub |
A |
p |
An |
C_lambda |
A |
Details
The default thresholding parameter is given in Theorem 2 of the reference.
Value
The default thresholding parameter for leading singular value in the soft-impute algorithm
References
Dubey, Xu and Yu (2021) <arxiv:2110.06450>
Local refinement for VAR1 change points detection.
Description
Perform local refinement for VAR1 change points detection.
Usage
local.refine.CV.VAR1(cpt_init, DATA, zeta_set, delta_local)
Arguments
cpt_init |
A |
DATA |
A |
zeta_set |
A |
delta_local |
A strictly |
Value
A list with the following structure:
cpt_hat |
A vector of estimated change point locations (sorted in strictly increasing order) |
zeta |
A scalar of selected zeta by cross-validation |
Author(s)
Daren Wang & Haotian Xu
References
Wang, Yu, Rinaldo and Willett (2019) <arxiv:1909.06359>
Local refinement for DPDU regression change points localisation.
Description
Perform local refinement for regression change points localisation.
Usage
local.refine.DPDU.regression(cpt_init, beta_hat, y, X, w = 0.9)
Arguments
cpt_init |
An |
beta_hat |
A |
y |
A |
X |
A |
w |
A |
Value
A vector of locally refined change points estimation.
Author(s)
Haotian Xu
References
Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.
Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.
Examples
d0 = 5
p = 30
n = 200
cpt_true = 100
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)
lambda_set = c(0.01, 0.1, 1, 2)
zeta_set = c(10, 15, 20)
temp = CV.search.DPDU.regression(y = data$y, X = data$X, lambda_set, zeta_set)
temp$test_error # test error result
# find the indices of lambda_set and zeta_set which minimizes the test error
min_idx = as.vector(arrayInd(which.min(temp$test_error), dim(temp$test_error)))
lambda_set[min_idx[2]]
zeta_set[min_idx[1]]
cpt_init = unlist(temp$cpt_hat[min_idx[1], min_idx[2]])
beta_hat = matrix(unlist(temp$beta_hat[min_idx[1], min_idx[2]]), ncol = length(cpt_init)+1)
cpt_refined = local.refine.DPDU.regression(cpt_init, beta_hat, data$y, data$X, w = 0.9)
Local refinement for VAR1 change points detection.
Description
Perform local refinement for VAR1 change points detection.
Usage
local.refine.VAR1(cpt_init, DATA, zeta)
Arguments
cpt_init |
A |
DATA |
A |
zeta |
A |
Value
An integer vector of locally refined change points estimation.
Author(s)
Daren Wang & Haotian Xu
References
Wang, Yu, Rinaldo and Willett (2019) <arxiv:1909.06359>.
See Also
Local refinement for network change points detection.
Description
Perform local refinement for network change points detection.
Usage
local.refine.network(
cpt_init,
data_mat1,
data_mat2,
self = FALSE,
w = 0.5,
tau2,
tau3 = Inf
)
Arguments
cpt_init |
A |
data_mat1 |
A |
data_mat2 |
A independent copy of data_mat1. |
self |
A |
w |
A |
tau2 |
A positive |
tau3 |
A positive |
Value
A numeric vector of locally refined change point locations.
Author(s)
Daren Wang & Haotian Xu
References
Wang, Yu and Rinaldo (2018) <arxiv:1809.09602>.
Examples
p = 15 # number of nodes
rho = 0.5 # sparsity parameter
block_num = 3 # number of groups for SBM
n = 100 # sample size for each segment
# connectivity matrix for the first and the third segments
conn1_mat = rho * matrix(c(0.6,1,0.6,1,0.6,0.5,0.6,0.5,0.6), nrow = 3)
# connectivity matrix for the second segment
conn2_mat = rho * matrix(c(0.6,0.5,0.6,0.5,0.6,1,0.6,1,0.6), nrow = 3)
set.seed(1)
can_vec = sample(1:p, replace = FALSE) # randomly assign nodes into groups
sbm1 = simu.SBM(conn1_mat, can_vec, n, symm = TRUE, self = TRUE)
sbm2 = simu.SBM(conn2_mat, can_vec, n, symm = TRUE, self = TRUE)
data_mat = cbind(sbm1$obs_mat, sbm2$obs_mat)
data_mat1 = data_mat[,seq(1,ncol(data_mat),2)]
data_mat2 = data_mat[,seq(2,ncol(data_mat),2)]
M = 10
intervals = WBS.intervals(M = M, lower = 1, upper = ncol(data_mat1))
temp = WBS.network(data_mat1, data_mat2, 1, ncol(data_mat1), intervals$Alpha,
intervals$Beta, delta = 5)
rho_hat = quantile(rowMeans(data_mat), 0.95)
tau = p*rho_hat*(log(n))^2/20 # default threshold given in the paper
cpt_init = unlist(thresholdBS(temp, tau)$cpt_hat[,1])
cpt_refined = local.refine.network(cpt_init, data_mat1, data_mat2, self = TRUE,
tau2 = p*rho_hat/3, tau3 = Inf)
cpt_WBS = 2*cpt_init
cpt_refined = 2*cpt_refined
Local refinement for univariate polynomials change point detection.
Description
Perform local refinement for univariate polynomials change point detection.
Usage
local.refine.poly(cpt_init, y, r, delta_lr)
Arguments
cpt_init |
An |
y |
A |
r |
An |
delta_lr |
A positive |
Value
An integer vector of locally refined change point estimation.
Author(s)
Haotian Xu
References
Yu and Chatterjee (2020) <arXiv:2007.09910>
Examples
set.seed(0)
cpt_true = c(20, 50, 170)
y = rnorm(300) + c(rep(0,20),rep(2,30),rep(0,120),rep(2,130))
plot.ts(y)
gamma_set = 3:9
DP_result = CV.search.DP.poly(y, r = 2, gamma_set, delta = 5)
min_idx = which.min(DP_result$test_error)
cpt_init = unlist(DP_result$cpt_hat[min_idx])
local.refine.poly(cpt_init, y, r = 2, delta_lr = 5)
Local refinement for regression change points localisation.
Description
Perform local refinement for regression change points localisation.
Usage
local.refine.regression(cpt_init, y, X, zeta)
Arguments
cpt_init |
An |
y |
A |
X |
A |
zeta |
A |
Value
A vector of locally refined change points estimation.
Author(s)
Daren Wang & Haotian Xu
References
Rinaldo, A., Wang, D., Wen, Q., Willett, R., & Yu, Y. (2021, March). Localizing changes in high-dimensional regression models. In International Conference on Artificial Intelligence and Statistics (pp. 2089-2097). PMLR.
Rinaldo, Wang, Wen, Willett and Yu (2020) <arxiv:2010.10410>
Examples
d0 = 10
p = 20
n = 100
cpt_true = c(30, 70)
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)
gamma_set = c(0.01, 0.1, 1)
lambda_set = c(0.01, 0.1, 1, 3)
temp = CV.search.DP.regression(y = data$y, X = data$X, gamma_set, lambda_set, delta = 2)
temp$test_error # test error result
# find the indices of gamma_set and lambda_set which minimizes the test error
min_idx = as.vector(arrayInd(which.min(temp$test_error), dim(temp$test_error)))
gamma_set[min_idx[1]]
lambda_set[min_idx[2]]
cpt_init = unlist(temp$cpt_hat[min_idx[1], min_idx[2]])
local.refine.regression(cpt_init, data$y, X = data$X, zeta = 0.5)
Local refinement of an initial estimator for univariate mean change points detection.
Description
Perform local refinement for univariate mean change points detection.
Usage
local.refine.univar(cpt_init, y)
Arguments
cpt_init |
An |
y |
A |
Value
An integer vector of locally refined change point estimation.
Author(s)
Haotian Xu
References
Wang, Yu and Rinaldo (2020) <doi:10.1214/20-EJS1710>.
Examples
set.seed(0)
cpt_true = c(20, 50, 170)
y = rnorm(300) + c(rep(0,20),rep(2,30),rep(0,120),rep(2,130))
gamma_set = 1:5
DP_result = CV.search.DP.univar(y, gamma_set, delta = 5)
min_idx = which.min(DP_result$test_error)
cpt_hat = unlist(DP_result$cpt_hat[min_idx])
Hausdorff.dist(cpt_hat, cpt_true)
cpt_LR = local.refine.univar(cpt_hat, y)
Hausdorff.dist(cpt_LR, cpt_true)
Transform a vector containing lower diagonal entries into a symmetric matrix of dimension p.
Description
Transform a vector containing lower diagonal entries into a symmetric matrix of dimension p.
Usage
lowertri2mat(lowertri_vec, p, diag = FALSE)
Arguments
lowertri_vec |
A |
p |
A |
diag |
A |
Value
A numeric p x p symmetric matrix.
Author(s)
Haotian Xu
Examples
A = matrix(1:16, 4, 4)
B = lowertri2mat(A[lower.tri(A)], 4, diag = FALSE)
C = lowertri2mat(A[lower.tri(A, diag = TRUE)], 4, diag = TRUE)
Online change point detection for network data.
Description
Perform online change point detection for network data by controlling the false alarm rate at level alpha or controlling the average run length gamma. The default choice of the tuning parameters tau1, tau2 and tau3 are used (see Section 4.1 of the reference).
Usage
online.network(
data_mat1,
data_mat2,
self = TRUE,
b_vec = NULL,
train_mat = NULL,
alpha = NULL,
gamma = NULL,
permu_num = NULL
)
Arguments
data_mat1 |
A |
data_mat2 |
A |
self |
A |
b_vec |
A |
train_mat |
A |
alpha |
A |
gamma |
An |
permu_num |
An |
Value
A list with the following structure:
cpt |
Estimated change point |
score |
A |
b_vec |
A |
Author(s)
Oscar Hernan Madrid Padilla & Haotian Xu
References
Yu, Padilla, Wang and Rinaldo (2021) <arxiv:2101.05477>
Examples
set.seed(123)
p = 15 # number of nodes
rho = 0.5 # sparsity parameter
block_num = 3 # number of groups for SBM
n = 100 # sample size for each segment
# connectivity matrix for the first and the third segments
conn1_mat = rho * matrix(c(0.6,1,0.6,1,0.6,0.5,0.6,0.5,0.6), nrow = 3)
# connectivity matrix for the second segment
conn2_mat = rho * matrix(c(0.6,0.5,0.6,0.5,0.6,1,0.6,1,0.6), nrow = 3)
set.seed(1)
can_vec = sample(1:p, replace = FALSE) # randomly assign nodes into groups
sbm1 = simu.SBM(conn1_mat, can_vec, n, symm = TRUE, self = TRUE)
sbm2 = simu.SBM(conn2_mat, can_vec, n, symm = TRUE, self = TRUE)
data_mat = cbind(sbm1$obs_mat, sbm2$obs_mat)
data_mat1 = data_mat[,seq(1,ncol(data_mat),2)]
data_mat2 = data_mat[,seq(2,ncol(data_mat),2)]
train_mat = simu.SBM(conn1_mat, can_vec, n = 150, symm = TRUE, self = TRUE)$obs_mat
temp = online.network(data_mat1, data_mat2, self = TRUE, b_vec = NULL, train_mat, alpha = 0.05,
gamma = NULL, permu_num = 20)
cpt_hat = 2 * temp$cpt
Online change point detection for network data with missing values.
Description
Perform online change point detection for network with missing values by controlling the false alarm rate at level alpha.
Usage
online.network.missing(
data_incomplete_list,
eta_list,
alpha_grid,
thresholds_array,
rho_hat,
pi_ub_hat,
C_lambda = 2/3,
delta = 5
)
Arguments
data_incomplete_list |
A |
eta_list |
A |
alpha_grid |
A |
thresholds_array |
A |
rho_hat |
A |
pi_ub_hat |
A |
C_lambda |
A |
delta |
An |
Value
Online change point estimator.
Author(s)
Haotian Xu
References
Dubey, Xu and Yu (2021) <arxiv:2110.06450>
See Also
calibrate.online.network.missing for calibrating thresholds.
Online change point detection with controlled false alarm rate or average run length.
Description
Perform online change point detection with controlled false alarm rate or average run length.
Usage
online.univar(
y_vec,
b_vec = NULL,
train_vec = NULL,
alpha = NULL,
gamma = NULL,
permu_num = NULL
)
Arguments
y_vec |
A |
b_vec |
A |
train_vec |
A |
alpha |
A |
gamma |
An |
permu_num |
An |
Value
A list with the following structure:
cpt_hat |
An |
b_vec |
A |
Author(s)
Haotian Xu
References
Yu, Padilla, Wang and Rinaldo (2020) <arxiv:2006.03283>
Examples
y_vec = rnorm(150) + c(rep(0, 100), rep(1, 50))
train_vec = rnorm(100)
# control the false alarm rate
temp1 = online.univar(y_vec = y_vec, train_vec = train_vec, alpha = 0.05, permu_num = 20)
temp1$cpt_hat
temp1$b_vec # calibrated threshold
Online change point detection with potentially multiple change points.
Description
Perform Online change point detection with potentially multiple change points.
Usage
online.univar.multi(
y_vec,
b_vec = NULL,
train_vec = NULL,
alpha = NULL,
gamma = NULL,
permu_num = NULL
)
Arguments
y_vec |
A |
b_vec |
A |
train_vec |
A |
alpha |
A |
gamma |
An |
permu_num |
An |
Details
#' @title Online change point detection with controlled average run length.
#' @description Perform online change point detection via CUSUM (single change point, type 2).
#' @param y_vec A numeric vector of observations.
#' @param gamma A integer scalar of interval length (>= 2).
#' @param tau_gamma A numeric scalar of threshold.
#' @param ... Additional arguments.
#' @return An integer scalar of estimated change points location.
#' @export
#' @author Haotian Xu
#' @examples
#' TO DO
online.univar.one2 = function(y_vec, gamma, tau_gamma, ...)
t = 1
FLAG = 0
while(FLAG == 0 & t <= length(y_vec))
t = t + 1
e = max(t-gamma, 0)
cusum_vec = sapply((e+1):(t-1), function(s) sqrt((t-s)*(s-e)/(t-e)) * abs(mean(y_vec[(e+1):s]) - mean(y_vec[(s+1):t])))
FLAG = 1 - prod(cusum_vec <= tau_gamma)
return(t)
#' @title Online change point detection via CUSUM (single change point, type 3).
#' @description Perform online change point detection via CUSUM (single change point, type 3).
#' @param y_vec A numeric vector of observations.
#' @param tau_vec A numeric vector of thresholds at time t>= 1.
#' @param ... Additional arguments.
#' @return An integer scalar of estimated change point location.
#' @export
#' @author Haotian Xu
#' @examples
#' TO DO
online.univar.one3 = function(y_vec, tau_vec, ...)
if(length(y_vec) != length(tau_vec))
stop("y_vec and tau_vec should have the same length.")
t = 1
FLAG = 0
while(FLAG == 0 & t <= length(y_vec))
t = t + 1
J = floor(log2(t))
j = 0
while(j < J & FLAG == 0)
j = j + 1
s_j = t - 2^(j-1)
cusum = sqrt((t-s_j)*s_j/t) * abs(mean(y_vec[1:s_j]) - mean(y_vec[(s_j+1):t]))
FLAG = (cusum > tau_vec[t])
return(t)
Value
An integer vector of estimated change points.
Author(s)
Haotian Xu
References
Yu, Padilla, Wang and Rinaldo (2020) <arxiv:2006.03283>
Examples
y_vec = rnorm(200) + c(rep(0, 50), rep(1, 100), rep(0, 50))
train_vec = rnorm(150)
# control the false alarm rate
temp1 = online.univar.multi(y_vec = y_vec, train_vec = train_vec, alpha = 0.05, permu_num = 20)
temp1
Simulate a dot product graph (without change point).
Description
Simulate a dot product graph (without change point). The generated data is a matrix with each column corresponding to the vectorized adjacency (sub)matrix at a time point. For example, if the network matrix is required to be symmetric and without self-loop, only the strictly lower diagonal entries are considered.
Usage
simu.RDPG(x_mat, n, symm = TRUE, self = FALSE)
Arguments
x_mat |
A |
n |
A |
symm |
A |
self |
A |
Value
A list with the following structure:
obs_mat |
A matrix, with each column be the vectorized adjacency (sub)matrix. For example, if "symm = TRUE" and "self = FALSE", only the strictly lower triangular matrix is considered. |
graphon_mat |
Underlying graphon matrix. |
Author(s)
Haotian Xu
Examples
p = 20 # number of nodes
n = 50 # sample size for each segment
lat_dim_num = 5 # number of latent dimensions
set.seed(1)
x_mat = matrix(runif(p*lat_dim_num), nrow = p, ncol = lat_dim_num)
x_tilde_mat = matrix(runif(p*lat_dim_num), nrow = p, ncol = lat_dim_num)
y_mat = rbind(x_tilde_mat[1:floor(p/4),], x_mat[(floor(p/4)+1):p,])
rdpg1 = simu.RDPG(x_mat, n, symm = TRUE, self = FALSE)
rdpg2 = simu.RDPG(y_mat, n, symm = TRUE, self = FALSE)
data1_mat = rdpg1$obs_mat
data2_mat = rdpg2$obs_mat
data_mat = cbind(data1_mat, data2_mat)
Simulate a Stochastic Block Model (without change point).
Description
Simulate a Stochastic Block Model (without change point). The generated data is a matrix with each column corresponding to the vectorized adjacency (sub)matrix at a time point. For example, if the network matrix is required to be symmetric and without self-loop, only the strictly lower diagonal entries are considered.
Usage
simu.SBM(connec_mat, can_vec, n, symm = FALSE, self = TRUE)
Arguments
connec_mat |
A |
can_vec |
A |
n |
A |
symm |
A |
self |
A |
Value
A list with the following structure:
obs_mat |
A matrix, with each column be the vectorized adjacency (sub)matrix. For example, if "symm = TRUE" and "self = FALSE", only the strictly lower triangular matrix is considered. |
graphon_mat |
Underlying graphon matrix. |
Author(s)
Daren Wang & Haotian Xu
References
Wang, Yu and Rinaldo (2018) <arxiv:1809.09602>.
Examples
p = 15 # number of nodes
rho = 0.5 # sparsity parameter
block_num = 3 # number of groups for SBM
n = 100 # sample size for each segment
# connectivity matrix for the first and the third segments
conn1_mat = rho * matrix(c(0.6,1,0.6,1,0.6,0.5,0.6,0.5,0.6), nrow = 3)
# connectivity matrix for the second segment
conn2_mat = rho * matrix(c(0.6,0.5,0.6,0.5,0.6,1,0.6,1,0.6), nrow = 3)
set.seed(1)
can_vec = sample(1:p, replace = FALSE) # randomly assign nodes into groups
sbm1 = simu.SBM(conn1_mat, can_vec, n, symm = TRUE, self = TRUE)
sbm2 = simu.SBM(conn2_mat, can_vec, n, symm = TRUE, self = TRUE)
data_mat = cbind(sbm1$obs_mat, sbm2$obs_mat)
Simulate a (stable) SEPP model (without change point).
Description
Simulate a (stable) SEPP model (without change point).
Usage
simu.SEPP(intercept, n, A, threshold, vzero = NULL)
Arguments
intercept |
A |
n |
An |
A |
A |
threshold |
A |
vzero |
A |
Value
A p-by-n matrix.
Author(s)
Daren Wang & Haotian Xu
References
Wang, Yu, & Willett (2020). Detecting Abrupt Changes in High-Dimensional Self-Exciting Poisson Processes. <arXiv:2006.03572>.
Examples
p = 10 # dimension
n = 50
s = 5 # sparsity
factor = 0.12 # large factor gives exact recovery
threshold = 4 # thresholding makes the process stable
intercept = 1/2 # intercept of the model. Assume to be known as in the existing literature
A1 = A2 = A3 = matrix(0, p, p)
diag(A1[,-1]) = 1
diag(A1) = 1
diag(A1[-1,]) = -1
A1 = A1*factor
A1[(s+1):p, (s+1):p] = 0
diag(A2[,-1]) = 1
diag(A2) = -1
diag(A2[-1,]) = 1
A2 = A2*factor
A2[(s+1):p, (s+1):p] = 0
diag(A3[,-1]) = 1
diag(A3) = 1
diag(A3[-1,]) = -1
A3 = A3*factor
A3[(s+1):p, (s+1):p] = 0
data1 = simu.SEPP(intercept, n, A1, threshold, vzero = NULL)
data2 = simu.SEPP(intercept, n, A2, threshold, vzero = data1[,n])
data3 = simu.SEPP(intercept, n, A3, threshold, vzero = data2[,n])
data = cbind(data1, data2, data3)
dim(data)
Simulate from a VAR1 model (without change point).
Description
Simulate data of size n and dimension p from a VAR1 model (without change point) with Gaussian i.i.d. error terms.
Usage
simu.VAR1(sigma, p, n, A, vzero = NULL)
Arguments
sigma |
A |
p |
An |
n |
An |
A |
A |
vzero |
A |
Value
A p-by-n matrix.
Author(s)
Daren Wang
References
Wang, Yu, Rinaldo and Willett (2019) <arxiv:1909.06359>
Examples
p = 10
sigma = 1
n = 100
A = matrix(rnorm(p*p), nrow = p)*0.1 # transition matrix
simu.VAR1(sigma, p, n, A)
Simulate a sparse regression model with change points in coefficients.
Description
Simulate a sparse regression model with change points in coefficients under temporal dependence.
Usage
simu.change.regression(
d0,
cpt_true,
p,
n,
sigma,
kappa,
cov_type = "I",
mod_X = "IID",
mod_e = "IID"
)
Arguments
d0 |
A |
cpt_true |
An |
p |
An |
n |
An |
sigma |
A |
kappa |
A |
cov_type |
A |
mod_X |
A |
mod_e |
A |
Value
A list with the following structure:
cpt_true |
A vector of true changepoints (sorted in strictly increasing order). |
X |
An n-by-p design matrix. |
y |
An n-dim vector of response variable. |
betafullmat |
A p-by-n matrix of coefficients. |
Author(s)
Daren Wang, Zifeng Zhao & Haotian Xu
References
Rinaldo, Wang, Wen, Willett and Yu (2020) <arxiv:2010.10410>; Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.
Examples
d0 = 10
p = 30
n = 100
cpt_true = c(10, 30, 40, 70, 90)
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)
Estimate graphon matrix by soft-impute for independent adjacency matrices with missing values.
Description
Estimate graphon matrix by soft-impute for independent adjacency matrices with missing values.
Usage
softImpute.network.missing(
data_incomplete_list,
eta_list,
lambda,
a,
it_max = 10000
)
Arguments
data_incomplete_list |
A |
eta_list |
A |
lambda |
A |
a |
A |
it_max |
An |
Value
Estimated graphon matrix
Author(s)
Haotian Xu
References
Dubey, Xu and Yu (2021) <arxiv:2110.06450>
Thresholding a BS object with threshold value tau.
Description
Given a BS object, perform thresholding to find the change point locations.
Usage
thresholdBS(BS_object, tau)
Arguments
BS_object |
A |
tau |
A positive |
Value
A list with the following structure:
BS_tree_trimmed |
BS_tree with change points which do not satisfy the thresholding criteria removed |
cpt_hat |
A matrix contains change point locations, values of corresponding statistic, and levels at which each change point is detected |
Author(s)
Haotian Xu
See Also
BS.univar, BS.uni.nonpar, BS.cov, WBS.univar, WBS.uni.nonpar, WBS.multi.nonpar, WBS.network, WBSIP.cov
Examples
y = c(rnorm(100, 0, 1), rnorm(100, 10, 10), rnorm(100, 40, 10))
temp = BS.univar(y, 1, 300, 5)
plot.ts(y)
points(x = tail(temp$S[order(temp$Dval)],4), y = y[tail(temp$S[order(temp$Dval)],4)], col = "red")
thresholdBS(temp, 20)
Interval trimming based on initial change point localisation.
Description
Performing the interval trimming for local refinement.
Usage
trim_interval(n, cpt_init, w = 0.9)
Arguments
n |
An |
cpt_init |
An |
w |
A |
Value
A matrix with each row be a trimmed interval.
Author(s)
Haotian Xu
References
Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.
A function to compute change points based on the multivariate nonparametic method with tuning parameter selected by FDR control.
Description
A function to compute change points based on the multivariate nonparametic method with tuning parameter selected by FDR control.
Usage
tuneBSmultinonpar(BS_object, Y)
Arguments
BS_object |
A "BS" object produced by |
Y |
A |
Value
A vector of estimated change points.
Author(s)
Oscar Hernan Madrid Padilla & Haotian Xu
References
Padilla, Yu, Wang and Rinaldo (2019) <arxiv:1910.13289>.
See Also
Examples
n = 70
v = c(floor(n/3), 2*floor(n/3)) # location of change points
p = 4
Y = matrix(0, p, n) # matrix for data
mu0 = rep(0, p) # mean of the data
mu1 = rep(0, p)
mu1[1:floor(p/2)] = 2
Sigma0 = diag(p) #Covariance matrices of the data
Sigma1 = diag(p)*2
# Generate data
for(t in 1:n){
if(t < v[1] || t > v[2]){
Y[,t] = MASS::mvrnorm(n = 1, mu0, Sigma0)
}
if(t >= v[1] && t < v[2]){
Y[,t] = MASS::mvrnorm(n = 1, mu1, Sigma1)
}
}## close for generate data
M = 8
intervals = WBS.intervals(M = M, lower = 1, upper = ncol(Y)) #Random intervals
K_max = 30
h = 5*(K_max*log(n)/n)^{1/p} # bandwith
temp = WBS.multi.nonpar(Y, Y, 1, ncol(Y), intervals$Alpha, intervals$Beta, h, delta = 10)
S = tuneBSmultinonpar(temp, Y)
Change points detection for dependent dynamic random dot product graph models.
Description
Perform Change points detection for dependent dynamic random dot product graph models. The tuning parameter tau for WBS is automatically selected based on the BIC-type scores defined in Equation (2.4) in Zou et al. (2014).
Usage
tuneBSnonparRDPG(BS_object, data_mat, lowerdiag = FALSE, d)
Arguments
BS_object |
A "BS" object produced by |
data_mat |
A |
lowerdiag |
A |
d |
A |
Value
A numeric vector of estimated change points.
Author(s)
Oscar Hernan Madrid Padilla & Haotian Xu
References
Padilla, Yu and Priebe (2019) <arxiv:1911.07494>.
See Also
Examples
### generate data
p = 20 # number of nodes
n = 50 # sample size for each segment
lat_dim_num = 5 # number of latent dimensions
set.seed(1)
x_mat = matrix(runif(p*lat_dim_num), nrow = p, ncol = lat_dim_num)
x_tilde_mat = matrix(runif(p*lat_dim_num), nrow = p, ncol = lat_dim_num)
y_mat = rbind(x_tilde_mat[1:floor(p/4),], x_mat[(floor(p/4)+1):p,])
rdpg1 = simu.RDPG(x_mat, n, symm = TRUE, self = FALSE)
rdpg2 = simu.RDPG(y_mat, n, symm = TRUE, self = FALSE)
data1_mat = rdpg1$obs_mat
data2_mat = rdpg2$obs_mat
data_mat = cbind(data1_mat, data2_mat)
### detect change points
M = 20 # number of random intervals for WBS
d = 10 # parameter for scaled PCA algorithm
delta = 5
intervals = WBS.intervals(M = M, lower = 1, upper = ncol(data_mat))
WBS_result = WBS.nonpar.RDPG(data_mat, lowerdiag = TRUE, d,
Alpha = intervals$Alpha, Beta = intervals$Beta, delta)
cpt_hat = tuneBSnonparRDPG(WBS_result, data_mat, lowerdiag = TRUE, d)
Wild binary segmentation for univariate nonparametric change points detection with tuning parameter selection.
Description
Perform wild binary segmentation with tuning parameter selection based on sample splitting.
Usage
tuneBSuninonpar(BS_object, Y, N)
Arguments
BS_object |
A "BS" object produced by |
Y |
A |
N |
A |
Value
A vector of estimated change points (sorted in strictly increasing order).
Author(s)
Oscar Hernan Madrid Padilla & Haotian Xu
References
Padilla, Yu, Wang and Rinaldo (2021) <doi:10.1214/21-EJS1809>.
See Also
BS.uni.nonpar and WBS.uni.nonpar.
Examples
Y = t(as.matrix(c(rnorm(100, 0, 1), rnorm(100, 0, 10), rnorm(50, 0, 40))))
W = Y # W is a copy of the matrix Y, it can be Y itself.
N = rep(1, 250)
M = 5
set.seed(123)
intervals = WBS.intervals(M = M, lower = 1, upper = ncol(Y))
BS_object = WBS.uni.nonpar(W, 1, ncol(Y), intervals$Alpha, intervals$Beta, N, delta = 5)
cpt_hat = tuneBSuninonpar(BS_object, Y, N)
Univariate mean change points detection based on standard or wild binary segmentation with tuning parameter selected by sSIC.
Description
Perform univariate mean change points detection based on standard or wild binary segmentation. The threshold parameter tau for WBS is automatically selected based on the sSIC score defined in Equation (4) in Fryzlewicz (2014).
Usage
tuneBSunivar(BS_object, y)
Arguments
BS_object |
A "BS" object produced by |
y |
A |
Value
A list with the following structure:
cpt |
A vector of estimated change point locations (sorted in strictly increasing order). |
tau |
A scalar of selected threshold tau based on sSIC. |
Author(s)
Daren Wang & Haotian Xu
References
Wang, Yu and Rinaldo (2020) <doi:10.1214/20-EJS1710>; Fryzlewicz (2014), Wild binary segmentation for multiple change-point detection, <DOI: 10.1214/14-AOS1245>.
See Also
BS.univar and WBS.univar.
Examples
set.seed(0)
cpt_true = c(20, 50, 170)
y = rnorm(300) + c(rep(0,20),rep(2,30),rep(0,120),rep(2,130))
## change points detection by WBS
intervals = WBS.intervals(M = 100, lower = 1, upper = length(y))
temp2 = WBS.univar(y, 1, length(y), intervals$Alpha, intervals$Beta, delta = 5)
WBS_result = tuneBSunivar(temp2, y)
cpt_WBS = WBS_result$cpt
Hausdorff.dist(cpt_WBS, cpt_true)