CV.search.DP.VAR1 {changepoints}

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 numeric matrix of observations with horizontal axis being time, and vertical axis being dimensions.

gamma_set

A numeric vector of candidate tuning parameters associated with the l_0 penalty.

lambda_set

A numeric vector of candidate tuning parameters for lasso penalty.

delta

A strictly integer scalar of minimum spacing.

eps

A numeric scalar of precision level for convergence of lasso.

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)