CV.search.DPDU.regression {changepoints}

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 numeric vector of response variable.

X

A numeric matrix of covariates with vertical axis being time.

lambda_set

A numeric vector of candidate tuning parameters for lasso penalty.

zeta_set

An integer vector of tuning parameter associated with l_0 penalty (minimum interval size).

eps

A numeric scalar of precision level for convergence of lasso.

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)