DP.SEPP {changepoints}

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 numeric matrix of observations with horizontal axis being time.

gamma

A numeric scalar of tuning parameter associated with the l_0 penalty.

lambda

A numeric scalar of tuning parameter for lasso penalty.

delta

An integer scalar of minimum spacing for dynamic programming.

delta2

An integer scalar representing the maximal of the change point spacing (for reducing computation cost).

intercept

A numeric scalar representing the intercept of the model, which is assumed to be known.

threshold

A numeric scalar representing the upper bound for each coordinate of X_t (for stability).

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