online.network {changepoints}

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 numeric matrix of observations with with horizontal axis being time, and with each column be the vectorized adjacency matrix.

data_mat2

A numeric matrix of observations with with horizontal axis being time, and with each column be the vectorized adjacency matrix (data_mat1 and data_mat2 are independent and have the same dimensions ).

self

A logic scalar indicating if adjacency matrices are required to have self-loop.

b_vec

A numeric vector of thresholds b_t with t >= 2.

train_mat

A numeric matrix of training data from a pre-change distribution(no change point), which is only needed to when b_vec is NULL in order to calibrate b_t.

alpha

A numeric scalar in (0,1) representing the level.

gamma

An integer scalar of desired average run length.

permu_num

An integer scalar of number of random permutation for calibration.

Value

A list with the following structure:

cpt

Estimated change point

score

A numeric vector of computed cumsum statistics

b_vec

A numeric vector of thresholds b_t with t >= 2

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