calibrate.online.network.missing: Calibrate step for online change point detection for network...
In changepoints: A Collection of Change-Point Detection Methods

calibrate.online.network.missing

R Documentation

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 `list` of adjacency matrices (with entries being 0 or 1) with missing values being coercing to 0.
`train_eta_list`	A `list` of matrices associated with data_incomplete_list, each matrix indicates the missing entries in corresponding adjacency matrix.
`threshold_len`	An `integer` scalar of the length of tuned thresholds.
`alpha_grid`	A `numeric` vector in (0,1) representing the desired false alarm rate.
`permu_num`	An `integer` scalar of number of random permutation for calibration.
`pi_lb_hat`	A `numeric` scalar of the lower bound of the missing probability.
`pi_ub_hat`	A `numeric` scalar of the upper bound of the missing probability.
`rho_hat`	A `numeric` scalar of the sparsity parameter.
`rank_hat`	An `integer` scalar of the rank of the underlying graphon matrix.
`C_lambda`	A `numeric` scalar of an absolute constant, which is set to be 2/3 by default.
`delta`	An `integer` scalar of minimum spacing.

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 `numeric` array of calibrated threshold

Author(s)

Haotian Xu

References

Dubey, Xu and Yu (2021) <arxiv:2110.06450>

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)

changepoints documentation built on Sept. 4, 2022, 5:06 p.m.