online.univar.multi {changepoints}

Online change point detection with potentially multiple change points.

Description

Perform Online change point detection with potentially multiple change points.

Usage

online.univar.multi(
  y_vec,
  b_vec = NULL,
  train_vec = NULL,
  alpha = NULL,
  gamma = NULL,
  permu_num = NULL
)

Arguments

y_vec

A numeric vector of observations.

b_vec

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

train_vec

A numeric vector 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 of desired false alarm rate.

gamma

An integer scalar of desired average run length.

permu_num

An integer scalar of number of random permutation for calibration.

Details

#' @title Online change point detection with controlled average run length. #' @description Perform online change point detection via CUSUM (single change point, type 2). #' @param y_vec A numeric vector of observations. #' @param gamma A integer scalar of interval length (>= 2). #' @param tau_gamma A numeric scalar of threshold. #' @param ... Additional arguments. #' @return An integer scalar of estimated change points location. #' @export #' @author Haotian Xu #' @examples #' TO DO online.univar.one2 = function(y_vec, gamma, tau_gamma, ...) t = 1 FLAG = 0 while(FLAG == 0 & t <= length(y_vec)) t = t + 1 e = max(t-gamma, 0) cusum_vec = sapply((e+1):(t-1), function(s) sqrt((t-s)*(s-e)/(t-e)) * abs(mean(y_vec[(e+1):s]) - mean(y_vec[(s+1):t]))) FLAG = 1 - prod(cusum_vec <= tau_gamma) return(t)

#' @title Online change point detection via CUSUM (single change point, type 3). #' @description Perform online change point detection via CUSUM (single change point, type 3). #' @param y_vec A numeric vector of observations. #' @param tau_vec A numeric vector of thresholds at time t>= 1. #' @param ... Additional arguments. #' @return An integer scalar of estimated change point location. #' @export #' @author Haotian Xu #' @examples #' TO DO online.univar.one3 = function(y_vec, tau_vec, ...) if(length(y_vec) != length(tau_vec)) stop("y_vec and tau_vec should have the same length.") t = 1 FLAG = 0 while(FLAG == 0 & t <= length(y_vec)) t = t + 1 J = floor(log2(t)) j = 0 while(j < J & FLAG == 0) j = j + 1 s_j = t - 2^(j-1) cusum = sqrt((t-s_j)*s_j/t) * abs(mean(y_vec[1:s_j]) - mean(y_vec[(s_j+1):t])) FLAG = (cusum > tau_vec[t]) return(t)

Value

An integer vector of estimated change points.

Author(s)

Haotian Xu

References

Yu, Padilla, Wang and Rinaldo (2020) <arxiv:2006.03283>

Examples

y_vec = rnorm(200) + c(rep(0, 50), rep(1, 100), rep(0, 50))
train_vec = rnorm(150)
# control the false alarm rate
temp1 = online.univar.multi(y_vec = y_vec, train_vec = train_vec, alpha = 0.05, permu_num = 20)
temp1