gStream {gStream}

Graph-Based Sequential Change-Point Detection

Description

This package can be used to estimate change-points in a sequence of sequentially generated observations, where the observation can be a vector or a data object, e.g., a network. A distance matrix is required.

The function gstream will report the graph-based test statistics and the thresholds used in the stopping rules for a given average run length.

Author(s)

Hao Chen and Lynna Chu

Maintainer: Hao Chen ([e-mail]) and Lynna Chu ([e-mail])

References

Chen, H. (2019) Sequential Change-point Detection Based on Nearest Neighbors. The Annals of Statistics, 47(3):1381-1407.

Chu, L. and Chen, H. (2018) Sequential Change-point Detection for High-dimensional and non-Euclidean Data. arXiv:1810.05973.

See Also

gstream

Examples

  # This example contains two distance matrices constructed using L2 distance (distM1 and distM2).
  #In this example, the data is treated as if it were being observed sequentally
  # in order to illustrate how the package works.

  # Example:
  # distM1 is a distance matrix constructed from a dataset with n=40 observation.
  # The first 20 observations are treated as historical observations.
  # It has been determined that there are no change-points among the
  # first 20 observations (see package gSeg for offline change-point detection).
  # There is change in mean when tau = 20 (This means a change happens 20 observations
  # after we start the tests. We start the test at N0+1 = 21.)
  # The following code shows the data generating scheme to create distM1:
  # (uncomment to run)
  # N0 = 20 # the first 20 observations are historical observations
  # N1 = N0 + 10
  # N2 = N1 + 10
  # d = 10
  # vmu = 10
  # set.seed(15)
  # y1 = matrix(0,N1,d)
  # y2 = matrix(0,N2-N1,d)
  # for (i in 1:N1) y1[i,] = rnorm(d)
  # for (i in 1:(N2-N1)) y2[i,] = rnorm(d, vmu)
  # y = rbind(y1,y2)
  # distM1 = as.matrix(dist(y))
  # diag(distM1) = max(distM1)+100

  # Uncomment the following to run
  # N0 = 20
  # L = 20 # the k-nn graph is constructed on only the L most recent observations.
  # k = 1

  # r1= gstream(distM1, L, N0, k, statistics="all", n0=0.3*L, n1=L-0.3*L,
  # ARL=200,alpha=0.05, skew.corr=TRUE,asymp=FALSE)

  # output results based on all four statistics; the scan statistics can be found in r1$scanZ
  # r1$tauhat # reports the locations where a change-point is detected
  # r1$b # reports the analytical approximations of the thresholds used in the stopping rules

  # Set ARL = 10,000
  # r1= gstream(distM1, L, N0, k, statistics="all", n0=0.3*L, n1=L-0.3*L,
  # ARL=10000,alpha=0.05, skew.corr=TRUE,asymp=FALSE) # uncomment to run this function