Pilliat: Pilliat multiple change-point detection algorithm
In HDCD: High-Dimensional Changepoint Detection

Pilliat

R Documentation

Pilliat multiple change-point detection algorithm

Description

R wrapper function for C implementation of the multiple change-point detection algorithm by \insertCitepilliat_optimal_2022;textualHDCD, using seeded intervals generated by Algorithm 4 in \insertCitemoen2023efficient;textualHDCD. For the sake of simplicity, detection thresholds are chosen independently of the width of the interval in which a change-point is tested for (so r=1 is set for all intervals).

Usage

Pilliat(
  X,
  threshold_d_const = 4,
  threshold_bj_const = 6,
  threshold_partial_const = 4,
  K = 2,
  alpha = 1.5,
  empirical = FALSE,
  threshold_dense = NULL,
  thresholds_partial = NULL,
  thresholds_bj = NULL,
  N = 100,
  tol = 0.01,
  rescale_variance = TRUE,
  test_all = FALSE,
  debug = FALSE
)

Arguments

`X`	Matrix of observations, where each row contains a time series
`threshold_d_const`	Leading constant for the analytical detection threshold for the dense statistic
`threshold_bj_const`	Leading constant for `p_0` when computing the detection threshold for the Berk-Jones statistic
`threshold_partial_const`	Leading constant for the analytical detection threshold for the partial sum statistic
`K`	Parameter for generating seeded intervals
`alpha`	Parameter for generating seeded intervals
`empirical`	If `TRUE`, detection thresholds are based on Monte Carlo simulation using `Pilliat_calibrate`
`threshold_dense`	Manually specified value of detection threshold for the dense statistic
`thresholds_partial`	Vector of manually specified detection thresholds for the partial sum statistic, for sparsities/partial sums `t=1,2,4,\ldots,2^{\lfloor \log_2(p)\rfloor}`
`thresholds_bj`	Vector of manually specified detection thresholds for the Berk-Jones statistic, order corresponding to `x=1,2,\ldots,x_0`
`N`	If `empirical=TRUE`, `N` is the number of Monte Carlo samples used
`tol`	If `empirical=TRUE`, `tol` is the false error probability tolerance
`rescale_variance`	If `TRUE`, each row of the data is re-scaled by a MAD estimate (see `rescale_variance`)
`test_all`	If `TRUE`, the algorithm tests for a change-point in all candidate positions of each considered interval
`debug`	If `TRUE`, diagnostic prints are provided during execution

Value

A list containing

`changepoints`	vector of estimated change-points
`number_of_changepoints`	number of changepoints
`scales`	vector of estimated noise level for each series
`startpoints`	start point of the seeded interval detecting the corresponding change-point in `changepoints`
`endpoints`	end point of the seeded interval detecting the corresponding change-point in `changepoints`

References

\insertAllCited

Examples

library(HDCD)
n = 50
p = 50
set.seed(100)
# Generating data
X = matrix(rnorm(n*p), ncol = n, nrow=p)
# Adding a single sparse change-point:
X[1:5, 26:n] = X[1:5, 26:n] +2

# Vanilla Pilliat:
res = Pilliat(X)
res$changepoints

# Manually setting leading constants for detection thresholds
res = Pilliat(X, threshold_d_const = 4, threshold_bj_const = 6, threshold_partial_const=4)
res$changepoints #estimated change-point locations

# Empirical choice of thresholds:
res = Pilliat(X, empirical = TRUE, N = 100, tol = 1/100)
res$changepoints

# Manual empirical choice of thresholds (equivalent to the above)
thresholds_emp = Pilliat_calibrate(n,p, N=100, tol=1/100)
thresholds_emp$thresholds_partial # thresholds for partial sum statistic
thresholds_emp$thresholds_bj # thresholds for Berk-Jones statistic
thresholds_emp$threshold_dense # thresholds for Berk-Jones statistic
res = Pilliat(X, threshold_dense =thresholds_emp$threshold_dense, 
              thresholds_bj = thresholds_emp$thresholds_bj,
              thresholds_partial =thresholds_emp$thresholds_partial )
res$changepoints

HDCD documentation built on June 22, 2024, 10:53 a.m.