| Title: | Sequential Test and Change-Point Detection Algorithms Based on E-Values / E-Detectors |
|---|---|
| Description: | Algorithms of nonparametric sequential test and online change-point detection for streams of univariate (sub-)Gaussian, binary, and bounded random variables, introduced in following publications - Shin et al. (2024) <doi:10.48550/arXiv.2203.03532>, Shin et al. (2021) <doi:10.48550/arXiv.2010.08082>. |
| Authors: | Jaehyeok Shin [aut, cre]
|
| Maintainer: | Jaehyeok Shin <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 0.9.8 |
| Built: | 2024-12-08 07:17:53 UTC |
| Source: | CRAN |
Algorithms of nonparametric sequential test and online change-point detection for streams of univariate (sub-)Gaussian, binary, and bounded random variables, introduced in following publications - Shin et al. (2024) doi:10.48550/arXiv.2203.03532, Shin et al. (2021) doi:10.48550/arXiv.2010.08082.
Maintainer: Jaehyeok Shin [email protected] (ORCID)
Useful links:
For each method and family, check whether delta parameters are within expected range with respect to the pre-change parameter.
checkDeltaRange(method, family, alternative, m_pre, delta_lower, delta_upper)checkDeltaRange(method, family, alternative, m_pre, delta_lower, delta_upper)
method |
Method of the sequential procedure.
|
family |
Distribution of underlying univariate observations.
|
alternative |
Alternative / post-change mean space
|
m_pre |
The boundary of mean parameter in null / pre-change space |
delta_lower |
Minimum gap between null / pre-change space and alternative / post-change one. It must be strictly positive for ST, SR and CU. Currently, GLRCU does not support the minimum gap, and this param will be ignored. |
delta_upper |
Maximum gap between null / pre-change space and alternative / post-change one. It must be strictly positive for ST, SR and CU. Currently, GLRCU does not support the maximum gap, and this param will be ignored. |
A list of
Boolean indicating whether it is acceptable or not.
Character describing why it is not acceptable.
Updated delta_upper for the case where the original input was NULL
Compute parameters to build baseline processes.
compute_baseline( alpha, delta_lower, delta_upper, psi_fn_list = generate_sub_G_fn(), v_min = 1, k_max = 200, tol = 1e-10 )compute_baseline( alpha, delta_lower, delta_upper, psi_fn_list = generate_sub_G_fn(), v_min = 1, k_max = 200, tol = 1e-10 )
alpha |
ARL parameter in (0,1) |
delta_lower |
Lower bound of target Delta. It must be positive and smaller than or equal to |
delta_upper |
Upper bound of target Delta. It must be positive and larger than or equal to |
psi_fn_list |
A list of R functions that computes psi and psi_star functions. Can be generated by |
v_min |
A lower bound of v function in the baseline process. Default is |
k_max |
Positive integer to determine the maximum number of baselines. Default is |
tol |
Tolerance of root-finding, positive numeric. Default is 1e-10. |
A list of 1. Parameters of baseline processes, 2. Mixing weights, 3. Auxiliary values for computation.
Given target variance process bounds for confidence sequences, compute baseline parameters.
compute_baseline_for_sample_size( alpha, v_upper, v_lower, psi_fn_list = generate_sub_G_fn(), skip_g_alpha = TRUE, v_min = 1, k_max = 200, tol = 1e-10 )compute_baseline_for_sample_size( alpha, v_upper, v_lower, psi_fn_list = generate_sub_G_fn(), skip_g_alpha = TRUE, v_min = 1, k_max = 200, tol = 1e-10 )
alpha |
ARL parameter in (0,1) |
v_upper |
Upper bound of the target variance process bound |
v_lower |
Lower bound of the target variance process bound. |
psi_fn_list |
A list of R functions that computes psi and psi_star functions. Can be generated by |
skip_g_alpha |
If true, we do not compute g_alpha and use log(1/alpha) instead. |
v_min |
A lower bound of v function in the baseline process. Default is |
k_max |
Positive integer to determine the maximum number of baselines. Default is |
tol |
Tolerance of root-finding, positive numeric. Default is 1e-10. |
A list of 1. Parameters of baseline processes, 2. Mixing weights, 3. Auxiliary values for computation.
For each exponential baseline family, convert delta range into corresponding lambdas and weights.
convertDeltaToExpParams( family, alternative, threshold, m_pre, delta_lower, delta_upper, k_max )convertDeltaToExpParams( family, alternative, threshold, m_pre, delta_lower, delta_upper, k_max )
family |
Distribution of underlying univariate observations.
|
alternative |
Alternative / post-change mean space
|
threshold |
Stopping threshold. We recommend to use log(1/alpha) for "ST" and "SR" methods where alpha is a testing level or 1/ARL. for "CU" and "GRLCU", we recommend to tune the threshold by using domain-specific sampler to hit the target ARL. |
m_pre |
The boundary of mean parameter in null / pre-change space |
delta_lower |
Minimum gap between null / pre-change space and alternative / post-change one. It must be strictly positive for ST, SR and CU. Currently, GLRCU does not support the minimum gap, and this param will be ignored. |
delta_upper |
Maximum gap between null / pre-change space and alternative / post-change one. It must be strictly positive for ST, SR and CU. Currently, GLRCU does not support the maximum gap, and this param will be ignored. |
k_max |
Positive integer to determine the maximum number of baselines. For GLRCU method, it is used as the lookup window size for GLRCU statistics. |
A list of weights and lambdas
Pre-defined psi_star functions for sub-Bernoulli family.
generate_sub_B_fn(p = 0.5)generate_sub_B_fn(p = 0.5)
p |
The boundary of mean space of the pre-change distributions (default = 0.5). |
A list of pre-defined psi_star functions for sub-Bernoulli family.
Pre-defined psi_star functions for sub-exponential family.
generate_sub_E_fn()generate_sub_E_fn()
A list of pre-defined psi_star functions for sub-exponential family.
Pre-defined psi_star functions for sub-Gaussian family.
generate_sub_G_fn(sig = 1)generate_sub_G_fn(sig = 1)
sig |
The sigma parameter of the sub-Gaussian family (default = 1). |
A list of pre-defined psi_star functions for sub-Gaussian family.
Apply log-sum-exp trick to a numeric vector.
logSumExpTrick(xs)logSumExpTrick(xs)
xs |
A numeric vector. |
log of sum of exp of xs, which is equal to log(sum(exp(xs))).
NormalCS class is used to compute always-valid confidence sequence for the standard normal process based on the STCP method.
new()
Create a new NormalCS object.
NormalCS$new(
alternative = c("two.sided", "greater", "less"),
alpha = 0.05,
n_upper = 1000,
n_lower = 1,
weights = NULL,
lambdas = NULL,
skip_g_alpha = TRUE,
k_max = 1000
)alternativeAlternative / post-change mean space
two.sided: Two-sided test / change detection
greater: Alternative /post-change mean is greater than null / pre-change one
less: Alternative /post-change mean is less than null / pre-change one
alphaUpper bound on the type 1 error of the confidence sequence.
n_upperUpper bound of the target sample interval
n_lowerLower bound of the target sample interval
weightsIf not null, the input weights will be used to initialize the object
instead of n_upper and n_lower.
lambdasIf not null, the input lambdas will be used to initialize the object.
instead of n_upper and n_lower.
skip_g_alphaIf true, we do not compute g_alpha and use log(1/alpha) instead.
k_maxPositive integer to determine the maximum number of baselines.
A new NormalCS object.
print()
Print summary of Stcp object.
NormalCS$print()
getAlpha()
Return the upper bound on the type 1 error
NormalCS$getAlpha()
getWeights()
Return weights of mixture of e-values / e-detectors.
NormalCS$getWeights()
getLambdas()
Return lambda parameters of mixture of e-values / e-detectors.
NormalCS$getLambdas()
computeWidth()
Compute the width of confidence interval at time n.
NormalCS$computeWidth(n)
nPositive time.
computeInterval()
Compute a vector of two end points of confidence interval at time n
NormalCS$computeInterval(n, x_bar = 0)
nPositive time.
x_barThe center of the confidence interval.
# Initialize two-sided standard normal confidence sequence # optimized for the interval [10, 100] normal_cs <- NormalCS$new( alternative = "two.sided", alpha = 0.05, n_upper = 100, n_lower = 10 ) # Compute confidence interval at n = 20 when observed sample mean = 0.5 normal_cs$computeInterval(20, x_bar = 0.5) # (Advanced) NormalCS supports general variance process. # Both n_upper and n_lower can be general positive numbers. normal_cs2 <- NormalCS$new( alternative = "two.sided", alpha = 0.05, n_upper = 100.5, n_lower = 10.5 ) # Confidence interval at n = 20.5 normal_cs$computeInterval(20.5, x_bar = 0.5)# Initialize two-sided standard normal confidence sequence # optimized for the interval [10, 100] normal_cs <- NormalCS$new( alternative = "two.sided", alpha = 0.05, n_upper = 100, n_lower = 10 ) # Compute confidence interval at n = 20 when observed sample mean = 0.5 normal_cs$computeInterval(20, x_bar = 0.5) # (Advanced) NormalCS supports general variance process. # Both n_upper and n_lower can be general positive numbers. normal_cs2 <- NormalCS$new( alternative = "two.sided", alpha = 0.05, n_upper = 100.5, n_lower = 10.5 ) # Confidence interval at n = 20.5 normal_cs$computeInterval(20.5, x_bar = 0.5)
Stcp class supports a unified framework for sequential tests and change detection algorithms for streams of univariate (sub-)Gaussian, binary, and bounded random variables.
new()
Create a new Stcp object.
Stcp$new(
method = c("ST", "SR", "CU", "GLRCU"),
family = c("Normal", "Ber", "Bounded"),
alternative = c("two.sided", "greater", "less"),
threshold = log(1/0.05),
m_pre = 0,
delta_lower = 0.1,
delta_upper = NULL,
weights = NULL,
lambdas = NULL,
k_max = 1000
)methodMethod of the sequential procedure.
ST: Sequential test based on a mixture of E-values.
SR: Sequential change detection based on e-SR procedure.
CU: Sequential change detection based on e-CUSUM procedure.
GLRCU: Sequential change detection based on GLR-CUSUM procedure.
familyDistribution of underlying univariate observations.
Normal: (sub-)Gaussian with sigma = 1.
Ber: Bernoulli distribution on {0,1}.
Bounded: General bounded distribution on [0,1]
alternativeAlternative / post-change mean space
two.sided: Two-sided test / change detection
greater: Alternative /post-change mean is greater than null / pre-change one
less: Alternative /post-change mean is less than null / pre-change one
thresholdStopping threshold. We recommend to use log(1/alpha) for "ST" and "SR" methods where alpha is a testing level or 1/ARL. for "CU" and "GRLCU", we recommend to tune the threshold by using domain-specific sampler to hit the target ARL.
m_preThe boundary of mean parameter in null / pre-change space
delta_lowerMinimum gap between null / pre-change space and alternative / post-change one. It must be strictly positive for ST, SR and CU. Currently, GLRCU does not support the minimum gap, and this param will be ignored.
delta_upperMaximum gap between null / pre-change space and alternative / post-change one. It must be strictly positive for ST, SR and CU. Currently, GLRCU does not support the maximum gap, and this param will be ignored.
weightsIf not null, the input weights will be used to initialize Stcp object.
lambdasIf not null, the input lambdas will be used to initialize Stcp object.
k_maxPositive integer to determine the maximum number of baselines. For GLRCU method, it is used as the lookup window size for GLRCU statistics.
A new Stcp object.
print()
Print summary of Stcp object.
Stcp$print()
getWeights()
Return weights of mixture of e-values / e-detectors.
Stcp$getWeights()
getLambdas()
Return lambda parameters of mixture of e-values / e-detectors.
Stcp$getLambdas()
getLogValue()
Return the log value of mixture of e-values / e-detectors.
Stcp$getLogValue()
getThreshold()
Return the threshold of the sequential test / change detection
Stcp$getThreshold()
isStopped()
Return TRUE if the sequential test / change detection was stopped by crossing the threshold.
Stcp$isStopped()
getTime()
Return the number of observations having been passed.
Stcp$getTime()
getStoppedTime()
Return the stopped time. If it has been never stopped, return zero.
Stcp$getStoppedTime()
reset()
Reset the stcp object to the initial setup.
Stcp$reset()
updateLogValues()
Update the log value and related fields by passing a vector of observations.
Stcp$updateLogValues(xs)
xsA numeric vector of observations.
updateLogValuesUntilStop()
Update the log value and related fields until the log value is crossing the boundary.
Stcp$updateLogValuesUntilStop(xs)
xsA numeric vector of observations.
updateAndReturnHistories()
Update the log value and related fields then return updated log values by passing a vector of observations.
Stcp$updateAndReturnHistories(xs)
xsA numeric vector of observations.
updateLogValuesByAvgs()
Update the log value and related fields by passing a vector of averages and number of corresponding samples.
Stcp$updateLogValuesByAvgs(x_bars, ns)
x_barsA numeric vector of averages.
nsA numeric vector of sample sizes.
updateLogValuesUntilStopByAvgs()
Update the log value and related fields by passing a vector of averages and number of corresponding samples until the log value is crossing the boundary.
Stcp$updateLogValuesUntilStopByAvgs(x_bars, ns)
x_barsA numeric vector of averages.
nsA numeric vector of sample sizes.
updateAndReturnHistoriesByAvgs()
Update the log value and related fields then return updated log values a vector of averages and number of corresponding samples.
Stcp$updateAndReturnHistoriesByAvgs(x_bars, ns)
x_barsA numeric vector of averages.
nsA numeric vector of sample sizes.
# Sequential Normal mean test H0: mu <= 0 # Initialize stcp object for this test. stcp <- Stcp$new(method = "ST", family = "Normal", alternative = "greater", threshold = log(1 / 0.05), m_pre = 0) # Update the observations obs <- c(1.0, 3.0, 2.0) stcp$updateLogValuesUntilStop(obs) # Check whether the sequential test is stopped stcp$isStopped() # TRUE # Check when the test was stopped stcp$getStoppedTime() # 3 # Although the number of obervaions was 4, the test was stopped at 3. stcp$getTime() # 3 # Get the log value of the mixutre of e-values at the current time (3) stcp$getLogValue() # 4.425555 # ...which is higher than the threshold log(1 / 0.05) ~ 2.996 stcp$getThreshold() # 2.995732 # Reset the test object stcp$reset() # Rerun the test but, at this time, we track updated log values log_values <- stcp$updateAndReturnHistories(obs) print(log_values) # 0.1159777 2.7002207 4.4255551 1.9746508 # Again, the test was stopped at 3rd observation stcp$getStoppedTime() # 3 # But, at this time, log values were evaluated until the 4th observation. stcp$getTime() # 4 # Print overall summary stcp # or stcp$print() or print(stcp) # stcp Model: # - Method: ST # - Family: Normal # - Alternative: greater # - Alpha: 0.05 # - m_pre: 0 # - Num. of mixing components: 55 # - Obs. have been passed: 4 # - Current log value: 1.974651 # - Is stopped before: TRUE # - Stopped time: 3# Sequential Normal mean test H0: mu <= 0 # Initialize stcp object for this test. stcp <- Stcp$new(method = "ST", family = "Normal", alternative = "greater", threshold = log(1 / 0.05), m_pre = 0) # Update the observations obs <- c(1.0, 3.0, 2.0) stcp$updateLogValuesUntilStop(obs) # Check whether the sequential test is stopped stcp$isStopped() # TRUE # Check when the test was stopped stcp$getStoppedTime() # 3 # Although the number of obervaions was 4, the test was stopped at 3. stcp$getTime() # 3 # Get the log value of the mixutre of e-values at the current time (3) stcp$getLogValue() # 4.425555 # ...which is higher than the threshold log(1 / 0.05) ~ 2.996 stcp$getThreshold() # 2.995732 # Reset the test object stcp$reset() # Rerun the test but, at this time, we track updated log values log_values <- stcp$updateAndReturnHistories(obs) print(log_values) # 0.1159777 2.7002207 4.4255551 1.9746508 # Again, the test was stopped at 3rd observation stcp$getStoppedTime() # 3 # But, at this time, log values were evaluated until the 4th observation. stcp$getTime() # 4 # Print overall summary stcp # or stcp$print() or print(stcp) # stcp Model: # - Method: ST # - Family: Normal # - Alternative: greater # - Alpha: 0.05 # - m_pre: 0 # - Num. of mixing components: 55 # - Obs. have been passed: 4 # - Current log value: 1.974651 # - Is stopped before: TRUE # - Stopped time: 3