| Title: | Dataset Shift with Outlier Scores |
| Version: | 0.1.2 |
| Description: | Test for no adverse shift in two-sample comparison when we have a training set, the reference distribution, and a test set. The approach is flexible and relies on a robust and powerful test statistic, the weighted AUC. Technical details are in Kamulete, V. M. (2021) <doi:10.48550/arXiv.1908.04000>. Modern notions of outlyingness such as trust scores and prediction uncertainty can be used as the underlying scores for example. |
| License: | GPL (≥ 3) |
| URL: | https://github.com/vathymut/dsos |
| BugReports: | https://github.com/vathymut/dsos/issues |
| Imports: | data.table (≥ 1.14.6), future.apply (≥ 1.10.0), ggplot2 (≥ 3.4.0), scales (≥ 1.2.1), simctest (≥ 2.6), stats (≥ 4.2.1) |
| Suggests: | fdrtool (≥ 1.2.17), knitr (≥ 1.42), rmarkdown (≥ 2.20), testthat (≥ 3.1.6) |
| VignetteBuilder: | knitr |
| Encoding: | UTF-8 |
| Language: | en-US |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | no |
| Packaged: | 2023-02-19 04:23:47 UTC; vathy |
| Author: | Vathy M. Kamulete 
[aut, cre],
Royal Bank of Canada (RBC) [cph] (Research supported and funded by RBC) |
| Maintainer: | Vathy M. Kamulete <vathymut@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2023-02-19 07:30:06 UTC |
dsos: Dataset Shift with Outlier Scores
Description
Test for no adverse shift in two-sample comparison when we have a training set, the reference distribution, and a test set. The approach is flexible and relies on a robust and powerful test statistic, the weighted AUC. Technical details are in Kamulete, V. M. (2021) arXiv:1908.04000. Modern notions of outlyingness such as trust scores and prediction uncertainty can be used as the underlying scores for example.
Author(s)
Maintainer: Vathy M. Kamulete vathymut@gmail.com (ORCID)
Other contributors:
Royal Bank of Canada (RBC) (Research supported and funded by RBC) [copyright holder]
See Also
Useful links:
Convert P-value to Bayes Factor
Description
Convert P-value to Bayes Factor
Usage
as_bf(pvalue)
Arguments
pvalue |
P-value. |
Value
Bayes Factor (scalar value).
References
Marsman, M., & Wagenmakers, E. J. (2017). Three insights from a Bayesian interpretation of the one-sided P value. Educational and Psychological Measurement, 77(3), 529-539.
See Also
[as_pvalue()] to convert Bayes factor to p-value.
Other bayesian-test:
as_pvalue(),
bf_compare(),
bf_from_os()
Examples
library(dsos)
bf_from_pvalue <- as_bf(pvalue = 0.5)
bf_from_pvalue
Convert Bayes Factor to P-value
Description
Convert Bayes Factor to P-value
Usage
as_pvalue(bf)
Arguments
bf |
Bayes factor. |
Value
p-value (scalar value).
References
Marsman, M., & Wagenmakers, E. J. (2017). Three insights from a Bayesian interpretation of the one-sided P value. Educational and Psychological Measurement, 77(3), 529-539.
See Also
[as_bf()] to convert p-value to Bayes factor.
Other bayesian-test:
as_bf(),
bf_compare(),
bf_from_os()
Examples
library(dsos)
pvalue_from_bf <- as_pvalue(bf = 1)
pvalue_from_bf
Asymptotic Test from Outlier Scores
Description
Test for no adverse shift with outlier scores. Like goodness-of-fit testing,
this two-sample comparison takes the training set, x_train as the
as the reference. The method checks whether the test set, x_test, is
worse off relative to this reference set. The function scorer assigns
an outlier score to each instance/observation in both training and test set.
Usage
at_from_os(os_train, os_test)
Arguments
os_train |
Outlier scores in training (reference) set. |
os_test |
Outlier scores in test set. |
Details
Li and Fine (2010) derives the asymptotic null distribution for the weighted
AUC (WAUC), the test statistic. This approach does not use permutations
and can, as a result, be much faster because it sidesteps the need to refit
the scoring function scorer. This works well for large samples. The
prefix at stands for asymptotic test to tell it apart from the
prefix pt, the permutation test.
Value
A named list of class outlier.test containing:
-
statistic: observed WAUC statistic -
seq_mct: sequential Monte Carlo test, when applicable -
p_value: p-value -
outlier_scores: outlier scores from training and test set
Notes
The outlier scores should all mimic out-of-sample behaviour. Mind that the training scores are not in-sample and thus, biased (overfitted) while the test scores are out-of-sample. The mismatch – in-sample versus out-of-sample scores – voids the test validity. A simple fix for this is to get the training scores from an indepedent (fresh) validation set; this follows the train/validation/test sample splitting convention and the validation set is effectively the reference set or distribution in this case.
References
Kamulete, V. M. (2022). Test for non-negligible adverse shifts. In The 38th Conference on Uncertainty in Artificial Intelligence. PMLR.
Gandy, A. (2009). Sequential implementation of Monte Carlo tests with uniformly bounded resampling risk. Journal of the American Statistical Association, 104(488), 1504-1511.
See Also
[at_oob()] for variant requiring a scoring function. [pt_from_os()] for permutation test with the outlier scores.
Other asymptotic-test:
at_oob()
Examples
library(dsos)
set.seed(12345)
os_train <- rnorm(n = 100)
os_test <- rnorm(n = 100)
test_result <- at_from_os(os_train, os_test)
test_result
Asymptotic Test With Out-Of-Bag Scores
Description
Test for no adverse shift with outlier scores. Like goodness-of-fit testing,
this two-sample comparison takes the training set, x_train as the
as the reference. The method checks whether the test set, x_test, is
worse off relative to this reference set. The function scorer assigns
an outlier score to each instance/observation in both training and test set.
Usage
at_oob(x_train, x_test, scorer)
Arguments
x_train |
Training (reference/validation) sample. |
x_test |
Test sample. |
scorer |
Function which returns a named list with outlier scores from
the training and test sample. The first argument to |
Details
Li and Fine (2010) derives the asymptotic null distribution for the weighted
AUC (WAUC), the test statistic. This approach does not use permutations
and can, as a result, be much faster because it sidesteps the need to refit
the scoring function scorer. This works well for large samples. The
prefix at stands for asymptotic test to tell it apart from the
prefix pt, the permutation test.
Value
A named list of class outlier.test containing:
-
statistic: observed WAUC statistic -
seq_mct: sequential Monte Carlo test, when applicable -
p_value: p-value -
outlier_scores: outlier scores from training and test set
Notes
The scoring function, scorer, predicts out-of-bag scores to mimic
out-of-sample behaviour. The suffix oob stands for out-of-bag to
highlight this point. This out-of-bag variant avoids refitting the
underlying algorithm from scorer at every permutation. It can, as a
result, be computationally appealing.
References
Kamulete, V. M. (2022). Test for non-negligible adverse shifts. In The 38th Conference on Uncertainty in Artificial Intelligence. PMLR.
Gandy, A. (2009). Sequential implementation of Monte Carlo tests with uniformly bounded resampling risk. Journal of the American Statistical Association, 104(488), 1504-1511.
See Also
[pt_oob()] for (faster) p-value approximation via out-of-bag predictions. [pt_refit()] for (slower) p-value approximation via refitting.
Other asymptotic-test:
at_from_os()
Examples
library(dsos)
set.seed(12345)
data(iris)
setosa <- iris[1:50, 1:4] # Training sample: Species == 'setosa'
versicolor <- iris[51:100, 1:4] # Test sample: Species == 'versicolor'
# Using fake scoring function
scorer <- function(tr, te) list(train=runif(nrow(tr)), test=runif(nrow(te)))
oob_test <- at_oob(setosa, versicolor, scorer = scorer)
oob_test
Bayesian and Frequentist Test from Outlier Scores
Description
Test for no adverse shift with outlier scores. Like goodness-of-fit testing,
this two-sample comparison takes the training (outlier) scores,
os_train, as the reference. The method checks whether the test
scores, os_test, are worse off relative to the training set.
Usage
bf_compare(os_train, os_test, threshold = 1/12, n_pt = 4000)
Arguments
os_train |
Outlier scores in training (reference) set. |
os_test |
Outlier scores in test set. |
threshold |
Threshold for adverse shift. Defaults to 1 / 12, the asymptotic value of the test statistic when the two samples are drawn from the same distribution. |
n_pt |
The number of permutations. |
Details
This compares the Bayesian to the frequentist approach for convenience.
The Bayesian test mimics 'bf_from_os()' and the frequentist one,
'pt_from_os()'. The Bayesian test computes Bayes factors based on the
asymptotic (defaults to 1/12) and the exchangeable threshold. The latter
calculates the threshold as the median weighted AUC (WAUC) after n_pt
permutations assuming outlier scores are exchangeable. This is recommended
for small samples. The frequentist test converts the one-sided (one-tailed)
p-value to the Bayes factor - see as_bf function.
Value
A list of factors (BF) for 3 different test specifications:
-
frequentist: Frequentist BF. -
bayes_noperm: Bayestion BF test with asymptotic threshold. -
bayes_perm: Bayestion BF with exchangeable threshold.
Notes
The outlier scores should all mimic out-of-sample behaviour. Mind that the training scores are not in-sample and thus, biased (overfitted) while the test scores are out-of-sample. The mismatch – in-sample versus out-of-sample scores – voids the test validity. A simple fix for this is to get the training scores from an indepedent (fresh) validation set; this follows the train/validation/test sample splitting convention and the validation set is effectively the reference set or distribution in this case.
See Also
[bf_from_os()] for bayes factor, the Bayesian test. [pt_from_os()] for p-value, the frequentist test.
Other bayesian-test:
as_bf(),
as_pvalue(),
bf_from_os()
Examples
library(dsos)
set.seed(12345)
os_train <- rnorm(n = 100)
os_test <- rnorm(n = 100)
bayes_test <- bf_compare(os_train, os_test)
bayes_test
# To run in parallel on local cluster, uncomment the next two lines.
# library(future)
# future::plan(future::multisession)
parallel_test <- bf_compare(os_train, os_test)
parallel_test
Bayesian Test from Outlier Scores
Description
Test for no adverse shift with outlier scores. Like goodness-of-fit testing,
this two-sample comparison takes the training (outlier) scores,
os_train, as the reference. The method checks whether the test
scores, os_test, are worse off relative to the training set.
Usage
bf_from_os(os_train, os_test, n_pt = 4000, threshold = 1/12)
Arguments
os_train |
Outlier scores in training (reference) set. |
os_test |
Outlier scores in test set. |
n_pt |
The number of permutations. |
threshold |
Threshold for adverse shift. Defaults to 1 / 12, the asymptotic value of the test statistic when the two samples are drawn from the same distribution. |
Details
The posterior distribution of the test statistic is based on n_pt
(boostrap) permutations. The method uses the Bayesian bootstrap as a
resampling procedure as in Gu et al (2008). Johnson (2005) shows to
leverage (turn) a test statistic into a Bayes factor. The test statistic
is the weighted AUC (WAUC).
Value
A named list of class outlier.bayes containing:
-
posterior: Posterior distribution of WAUC test statistic -
threshold: WAUC threshold for adverse shift -
adverse_probability: probability of adverse shift -
bayes_factor: Bayes factor -
outlier_scores: outlier scores from training and test set
Notes
The outlier scores should all mimic out-of-sample behaviour. Mind that the training scores are not in-sample and thus, biased (overfitted) while the test scores are out-of-sample. The mismatch – in-sample versus out-of-sample scores – voids the test validity. A simple fix for this is to get the training scores from an indepedent (fresh) validation set; this follows the train/validation/test sample splitting convention and the validation set is effectively the reference set or distribution in this case.
References
Kamulete, V. M. (2023). Are you OK? A Bayesian test for adverse shift. Manuscript in preparation.
Johnson, V. E. (2005). Bayes factors based on test statistics. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(5), 689-701.
Gu, J., Ghosal, S., & Roy, A. (2008). Bayesian bootstrap estimation of ROC curve. Statistics in medicine, 27(26), 5407-5420.
See Also
Other bayesian-test:
as_bf(),
as_pvalue(),
bf_compare()
Examples
library(dsos)
set.seed(12345)
os_train <- rnorm(n = 100)
os_test <- rnorm(n = 100)
bayes_test <- bf_from_os(os_train, os_test)
bayes_test
# To run in parallel on local cluster, uncomment the next two lines.
# library(future)
# future::plan(future::multisession)
parallel_test <- bf_from_os(os_train, os_test)
parallel_test
Plot Bayesian test for no adverse shift.
Description
Plot Bayesian test for no adverse shift.
Usage
## S3 method for class 'outlier.bayes'
plot(x, ...)
Arguments
x |
A |
... |
Placeholder to be compatible with S3 method |
Value
A ggplot2 plot with outlier scores and p-value.
See Also
Other s3-method:
plot.outlier.test(),
print.outlier.bayes(),
print.outlier.test()
Examples
set.seed(12345)
os_train <- rnorm(n = 3e2)
os_test <- rnorm(n = 3e2)
test_to_plot <- bf_from_os(os_train, os_test)
plot(test_to_plot)
Plot frequentist test for no adverse shift.
Description
Plot frequentist test for no adverse shift.
Usage
## S3 method for class 'outlier.test'
plot(x, ...)
Arguments
x |
A |
... |
Placeholder to be compatible with S3 method |
Value
A ggplot2 plot with outlier scores and p-value.
See Also
Other s3-method:
plot.outlier.bayes(),
print.outlier.bayes(),
print.outlier.test()
Examples
set.seed(12345)
os_train <- rnorm(n = 3e2)
os_test <- rnorm(n = 3e2)
test_to_plot <- at_from_os(os_train, os_test)
# Also: pt_from_os(os_train, os_test) for permutation test
plot(test_to_plot)
Print Bayesian test for no adverse shift.
Description
Print Bayesian test for no adverse shift.
Usage
## S3 method for class 'outlier.bayes'
print(x, ...)
Arguments
x |
A |
... |
Placeholder to be compatible with S3 method |
Value
Print to screen: display Bayes factor and other information.
See Also
Other s3-method:
plot.outlier.bayes(),
plot.outlier.test(),
print.outlier.test()
Examples
set.seed(12345)
os_train <- rnorm(n = 3e2)
os_test <- rnorm(n = 3e2)
test_to_print <- bf_from_os(os_train, os_test)
test_to_print
Print frequentist test for no adverse shift.
Description
Print frequentist test for no adverse shift.
Usage
## S3 method for class 'outlier.test'
print(x, ...)
Arguments
x |
A |
... |
Placeholder to be compatible with S3 method |
Value
Print to screen: display p-value and other information.
See Also
Other s3-method:
plot.outlier.bayes(),
plot.outlier.test(),
print.outlier.bayes()
Examples
set.seed(12345)
os_train <- rnorm(n = 3e2)
os_test <- rnorm(n = 3e2)
test_to_print <- at_from_os(os_train, os_test)
# Also: pt_from_os(os_train, os_test) for permutation test
test_to_print
Permutation Test from Outlier Scores
Description
Test for no adverse shift with outlier scores. Like goodness-of-fit testing,
this two-sample comparison takes the training (outlier) scores,
os_train, as the reference. The method checks whether the test
scores, os_test, are worse off relative to the training set.
Usage
pt_from_os(os_train, os_test, n_pt = 2000)
Arguments
os_train |
Outlier scores in training (reference) set. |
os_test |
Outlier scores in test set. |
n_pt |
The number of permutations. |
Details
The null distribution of the test statistic is based on n_pt
permutations. For speed, this is implemented as a sequential Monte Carlo test
with the simctest package. See Gandy (2009) for details. The prefix
pt refers to permutation test. This approach does not use the
asymptotic null distribution for the test statistic. This is the recommended
approach for small samples. The test statistic is the weighted AUC (WAUC).
Value
A named list of class outlier.test containing:
-
statistic: observed WAUC statistic -
seq_mct: sequential Monte Carlo test, when applicable -
p_value: p-value -
outlier_scores: outlier scores from training and test set
Notes
The outlier scores should all mimic out-of-sample behaviour. Mind that the training scores are not in-sample and thus, biased (overfitted) while the test scores are out-of-sample. The mismatch – in-sample versus out-of-sample scores – voids the test validity. A simple fix for this is to get the training scores from an indepedent (fresh) validation set; this follows the train/validation/test sample splitting convention and the validation set is effectively the reference set or distribution in this case.
References
Kamulete, V. M. (2022). Test for non-negligible adverse shifts. In The 38th Conference on Uncertainty in Artificial Intelligence. PMLR.
Gandy, A. (2009). Sequential implementation of Monte Carlo tests with uniformly bounded resampling risk. Journal of the American Statistical Association, 104(488), 1504-1511.
See Also
[pt_oob()] for variant requiring a scoring function. [at_from_os()] for asymptotic test with the outlier scores.
Other permutation-test:
pt_oob(),
pt_refit()
Examples
library(dsos)
set.seed(12345)
os_train <- rnorm(n = 100)
os_test <- rnorm(n = 100)
null_test <- pt_from_os(os_train, os_test)
null_test
Permutation Test With Out-Of-Bag Scores
Description
Test for no adverse shift with outlier scores. Like goodness-of-fit testing,
this two-sample comparison takes the training set, x_train as the
as the reference. The method checks whether the test set, x_test, is
worse off relative to this reference set. The function scorer assigns
an outlier score to each instance/observation in both training and test set.
Usage
pt_oob(x_train, x_test, scorer, n_pt = 2000)
Arguments
x_train |
Training (reference/validation) sample. |
x_test |
Test sample. |
scorer |
Function which returns a named list with outlier scores from
the training and test sample. The first argument to |
n_pt |
The number of permutations. |
Details
The null distribution of the test statistic is based on n_pt
permutations. For speed, this is implemented as a sequential Monte Carlo test
with the simctest package. See Gandy (2009) for details. The prefix
pt refers to permutation test. This approach does not use the
asymptotic null distribution for the test statistic. This is the recommended
approach for small samples. The test statistic is the weighted AUC (WAUC).
Value
A named list of class outlier.test containing:
-
statistic: observed WAUC statistic -
seq_mct: sequential Monte Carlo test, when applicable -
p_value: p-value -
outlier_scores: outlier scores from training and test set
Notes
The scoring function, scorer, predicts out-of-bag scores to mimic
out-of-sample behaviour. The suffix oob stands for out-of-bag to
highlight this point. This out-of-bag variant avoids refitting the
underlying algorithm from scorer at every permutation. It can, as a
result, be computationally appealing.
References
Kamulete, V. M. (2022). Test for non-negligible adverse shifts. In The 38th Conference on Uncertainty in Artificial Intelligence. PMLR.
Gandy, A. (2009). Sequential implementation of Monte Carlo tests with uniformly bounded resampling risk. Journal of the American Statistical Association, 104(488), 1504-1511.
See Also
[pt_refit()] for (slower) p-value approximation via refitting. [at_oob()] for p-value approximation from asymptotic null distribution.
Other permutation-test:
pt_from_os(),
pt_refit()
Examples
library(dsos)
set.seed(12345)
data(iris)
idx <- sample(nrow(iris), 2 / 3 * nrow(iris))
iris_train <- iris[idx, ]
iris_test <- iris[-idx, ]
# Use a synthetic (fake) scoring function for illustration
scorer <- function(tr, te) list(train=runif(nrow(tr)), test=runif(nrow(te)))
pt_test <- pt_oob(iris_train, iris_test, scorer = scorer)
pt_test
Permutation Test By Refitting
Description
Test for no adverse shift with outlier scores. Like goodness-of-fit testing,
this two-sample comparison takes the training set, x_train as the
as the reference. The method checks whether the test set, x_test, is
worse off relative to this reference set. The function scorer assigns
an outlier score to each instance/observation in both training and test set.
Usage
pt_refit(x_train, x_test, scorer, n_pt = 2000)
Arguments
x_train |
Training (reference/validation) sample. |
x_test |
Test sample. |
scorer |
Function which returns a named list with outlier scores from
the training and test sample. The first argument to |
n_pt |
The number of permutations. |
Details
The null distribution of the test statistic is based on n_pt
permutations. For speed, this is implemented as a sequential Monte Carlo test
with the simctest package. See Gandy (2009) for details. The prefix
pt refers to permutation test. This approach does not use the
asymptotic null distribution for the test statistic. This is the recommended
approach for small samples. The test statistic is the weighted AUC (WAUC).
Value
A named list of class outlier.test containing:
-
statistic: observed WAUC statistic -
seq_mct: sequential Monte Carlo test, when applicable -
p_value: p-value -
outlier_scores: outlier scores from training and test set
Notes
The scoring function, scorer, predicts out-of-sample scores by
refitting the underlying algorithm from scorer at every permutation
The suffix refit emphasizes this point. This is in contrast to the
out-of-bag variant, pt_oob, which only fits once. This method can be
be computationally expensive.
References
Kamulete, V. M. (2022). Test for non-negligible adverse shifts. In The 38th Conference on Uncertainty in Artificial Intelligence. PMLR.
Gandy, A. (2009). Sequential implementation of Monte Carlo tests with uniformly bounded resampling risk. Journal of the American Statistical Association, 104(488), 1504-1511.
See Also
[pt_oob()] for (faster) p-value approximation via out-of-bag predictions. [at_oob()] for p-value approximation from asymptotic null distribution.
Other permutation-test:
pt_from_os(),
pt_oob()
Examples
library(dsos)
set.seed(12345)
data(iris)
setosa <- iris[1:50, 1:4] # Training sample: Species == 'setosa'
versicolor <- iris[51:100, 1:4] # Test sample: Species == 'versicolor'
scorer <- function(tr, te) list(train=runif(nrow(tr)), test=runif(nrow(te)))
pt_test <- pt_refit(setosa, versicolor, scorer = scorer)
pt_test
Weighted AUC from Outlier Scores
Description
Computes the weighted AUC with the weighting scheme described in Kamulete, V. M. (2021). This assumes that the training set is the reference distribution and specifies a particular functional form to derive weights from threshold scores.
Usage
wauc_from_os(os_train, os_test, weight = NULL)
Arguments
os_train |
Outlier scores in training (reference) set. |
os_test |
Outlier scores in test set. |
weight |
Numeric vector of weights of length
|
Value
The weighted AUC (scalar value) given the weighting scheme.
References
Kamulete, V. M. (2022). Test for non-negligible adverse shifts. In The 38th Conference on Uncertainty in Artificial Intelligence. PMLR.
Examples
library(dsos)
set.seed(12345)
os_train <- rnorm(n = 100)
os_test <- rnorm(n = 100)
test_stat <- wauc_from_os(os_train, os_test)