pt_from_os {dsos}R Documentation

Permutation Test from Outlier Scores


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.


pt_from_os(os_train, os_test, n_pt = 2000)



Outlier scores in training (reference) set.


Outlier scores in test set.


The number of permutations.


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).


A named list of class outlier.test containing:


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.


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()


os_train <- rnorm(n = 100)
os_test <- rnorm(n = 100)
null_test <- pt_from_os(os_train, os_test)

[Package dsos version 0.1.2 Index]