ML score check: checking the validity of machine learning and computer vision scores
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mlscorecheck: testing the consistency of machine learning performance scores
.. contents:: :depth: 3
Performance scores of a machine learning technique (binary/multiclass classification, regression) are reported on a dataset and look suspicious (exceptionally high scores possibly due to a typo, uncommon evaluation methodology, data leakage in preparation, incorrect use of statistics, etc.). With the tools implemented in the package mlscorecheck, one can test if the reported performance scores are consistent with each other and the assumptions on the experimental setup up.
Testing is as simple as the following example illustrated. Suppose the accuracy, sensitivity and specificity scores are reported for a binary classification testset consisting of p=100 and n=200 samples. All this information is supplied to the suitable test function and the result shows that that inconsistencies were identified: the scores could not be calculated from the confusion matrix of the testset:
.. code-block:: Python
from mlscorecheck.check.binary import check_1_testset_no_kfold
result = check_1_testset_no_kfold(
testset={'p': 100, 'n': 200},
scores={'acc': 0.9567, 'sens': 0.8545, 'spec': 0.9734},
eps=1e-4
)
result['inconsistency']
# True
The consistency tests are numerical and not statistical: if inconsistencies are identified, it means that either the assumptions on the experimental setup or the reported scores are incorrect.
If you use the package, please consider citing the following paper:
.. code-block:: BibTex
@misc{fazekas2023testing, title={Testing the Consistency of Performance Scores Reported for Binary Classification Problems}, author={Attila Fazekas and György Kovács}, year={2023}, eprint={2310.12527}, archivePrefix={arXiv}, primaryClass={cs.LG} }
The package has only basic requirements when used for consistency testing:
numpypulpscikit-learn.. code-block:: bash
pip install numpy pulp
In order to execute the unit tests for the computer algebra components or reproduce the algebraic solutions, either sympy or sage needs to be installed. The installation of sympy can be done in the usual way. To install sage in a conda environment, one needs to add the conda-forge channel first:
.. code-block:: bash
conda config --add channels conda-forge
conda install sage
The mlscorecheck package can be installed from the PyPI repository by issuing
.. code-block:: bash
pip install mlscorecheck
Alternatively, one can clone the latest version of the package from GitHub and install it into the active virtual environment using the following command:
.. code-block:: bash
git clone git@github.com:FalseNegativeLab/mlscorecheck.git
cd mlscorecheck
pip install .
The evaluation of the performance of machine learning techniques, whether for original theoretical advancements or applications in specific fields, relies heavily on performance scores (https://en.wikipedia.org/wiki/Evaluation_of_binary_classifiers). Although reported performance scores are employed as primary indicators of research value, they often suffer from methodological problems, typos, and insufficient descriptions of experimental settings. These issues contribute to the replication crisis (https://en.wikipedia.org/wiki/Replication_crisis) and ultimately entire fields of research ([RV], [EHG]). Even systematic reviews can suffer from using incomparable performance scores for ranking research papers [RV]_.
In practice, the performance scores cannot take any values independently, the scores reported for the same experiment are constrained by the experimental setup and need to express some internal consistency. For many commonly used experimental setups it is possible to develop numerical techniques to test if the scores could be the outcome of the presumed experiment on the presumed dataset. This package implements such consistency tests for some common experimental setups. We highlight that the developed tests cannot guarantee that the scores are surely calculated by some standards or a presumed evaluation protocol. However, if the tests fail and inconsistencies are detected, it means that the scores are not calculated by the presumed protocols with certainty. In this sense, the specificity of the test is 1.0, the inconsistencies being detected are inevitable.
For further information, see
In general, there are three inputs to the consistency testing functions:
k decimal places. The numerical uncertainty estimates the maximum difference of the reported score and its true value. For example, having the accuracy score 0.9489 published (4 decimal places), one can suppose that it is rounded, therefore, the numerical uncertainty is 0.00005 (10^(-4)/2). To be more conservative, one can assume that the score was ceiled or floored. In this case, the numerical uncertainty becomes 0.0001 (10^(-4)).In this subsection, we illustrate the various ways the experimental setup can be specified.
Specification of one testset or dataset ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
There are multiple ways to specify datasets and entire experiments consisting of multiple datasets evaluated in differing ways of cross-validations.
A simple binary classification testset consisting of p positive samples (usually labelled 1) and n negative samples (usually labelled 0) can be specified as
.. code-block:: Python
testset = {"p": 10, "n": 20}
We note that alternative notations, like using n_positive, n_minority or n_1 instead of p and similarly, n_negative, n_majority and n_0 instead of n are supported.
One can also specify a commonly used dataset by its name and the package will look up the p and n counts of the datasets from its internal registry (based on the representations in the common-datasets package):
.. code-block:: Python
dataset = {"dataset_name": "common_datasets.ADA"}
To see the list of supported datasets and corresponding counts, issue
.. code-block:: Python
from mlscorecheck.experiments import dataset_statistics
print(dataset_statistics)
Specification of a folding ^^^^^^^^^^^^^^^^^^^^^^^^^^
The specification of foldings is needed when the scores are computed in cross-validation scenarios. We distinguish two main cases: in the first case, the number of positive and negative samples in the folds are known, or can be derived from the attributes of the dataset (for example, by stratification); in the second case, the statistics of the folds are not known, but the number of folds and potential repetitions are known.
In the first case, when the folds are known, one can specify them by listing them:
.. code-block:: Python
folding = {
"folds": [
{"p": 5, "n": 10},
{"p": 4, "n": 10},
{"p": 5, "n": 10}
]
}
This folding can represent the evaluation of a dataset with 14 positive and 30 negative samples in a 3-fold stratified cross-validation scenario.
Knowing that the folding is derived by some standard stratification techniques, one can just specify the parameters of the folding:
.. code-block:: Python
folding = {"n_folds": 3, "n_repeats": 1, "strategy": "stratified_sklearn"}
In this specification, it is assumed that the samples are distributed into the folds according to the sklearn stratification implementation.
Finally, if neither the folds nor the folding strategy is known, one can simply specify the folding with its parameters (assuming a repeated k-fold scheme):
.. code-block:: Python
folding = {"n_folds": 3, "n_repeats": 2}
Note that not all consistency testing functions support the latter case (not knowing the exact structure of the folds).
Specification of an evaluation ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
A dataset and a folding constitute an evaluation, and many of the test functions take evaluations as parameters describing the scenario:
.. code-block:: Python
evaluation = {
"dataset": {"p": 10, "n": 50},
"folding": {"n_folds": 5, "n_repeats": 1, "strategy": "stratified_sklearn"}
}
When it comes to the aggregation of scores (either over multiple folds, multiple datasets or both), there are two approaches in the literature. In the Mean of Scores (MoS) scenario, the scores are calculated for each fold/dataset, and the mean of the scores is determined as the score characterizing the entire experiment. In the Score of Means (SoM) approach, first the overall confusion matrix is determined, and then the scores are calculated based on these total figures. The advantage of the MoS approach over SoM is that it is possible to estimate the standard deviation of the scores, however, its disadvantage is that the average of non-linear scores might be distorted and some score might become undefined on when the folds are extremely small (typically in the case of small and imbalanced data).
The mlscorecheck package supports both approaches, however, by design, to increase awareness, different functions are provided for the different approaches, usually indicated by the '_mos' or '_som' suffixes in the function names.
The consistency tests can be grouped to three classes, and it is the problem and the experimental setup determining which internal implementation is applicable:
Depending on the experimental setup, the consistency tests developed for binary classification problems support a variety of performance scores: when aggregated performance scores (averages on folds or datasets) are reported, only accuracy (acc), sensitivity (sens), specificity (spec) and balanced accuracy (bacc) are supported; when cross-validation is not involved in the experimental setup, the list of supported scores reads as follows (with abbreviations in parentheses):
acc),sens),spec),ppv),npv),bacc),f1),f1n),fbp),fbn),fm),upm),gm),mk),lrp),lrn),mcc),bm),pt),dor),ji),kappa).We note that synonyms and full names are also supported, for example:
sens are sensitivity, true_positive_rate, tpr and recall,spec are specificity, true_negative_rate, tnr and selectivity,ppv are positive_predictive_value and precision.Similarly, complements are supported as:
false_positive_rate or fpr as a complement of spec,false_negative_rate or fnr as a complement of sens.The tests are designed to detect inconsistencies. If the resulting inconsistency flag is False, the scores can still be calculated in non-standard ways. However, if the resulting inconsistency flag is True, it conclusively indicates that inconsistencies are detected, and the reported scores could not be the outcome of the presumed experiment.
In the rest of the section, we illustrate some of the test functions, for further details and the full list of supported scenarios, see https://mlscorecheck.readthedocs.io/en/latest/.
A scenario like this is having one single test set to which classification is applied and the scores are computed from the resulting confusion matrix. For example, given a test image, which is segmented and the scores of the segmentation (as a binary classification of pixels) are calculated and reported.
In the example below, the scores are artificially generated to be consistent, and accordingly, the test did not identify inconsistencies at the 1e-2 level of numerical uncertainty.
.. code-block:: Python
from mlscorecheck.check.binary import check_1_testset_no_kfold
testset = {'p': 530, 'n': 902}
scores = {'acc': 0.62, 'sens': 0.22, 'spec': 0.86, 'f1p': 0.3, 'fm': 0.32}
result = check_1_testset_no_kfold(
testset=testset,
scores=scores,
eps=1e-2
)
result['inconsistency']
# False
The interpretation of the outcome is that given a testset containing 530 positive and 902 negative samples, the reported scores can be the outcome of an evaluation. In the result structure one can find further information about the test. Namely, under the key n_valid_tptn_pairs one finds the number of tp and tn combinations which can lead to the reported performance scores with the given numerical uncertainty.
If one of the scores is altered, like accuracy is changed to 0.92, the configuration becomes infeasible:
.. code-block:: Python
scores = {'acc': 0.92, 'sens': 0.22, 'spec': 0.86, 'f1p': 0.3, 'fm': 0.32}
result = check_1_testset_no_kfold(
testset=testset,
scores=scores,
eps=1e-2
)
result['inconsistency']
# True
As the inconsistency flag shows, here inconsistencies were identified, there are no such tp and tn combinations which would end up with the reported scores. Either the assumption on the properties of the dataset, or the scores are incorrect.
This scenario is the most common in the literature. A classification technique is executed to each fold in a (repeated) k-fold scenario, the scores are calculated for each fold, and the average of the scores is reported with some numerical uncertainty due to rounding/ceiling/flooring. Because of the averaging, this test supports only the linear scores (acc, sens, spec, bacc) which usually are among the most commonly reported scores. The test constructs a linear integer program describing the scenario with the true positive and true negative parameters of all folds and checks its feasibility.
In the example below, a consistent set of figures is tested:
.. code-block:: Python
from mlscorecheck.check.binary import check_1_dataset_known_folds_mos
dataset = {'p': 126, 'n': 131}
folding = {'folds': [{'p': 52, 'n': 94}, {'p': 74, 'n': 37}]}
scores = {'acc': 0.573, 'sens': 0.768, 'bacc': 0.662}
result = check_1_dataset_known_folds_mos(
dataset=dataset,
folding=folding,
scores=scores,
eps=1e-3
)
result['inconsistency']
# False
As indicated by the output flag, no inconsistencies were identified. The result dictionary contains some further details of the test. Most notably, under the lp_status key, one can find the status of the linear programming solver. Additionally, under the lp_configuration key, one can find the values of all true positive and true negative variables in all folds at the time of the termination of the solver. Furthermore, all scores are calculated for the individual folds and the entire dataset, as well.
If one of the scores is adjusted, for example, sensitivity is changed to 0.568, the configuration becomes infeasible:
.. code-block:: Python
scores = {'acc': 0.573, 'sens': 0.568, 'bacc': 0.662}
result = check_1_dataset_known_folds_mos(
dataset=dataset,
folding=folding,
scores=scores,
eps=1e-3
)
result['inconsistency']
# True
Finally, we mention that if there are hints for bounds on the scores in the folds (for example, when the minimum and maximum scores across the folds are reported), one can add these figures to strengthen the test. In the next example, score bounds on accuracy have been added to each fold. This means the test checks if the reported scores can be achieved with a true positive and true negative configuration with the specified lower and upper bounds for the scores in the individual folds:
.. code-block:: Python
dataset = {'dataset_name': 'common_datasets.glass_0_1_6_vs_2'}
folding = {'n_folds': 4, 'n_repeats': 2, 'strategy': 'stratified_sklearn'}
scores = {'acc': 0.9, 'spec': 0.9, 'sens': 0.6, 'bacc': 0.1, 'f1': 0.95}
result = check_1_dataset_known_folds_mos(
dataset=dataset,
folding=folding,
fold_score_bounds={'acc': (0.8, 1.0)},
scores=scores,
eps=1e-2,
numerical_tolerance=1e-6
)
result['inconsistency']
# True
Note that in this example, although f1 is provided, it is completely ignored as the aggregated tests work only for the four linear scores.
Similar tests are provided for the SoM aggregation as well, for further details see https://mlscorecheck.readthedocs.io/en/latest/.
In this scenario there are n different testsets, the classifier is evaluated on each testsets, and the scores are aggregated by the SoM aggregation. This scenario is similar to the "1 dataset k-fold SoM" case, except the scores are aggregated over testsets rather than folds. The output of the test is structured similarly as in the "1 dataset k-fold SoM" case. In the following example, a consistent case is tested.
.. code-block:: Python
from mlscorecheck.check.binary import check_n_testsets_som_no_kfold
testsets = [{'p': 405, 'n': 223}, {'p': 3, 'n': 422}, {'p': 109, 'n': 404}]
scores = {'acc': 0.4719, 'npv': 0.6253, 'f1p': 0.3091}
results = check_n_testsets_som_no_kfold(
testsets=testsets,
scores=scores,
eps=0.0001
)
results["inconsistency"]
# False
If one of the scores is slightly adjusted, for example, npv changed to 0.6263, the configuration becomes infeasible:
.. code-block:: Python
scores['npv'] = 0.6263
results = check_n_testsets_som_no_kfold(
testsets=testsets,
scores=scores,
eps=0.0001
)
results["inconsistency"]
# True
Similar tests are provided for the MoS aggregation as well, for further details see https://mlscorecheck.readthedocs.io/en/latest/.
In this scenario, scores are calculated in the MoS manner for each dataset, and then aggregated again across the datasets. Again, because of the averaging, only the four linear scores (acc, sens, spec, bacc) are supported. In the following example a consistent scenario is checked with three datasets and without score bounds specified at any level:
.. code-block:: Python
from mlscorecheck.check.binary import check_n_datasets_mos_known_folds_mos
evaluation0 = {
'dataset': {'p': 118, 'n': 95},
'folding': {'folds': [{'p': 22, 'n': 23}, {'p': 96, 'n': 72}]}
}
evaluation1 = {
'dataset': {'p': 781, 'n': 423},
'folding': {'folds': [{'p': 300, 'n': 200}, {'p': 481, 'n': 223}]}
}
evaluations = [evaluation0, evaluation1]
scores = {'acc': 0.61, 'sens': 0.709, 'spec': 0.461, 'bacc': 0.585}
result = check_n_datasets_mos_known_folds_mos(
evaluations=evaluations,
scores=scores,
eps=1e-3
)
result['inconsistency']
# False
Again, the details of the analysis are accessible under the lp_status and lp_configuration keys. Adding an adjustment to the scores (turning accuracy to 0.71), the configuration becomes infeasible:
.. code-block:: Python
scores = {'acc': 0.71, 'sens': 0.709, 'spec': 0.461}
result = check_n_datasets_mos_known_folds_mos(
evaluations=evaluations,
scores=scores,
eps=1e-3
)
result['inconsistency']
# True
If there are hints on the minimum and maximum scores across the datasets, one can add those bounds through the dataset_score_bounds parameter to strengthen the test.
Similar tests are provided for the SoM aggregation and the mixing of MoS and SoM aggregation, as well, for further details see https://mlscorecheck.readthedocs.io/en/latest/.
In many cases, it is not stated explicitly if stratification was applied or not, only the use of k-fold is phrased in papers. Not knowing the folding structure, the MoS aggregated tests cannot be used. However, if the cardinality of the minority class is not too big (a couple of dozens), then all potential k-fold configurations can be generated, and the MoS tests can be applied to each. If the scores are inconsistent with each, it means that no k-fold could result the scores. There are two functions supporting these exhaustive tests, one for the dataset level, and one for the experiment level.
Given a dataset and knowing that k-fold cross-validation was applied with MoS aggregation, but stratification is not mentioned, the following sample code demonstrates the use of the exhaustive test, with a consistent setup:
.. code-block:: Python
from mlscorecheck.check.binary import check_1_dataset_unknown_folds_mos
dataset = {'p': 126, 'n': 131}
folding = {'n_folds': 2, 'n_repeats': 1}
scores = {'acc': 0.573, 'sens': 0.768, 'bacc': 0.662}
result = check_1_dataset_unknown_folds_mos(
dataset=dataset,
folding=folding,
scores=scores,
eps=1e-3
)
result['inconsistency']
# False
If the balanced accuracy score is adjusted to 0.862, the configuration becomes infeasible:
.. code-block:: Python
scores = {'acc': 0.573, 'sens': 0.768, 'bacc': 0.862}
result = check_1_dataset_unknown_folds_mos(
dataset=dataset,
folding=folding,
scores=scores,
eps=1e-3
)
result['inconsistency']
# True
In the result of the tests, under the key details one can find the results for all possible fold combinations.
The following scenario is similar in the sense that MoS aggregation is applied to multiple datasets with unknown folding:
.. code-block:: Python
from mlscorecheck.check.binary import check_n_datasets_mos_unknown_folds_mos
evaluation0 = {
'dataset': {'p': 13, 'n': 73},
'folding': {'n_folds': 4, 'n_repeats': 1}
}
evaluation1 = {
'dataset': {'p': 7, 'n': 26},
'folding': {'n_folds': 3, 'n_repeats': 1}
}
evaluations = [evaluation0, evaluation1]
scores = {'acc': 0.357, 'sens': 0.323, 'spec': 0.362, 'bacc': 0.343}
result = check_n_datasets_mos_unknown_folds_mos(
evaluations=evaluations,
scores=scores,
eps=1e-3
)
result['inconsistency']
# False
The setup is consistent. However, if the balanced accuracy is changed to 0.9, the configuration becomes infeasible:
.. code-block:: Python
scores = {'acc': 0.357, 'sens': 0.323, 'spec': 0.362, 'bacc': 0.9}
result = check_n_datasets_mos_unknown_folds_mos(
evaluations=evaluations,
scores=scores,
eps=1e-3
)
result['inconsistency']
# True
The biggest challenge with aggregated scores is that the ways of aggregation at the dataset and experiment level are rarely disclosed explicitly. Even in this case the tools presented in the previous section can be used since there are hardly any further ways of meaningful averaging than (MoS on folds, MoS on datasets), (SoM on folds, MoS on datasets), (SoM on folds, SoM on datasets), hence, if a certain set of scores is inconsistent with each of these possibilities, one can safely say that the results do not satisfy the reasonable expectations.
In multiclass classification scenarios single testsets and k-fold cross-validation on a single dataset are supported with both the micro-averaging and macro-averaging aggregation strategies. The list of supported scores depends on the experimental setup, when applicable, all 20 scores listed for binary classification are supported, when the test operates in terms of linear programming, only accuracy, sensitivity, specificity and balanced accuracy are supported.
In a multiclass scenario, the commonly used approach is for measuring the performance of a classification technique is to calculate the micro or macro-averaged scores. In the micro-averaging approach, the confusion matrices of the individual classes are aggregated, and the scores are calculated from the aggregated confusion matrix. In the macro-averaging approach, the scores are calculated for each class, and the average of the scores is reported. The micro-averaging approach is more robust to class imbalance, however, it is not possible to estimate the standard deviation of the scores. The macro-averaging approach is more sensitive to class imbalance, but it is possible to estimate the standard deviation of the scores.
In this scenario, we suppose there is a multiclass classification testset and the class level scores on the testset are aggregated by micro-averaging. The test is based on exhaustive enumeration, so all 20 performance scores are supported. In the first example, we test an artificially generated, consistent scenario:
.. code-block:: Python
from mlscorecheck.check.multiclass import check_1_testset_no_kfold_micro
testset = {0: 10, 1: 100, 2: 80}
scores = {
'acc': 0.5158, 'sens': 0.2737, 'spec': 0.6368,
'bacc': 0.4553, 'ppv': 0.2737, 'npv': 0.6368
}
results = check_1_testset_no_kfold_micro(
testset=testset,
scores=scores,
eps=1e-4
)
results['inconsistency']
# False
As the test confirms, the setup is consistent. However, if one of the scores is adjusted a little, for example, accuracy is changed to 0.5258, the configuration becomes infeasible:
.. code-block:: Python
scores['acc'] = 0.5258
results = check_1_testset_no_kfold_micro(
testset=testset,
scores=scores,
eps=1e-4
)
results['inconsistency']
# True
Similar functionality is provided for macro-averaging, for further details see https://mlscorecheck.readthedocs.io/en/latest/.
In this scenario, we assume there is a multiclass classification dataset, which is evaluated in a k-fold cross-validation scenario, the class level scores are calculated by micro-averaging, and the fold level results are aggregated in the score of means fashion. The test is based on exhaustive enumeration, therefore, all 20 performance scores are supported.
In the first example, we test an artificially generated, consistent scenario:
.. code-block:: Python
from mlscorecheck.check.multiclass import check_1_dataset_known_folds_som_micro
dataset = {0: 86, 1: 96, 2: 59, 3: 105}
folding = {'folds': [{0: 43, 1: 48, 2: 30, 3: 52}, {0: 43, 1: 48, 2: 29, 3: 53}]}
scores = {'acc': 0.6272, 'sens': 0.2543, 'spec': 0.7514, 'f1p': 0.2543}
result = check_1_dataset_known_folds_som_micro(
dataset=dataset,
folding=folding,
scores=scores,
eps=1e-4
)
result['inconsistency']
# False
As the test confirms, the scenario is feasible. However, if one of the scores is adjusted a little, for example, sensitivity is changed to 0.2553, the configuration becomes infeasible:
.. code-block:: Python
scores['sens'] = 0.2553
result = check_1_dataset_known_folds_som_micro(
dataset=dataset,
folding=folding,
scores=scores,
eps=1e-4
)
result['inconsistency']
# True
Similar functionality is provided for mean of scores aggregation and macro averaging, for further details see https://mlscorecheck.readthedocs.io/en/latest/.
From the point of view of consistency testing, regression is the hardest problem as the predictions can produce any performance scores. The tests implemented in the package allow testing the relation of the mean squared error (mse), root mean squared error (rmse), mean average error (mae) and r^2 scores (r2).
In this scenario, we assume there is a regression testset, and the performance scores are calculated on the testset.
In the first example, we test an artificially generated, consistent scenario:
.. code-block:: Python
from mlscorecheck.check.regression import check_1_testset_no_kfold
var = 0.0831619 # the variance of the target values in the testset
n_samples = 100
scores = {'mae': 0.0254, 'r2': 0.9897}
result = check_1_testset_no_kfold(
var=var,
n_samples=n_samples,
scores=scores,
eps=1e-4
)
result['inconsistency']
# False
As the results show, there is no inconsistency detected. However, if the mae score is adjusted slightly to 0.03, the configuration becomes inconsistent:
.. code-block:: Python
scores['mae'] = 0.03
result = check_1_testset_no_kfold(
var=var,
n_samples=n_samples,
scores=scores,
eps=1e-4
)
result['inconsistency']
# True
Certain fields have unique, systematic and recurring problems in terms of evaluation methodologies. The aim of this part of the package is to provide bundles of consistency tests for the most typical scenarios of a field.
The list of currently supported problems, datasets and tests are summarized below, for more details see the documentation: https://mlscorecheck.readthedocs.io/en/latest/
The supported scenarios:
We kindly encourage any experts to provide further, field specific dataset and experiment specifications and test bundles to facilitate the reporting of clean and reproducible results in any field related to binary classification!
.. [RV] Kovács, G. and Fazekas, A.: "A new baseline for retinal vessel segmentation: Numerical identification and correction of methodological inconsistencies affecting 100+ papers", Medical Image Analysis, 2022(1), pp. 102300
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