Raku Land

ML::ROCFunctions

zef:antononcube

ML::ROCFunctions

This repository has the code of a Raku package for Receiver Operating Characteristic (ROC) functions.

The ROC framework is used for analysis and tuning of binary classifiers, [Wk1]. (The classifiers are assumed to classify into a positive/true label or a negative/false label. )

For computational introduction to ROC utilization (in Mathematica) see the article "Basic example of using ROC with Linear regression", [AA1].

The examples below use the packages "Data::Generators", "Data::Reshapers", and "Data::Summarizers", described in the article "Introduction to data wrangling with Raku", [AA2].


Installation

Via zef-ecosystem:

zef install ML::ROCFunctions

From GitHub:

zef install https://github.com/antononcube/Raku-ML-ROCFunctions

Usage examples

Properties

Here are some retrieval functions:

use ML::ROCFunctions;
say roc-functions('properties');
# (FunctionInterpretations FunctionNames Functions Methods Properties)
roc-functions('FunctionInterpretations')
# {ACC => accuracy, AUROC => area under the ROC curve, Accuracy => same as ACC, F1 => F1 score, FDR => false discovery rate, FNR => false negative rate, FOR => false omission rate, FPR => false positive rate, MCC => Matthews correlation coefficient, NPV => negative predictive value, PPV => positive predictive value, Precision => same as PPV, Recall => same as TPR, SPC => specificity, Sensitivity => same as TPR, TNR => true negative rate, TPR => true positive rate}
say roc-functions('FPR');
# &FPR

Single ROC record

Definition: A ROC record (ROC-hash or ROC-hash-map) is an object of type Associative that has the keys: "FalseNegative", "FalsePositive", "TrueNegative", "TruePositive". Here is an example:

{FalseNegative => 50, FalsePositive => 51, TrueNegative => 60, TruePositive => 39}

Here we generate a random "dataset" with columns "Actual" and "Predicted" that have the values "true" and "false" and show the summary:

use Data::Generators;
use Data::Summarizers;
my @dfRandomLabels = random-tabular-dataset(200, <Actual Predicted>, generators=>{Actual => <true false>, Predicted => <true false>});
records-summary(@dfRandomLabels)
# +--------------+--------------+
# | Actual       | Predicted    |
# +--------------+--------------+
# | true  => 107 | true  => 101 |
# | false => 93  | false => 99  |
# +--------------+--------------+

Here is a sample of the dataset:

use Data::Reshapers;
to-pretty-table(@dfRandomLabels.pick(6))
# +--------+-----------+
# | Actual | Predicted |
# +--------+-----------+
# | false  |    true   |
# | false  |    true   |
# | false  |   false   |
# | false  |   false   |
# |  true  |   false   |
# |  true  |    true   |
# +--------+-----------+

Here we make the corresponding ROC hash-map:

to-roc-hash('true', 'false', @dfRandomLabels.map({$_<Actual>}), @dfRandomLabels.map({$_<Predicted>}))
# {FalseNegative => 54, FalsePositive => 48, TrueNegative => 45, TruePositive => 53}

Multiple ROC records

Here we make random dataset with entries that associated with a certain threshold parameter with three unique values:

my @dfRandomLabels2 = random-tabular-dataset(200, <Threshold Actual Predicted>, generators=>{Threshold => (0.2, 0.4, 0.6), Actual => <true false>, Predicted => <true false>});
records-summary(@dfRandomLabels2)
# +--------------+--------------+-----------------+
# | Actual       | Predicted    | Threshold       |
# +--------------+--------------+-----------------+
# | false => 101 | false => 109 | Min    => 0.2   |
# | true  => 99  | true  => 91  | 1st-Qu => 0.2   |
# |              |              | Mean   => 0.399 |
# |              |              | Median => 0.4   |
# |              |              | 3rd-Qu => 0.6   |
# |              |              | Max    => 0.6   |
# +--------------+--------------+-----------------+

Remark: Threshold parameters are typically used while tuning Machine Learning (ML) classifiers.

Here we group the rows of the dataset by the unique threshold values:

my %groups = group-by(@dfRandomLabels2, 'Threshold');
records-summary(%groups)
# summary of 0.6 =>
# +---------------+-------------+-------------+
# | Threshold     | Predicted   | Actual      |
# +---------------+-------------+-------------+
# | Min    => 0.6 | false => 44 | false => 35 |
# | 1st-Qu => 0.6 | true  => 21 | true  => 30 |
# | Mean   => 0.6 |             |             |
# | Median => 0.6 |             |             |
# | 3rd-Qu => 0.6 |             |             |
# | Max    => 0.6 |             |             |
# +---------------+-------------+-------------+
# summary of 0.4 =>
# +---------------+-------------+-------------+
# | Threshold     | Predicted   | Actual      |
# +---------------+-------------+-------------+
# | Min    => 0.4 | true  => 37 | false => 35 |
# | 1st-Qu => 0.4 | false => 32 | true  => 34 |
# | Mean   => 0.4 |             |             |
# | Median => 0.4 |             |             |
# | 3rd-Qu => 0.4 |             |             |
# | Max    => 0.4 |             |             |
# +---------------+-------------+-------------+
# summary of 0.2 =>
# +---------------+-------------+-------------+
# | Threshold     | Predicted   | Actual      |
# +---------------+-------------+-------------+
# | Min    => 0.2 | true  => 33 | true  => 35 |
# | 1st-Qu => 0.2 | false => 33 | false => 31 |
# | Mean   => 0.2 |             |             |
# | Median => 0.2 |             |             |
# | 3rd-Qu => 0.2 |             |             |
# | Max    => 0.2 |             |             |
# +---------------+-------------+-------------+

Here we find and print the ROC records (hash-maps) for each unique threshold value:

my @rocs = do for %groups.kv -> $k, $v { 
  to-roc-hash('true', 'false', $v.map({$_<Actual>}), $v.map({$_<Predicted>})) 
}
.say for @rocs;
# {FalseNegative => 18, FalsePositive => 9, TrueNegative => 26, TruePositive => 12}
# {FalseNegative => 16, FalsePositive => 19, TrueNegative => 16, TruePositive => 18}
# {FalseNegative => 20, FalsePositive => 18, TrueNegative => 13, TruePositive => 15}

Application of ROC functions

Here we define a list of ROC functions:

my @funcs = (&PPV, &NPV, &TPR, &ACC, &SPC, &MCC);
# [&PPV &NPV &TPR &ACC &SPC &MCC]

Here we apply each ROC function to each of the ROC records obtained above:

my @rocRes = @rocs.map( -> $r { @funcs.map({ $_.name => $_($r) }).Hash });
say to-pretty-table(@rocRes);
# +-----------+----------+----------+----------+----------+----------+
# |    MCC    |   ACC    |   PPV    |   SPC    |   TPR    |   NPV    |
# +-----------+----------+----------+----------+----------+----------+
# |  0.152075 | 0.584615 | 0.571429 | 0.742857 | 0.400000 | 0.590909 |
# | -0.013481 | 0.492754 | 0.486486 | 0.457143 | 0.529412 | 0.500000 |
# | -0.152080 | 0.424242 | 0.454545 | 0.419355 | 0.428571 | 0.393939 |
# +-----------+----------+----------+----------+----------+----------+

References

Articles

[Wk1] Wikipedia entry, "Receiver operating characteristic".

[AA1] Anton Antonov, "Basic example of using ROC with Linear regression", (2016), MathematicaForPrediction at WordPress.

[AA2] Anton Antonov, "Introduction to data wrangling with Raku", (2021), RakuForPrediction at WordPress.

Packages

[AAp1] Anton Antonov, ROCFunctions Mathematica package, (2016-2022), MathematicaForPrediction at GitHub/antononcube.

[AAp2] Anton Antonov, ROCFunctions R package, (2021), R-packages at GitHub/antononcube.

[AAp3] Anton Antonov, Data::Generators Raku package, (2021), GitHub/antononcube.

[AAp4] Anton Antonov, Data::Reshapers Raku package, (2021), GitHub/antononcube.

[AAp5] Anton Antonov, Data::Summarizers Raku package, (2021), GitHub/antononcube.