ML::ROCFunctions

This blog post proclaims and describes the Raku package “ML::ROCFunctions”, [AAp0], that facilitates the utilization of 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].

This package has counterparts in Mathematica, Python, and R. See [AAp1, AAp2, AAp3].

The examples below use the packages “Data::Generators”, [AAp4, AA3], “Data::Reshapers”, [AAp5], and “Data::Summarizers”, [AAp6], 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:

{perl6, eval=FALSE} {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)

# +--------------+--------------+
# | Predicted    | Actual       |
# +--------------+--------------+
# | true  => 103 | false => 106 |
# | false => 97  | true  => 94  |
# +--------------+--------------+

Here is a sample of the dataset:

use Data::Reshapers;
to-pretty-table(@dfRandomLabels.pick(6))

# +-----------+--------+
# | Predicted | Actual |
# +-----------+--------+
# |   false   | false  |
# |    true   | false  |
# |   false   |  true  |
# |   false   | false  |
# |    true   | false  |
# |   false   |  true  |
# +-----------+--------+

Here we make the corresponding ROC hash-map:

to-roc-hash('true', 'false', @dfRandomLabels.map({$_<Actual>}), @dfRandomLabels.map({$_<Predicted>}))

# {FalseNegative => 49, FalsePositive => 58, TrueNegative => 48, TruePositive => 45}

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)

# +--------------+-----------------+--------------+
# | Predicted    | Threshold       | Actual       |
# +--------------+-----------------+--------------+
# | true  => 105 | Min    => 0.2   | false => 107 |
# | false => 95  | 1st-Qu => 0.2   | true  => 93  |
# |              | Mean   => 0.402 |              |
# |              | 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 0.4 =>
# +---------------+-------------+-------------+
# | Threshold     | Actual      | Predicted   |
# +---------------+-------------+-------------+
# | Min    => 0.4 | false => 37 | true  => 36 |
# | 1st-Qu => 0.4 | true  => 35 | false => 36 |
# | Mean   => 0.4 |             |             |
# | Median => 0.4 |             |             |
# | 3rd-Qu => 0.4 |             |             |
# | Max    => 0.4 |             |             |
# +---------------+-------------+-------------+
# summary of 0.6 =>
# +-------------+---------------+-------------+
# | Actual      | Threshold     | Predicted   |
# +-------------+---------------+-------------+
# | true  => 33 | Min    => 0.6 | false => 33 |
# | false => 32 | 1st-Qu => 0.6 | true  => 32 |
# |             | Mean   => 0.6 |             |
# |             | Median => 0.6 |             |
# |             | 3rd-Qu => 0.6 |             |
# |             | Max    => 0.6 |             |
# +-------------+---------------+-------------+
# summary of 0.2 =>
# +---------------+-------------+-------------+
# | Threshold     | Actual      | Predicted   |
# +---------------+-------------+-------------+
# | Min    => 0.2 | false => 38 | true  => 37 |
# | 1st-Qu => 0.2 | true  => 25 | false => 26 |
# | 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 => 19, FalsePositive => 20, TrueNegative => 17, TruePositive => 16}
# {FalseNegative => 15, FalsePositive => 14, TrueNegative => 18, TruePositive => 18}
# {FalseNegative => 11, FalsePositive => 23, TrueNegative => 15, TruePositive => 14}

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);

# +----------+-----------+----------+----------+----------+----------+
# |   ACC    |    MCC    |   NPV    |   PPV    |   TPR    |   SPC    |
# +----------+-----------+----------+----------+----------+----------+
# | 0.458333 | -0.083398 | 0.472222 | 0.444444 | 0.457143 | 0.459459 |
# | 0.553846 |  0.107970 | 0.545455 | 0.562500 | 0.545455 | 0.562500 |
# | 0.460317 | -0.045894 | 0.576923 | 0.378378 | 0.560000 | 0.394737 |
# +----------+-----------+----------+----------+----------+----------+

ROC plots

Often classifiers are evaluated using ROC curves of FPR-vs-TPR. Here is a plot made with Mathematica using the Mathematica-to-Raku connection described in [AA4]:

ROC-curver-for-Tries-classifier-over-Titanic-data