Why Naive Bayes works

MNIST: probabilistic digit classification (Naive Bayes)

MNIST case with RubixML GaussianNB

Run the RubixML version to train GaussianNB on the same toy samples and predict a new normalized image.

Example of use


                
<?php

use app\classes\MnistLoader;
use Rubix\ML\Classifiers\GaussianNB;
use Rubix\ML\CrossValidation\Metrics\Accuracy;
use Rubix\ML\Datasets\Labeled;
use Rubix\ML\Datasets\Unlabeled;
use Rubix\ML\Extractors\CSV;

try {
    // Build the training and test datasets from the filtered CSV rows.
    $trainRows = MnistLoader::loadIterable('train.csv', categoricalLabels: true, normalize: true, digits: [0, 1]);
    $testRows = MnistLoader::loadIterable('test.csv', categoricalLabels: true, normalize: true, digits: [0, 1]);

    $dataset = Labeled::fromIterator($trainRows);
    $testDataset = Labeled::fromIterator($testRows);
} catch (Exception $e) {
    echo '<div class="alert alert-danger" role="alert">' . htmlspecialchars($e->getMessage(), ENT_QUOTES, 'UTF-8') . '</div>';
    exit;
}

$model = new GaussianNB();
$model->train($dataset);

$predictions = [];
$testingLabels = $testDataset->labels();

foreach ($testDataset->samples() as $i => $x) {
    $prediction = $model->predict(new Unlabeled([$x]))[0];
    $predictions[] = $prediction;
}

$metric = new Accuracy();
$score = $metric->score($predictions, $testingLabels);

echo 'Train samples handled: ' . number_format($dataset->numSamples()) . PHP_EOL;
echo 'Test samples handled: ' . number_format($testDataset->numSamples()) . PHP_EOL . PHP_EOL;
echo 'Accuracy: ' . round($score * 100, 2) . '%';

Sample of digit: 0

Predicted digit: 0

Sample of digit: 1

Predicted digit: 1

Result: Memory: 0 Mb Time running: < 0.001 sec.


                Train samples handled: 12,666
Test samples handled: 2,116

Accuracy: 99.15%

RubixML returns the predicted class label for the new sample. Because the data and assumption are the same, the result should almost identical to the pure PHP implementation.