Implement first regression scoring function UnivariateLinearRegression
This commit is contained in:
Arkadiusz Kondas
parent
fbf84ca95f
commit
9e5b3a0c69
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@ -0,0 +1,81 @@
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<?php
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declare(strict_types=1);
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namespace Phpml\FeatureSelection\ScoringFunction;
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use Phpml\FeatureSelection\ScoringFunction;
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use Phpml\Math\Matrix;
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use Phpml\Math\Statistic\Mean;
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/**
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* Quick linear model for testing the effect of a single regressor,
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* sequentially for many regressors.
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*
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* This is done in 2 steps:
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*
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* 1. The cross correlation between each regressor and the target is computed,
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* that is, ((X[:, i] - mean(X[:, i])) * (y - mean_y)) / (std(X[:, i]) *std(y)).
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* 2. It is converted to an F score then to a p-value.
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*
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* Ported from scikit-learn f_regression function (http://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.f_regression.html#sklearn.feature_selection.f_regression)
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*/
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final class UnivariateLinearRegression implements ScoringFunction
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{
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/**
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* @var bool
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*/
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private $center;
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/**
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* @param bool $center - if true samples and targets will be centered
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*/
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public function __construct(bool $center = true)
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{
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$this->center = $center;
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}
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public function score(array $samples, array $targets): array
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{
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if ($this->center) {
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$this->centerTargets($targets);
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$this->centerSamples($samples);
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}
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$correlations = [];
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foreach ($samples[0] as $index => $feature) {
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$featureColumn = array_column($samples, $index);
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$correlations[$index] =
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(Matrix::dot($targets, $featureColumn)[0] / (new Matrix($featureColumn, false))->transpose()->frobeniusNorm())
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/ (new Matrix($targets, false))->frobeniusNorm();
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}
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$degreesOfFreedom = count($targets) - ($this->center ? 2 : 1);
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return array_map(function (float $correlation) use ($degreesOfFreedom): float {
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return $correlation ** 2 / (1 - $correlation ** 2) * $degreesOfFreedom;
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}, $correlations);
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}
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private function centerTargets(&$targets): void
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{
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$mean = Mean::arithmetic($targets);
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foreach ($targets as &$target) {
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$target -= $mean;
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}
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}
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private function centerSamples(&$samples): void
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{
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$means = [];
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foreach ($samples[0] as $index => $feature) {
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$means[$index] = Mean::arithmetic(array_column($samples, $index));
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}
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foreach ($samples as &$sample) {
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foreach ($sample as $index => &$feature) {
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$feature -= $means[$index];
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}
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}
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}
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}
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@ -236,6 +236,29 @@ class Matrix
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return $this->getDeterminant() == 0;
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}
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/**
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* Frobenius norm (Hilbert–Schmidt norm, Euclidean norm) (‖A‖F)
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* Square root of the sum of the square of all elements.
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*
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* https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
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*
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* _____________
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* /ᵐ ⁿ
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* ‖A‖F = √ Σ Σ |aᵢⱼ|²
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* ᵢ₌₁ ᵢ₌₁
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*/
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public function frobeniusNorm(): float
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{
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$squareSum = 0;
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for ($i = 0; $i < $this->rows; ++$i) {
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for ($j = 0; $j < $this->columns; ++$j) {
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$squareSum += ($this->matrix[$i][$j]) ** 2;
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}
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}
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return sqrt($squareSum);
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}
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/**
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* Returns the transpose of given array
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*/
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@ -259,7 +282,7 @@ class Matrix
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/**
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* Element-wise addition or substraction depending on the given sign parameter
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*/
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protected function _add(self $other, int $sign = 1): self
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private function _add(self $other, int $sign = 1): self
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{
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$a1 = $this->toArray();
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$a2 = $other->toArray();
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@ -277,7 +300,7 @@ class Matrix
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/**
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* Returns diagonal identity matrix of the same size of this matrix
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*/
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protected function getIdentity(): self
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private function getIdentity(): self
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{
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$array = array_fill(0, $this->rows, array_fill(0, $this->columns, 0));
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for ($i = 0; $i < $this->rows; ++$i) {
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@ -0,0 +1,29 @@
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<?php
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declare(strict_types=1);
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namespace Phpml\Tests\FeatureSelection\ScoringFunction;
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use Phpml\FeatureSelection\ScoringFunction\UnivariateLinearRegression;
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use PHPUnit\Framework\TestCase;
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final class UnivariateLinearRegressionTest extends TestCase
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{
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public function testRegressionScore(): void
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{
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$samples = [[73676, 1996], [77006, 1998], [10565, 2000], [146088, 1995], [15000, 2001], [65940, 2000], [9300, 2000], [93739, 1996], [153260, 1994], [17764, 2002], [57000, 1998], [15000, 2000]];
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$targets = [2000, 2750, 15500, 960, 4400, 8800, 7100, 2550, 1025, 5900, 4600, 4400];
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$function = new UnivariateLinearRegression();
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self::assertEquals([6.97286, 6.48558], $function->score($samples, $targets), '', 0.0001);
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}
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public function testRegressionScoreWithoutCenter(): void
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{
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$samples = [[73676, 1996], [77006, 1998], [10565, 2000], [146088, 1995], [15000, 2001], [65940, 2000], [9300, 2000], [93739, 1996], [153260, 1994], [17764, 2002], [57000, 1998], [15000, 2000]];
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$targets = [2000, 2750, 15500, 960, 4400, 8800, 7100, 2550, 1025, 5900, 4600, 4400];
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$function = new UnivariateLinearRegression(false);
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self::assertEquals([1.74450, 18.08347], $function->score($samples, $targets), '', 0.0001);
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}
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}
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@ -8,6 +8,7 @@ use Phpml\Dataset\Demo\IrisDataset;
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use Phpml\Exception\InvalidArgumentException;
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use Phpml\Exception\InvalidOperationException;
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use Phpml\FeatureSelection\ScoringFunction\ANOVAFValue;
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use Phpml\FeatureSelection\ScoringFunction\UnivariateLinearRegression;
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use Phpml\FeatureSelection\SelectKBest;
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use PHPUnit\Framework\TestCase;
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@ -45,6 +46,21 @@ final class SelectKBestTest extends TestCase
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self::assertEquals(2, count($samples[0]));
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}
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public function testSelectKBestWithRegressionScoring(): void
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{
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$samples = [[73676, 1996, 2], [77006, 1998, 5], [10565, 2000, 4], [146088, 1995, 2], [15000, 2001, 2], [65940, 2000, 2], [9300, 2000, 2], [93739, 1996, 2], [153260, 1994, 2], [17764, 2002, 2], [57000, 1998, 2], [15000, 2000, 2]];
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$targets = [2000, 2750, 15500, 960, 4400, 8800, 7100, 2550, 1025, 5900, 4600, 4400];
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$selector = new SelectKBest(new UnivariateLinearRegression(), 2);
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$selector->fit($samples, $targets);
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$selector->transform($samples);
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self::assertEquals(
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[[73676, 1996], [77006, 1998], [10565, 2000], [146088, 1995], [15000, 2001], [65940, 2000], [9300, 2000], [93739, 1996], [153260, 1994], [17764, 2002], [57000, 1998], [15000, 2000]],
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$samples
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);
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}
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public function testThrowExceptionOnEmptyTargets(): void
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{
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$this->expectException(InvalidArgumentException::class);
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@ -251,4 +251,55 @@ class MatrixTest extends TestCase
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$dot = [6, 12];
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$this->assertEquals($dot, Matrix::dot($matrix2, $matrix1));
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}
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/**
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* @dataProvider dataProviderForFrobeniusNorm
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*/
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public function testFrobeniusNorm(array $matrix, float $norm): void
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{
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$matrix = new Matrix($matrix);
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$this->assertEquals($norm, $matrix->frobeniusNorm(), '', 0.0001);
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}
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public function dataProviderForFrobeniusNorm()
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{
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return [
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[
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[
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[1, -7],
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[2, 3],
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], 7.93725,
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],
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[
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[
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[1, 2, 3],
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[2, 3, 4],
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[3, 4, 5],
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], 9.643651,
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],
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[
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[
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[1, 5, 3, 9],
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[2, 3, 4, 12],
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[4, 2, 5, 11],
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], 21.330729,
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],
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[
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[
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[1, 5, 3],
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[2, 3, 4],
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[4, 2, 5],
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[6, 6, 3],
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], 13.784049,
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],
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[
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[
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[5, -4, 2],
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[-1, 2, 3],
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[-2, 1, 0],
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], 8,
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],
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];
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}
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}
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