284 lines
8.7 KiB
PHP
284 lines
8.7 KiB
PHP
<?php
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declare(strict_types=1);
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namespace Phpml\Classification\Linear;
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use Closure;
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use Exception;
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use Phpml\Exception\InvalidArgumentException;
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use Phpml\Helper\Optimizer\ConjugateGradient;
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class LogisticRegression extends Adaline
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{
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/**
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* Batch training: Gradient descent algorithm (default)
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*/
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public const BATCH_TRAINING = 1;
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/**
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* Online training: Stochastic gradient descent learning
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*/
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public const ONLINE_TRAINING = 2;
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/**
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* Conjugate Batch: Conjugate Gradient algorithm
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*/
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public const CONJUGATE_GRAD_TRAINING = 3;
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/**
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* Cost function to optimize: 'log' and 'sse' are supported <br>
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* - 'log' : log likelihood <br>
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* - 'sse' : sum of squared errors <br>
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*
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* @var string
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*/
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protected $costFunction = 'log';
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/**
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* Regularization term: only 'L2' is supported
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*
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* @var string
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*/
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protected $penalty = 'L2';
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/**
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* Lambda (λ) parameter of regularization term. If λ is set to 0, then
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* regularization term is cancelled.
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*
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* @var float
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*/
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protected $lambda = 0.5;
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/**
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* Initalize a Logistic Regression classifier with maximum number of iterations
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* and learning rule to be applied <br>
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*
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* Maximum number of iterations can be an integer value greater than 0 <br>
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* If normalizeInputs is set to true, then every input given to the algorithm will be standardized
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* by use of standard deviation and mean calculation <br>
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*
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* Cost function can be 'log' for log-likelihood and 'sse' for sum of squared errors <br>
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*
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* Penalty (Regularization term) can be 'L2' or empty string to cancel penalty term
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*
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* @throws InvalidArgumentException
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*/
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public function __construct(
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int $maxIterations = 500,
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bool $normalizeInputs = true,
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int $trainingType = self::CONJUGATE_GRAD_TRAINING,
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string $cost = 'log',
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string $penalty = 'L2'
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) {
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$trainingTypes = range(self::BATCH_TRAINING, self::CONJUGATE_GRAD_TRAINING);
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if (!in_array($trainingType, $trainingTypes, true)) {
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throw new InvalidArgumentException(
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'Logistic regression can only be trained with '.
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'batch (gradient descent), online (stochastic gradient descent) '.
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'or conjugate batch (conjugate gradients) algorithms'
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);
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}
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if (!in_array($cost, ['log', 'sse'], true)) {
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throw new InvalidArgumentException(
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"Logistic regression cost function can be one of the following: \n".
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"'log' for log-likelihood and 'sse' for sum of squared errors"
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);
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}
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if ($penalty !== '' && strtoupper($penalty) !== 'L2') {
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throw new InvalidArgumentException('Logistic regression supports only \'L2\' regularization');
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}
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$this->learningRate = 0.001;
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parent::__construct($this->learningRate, $maxIterations, $normalizeInputs);
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$this->trainingType = $trainingType;
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$this->costFunction = $cost;
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$this->penalty = $penalty;
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}
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/**
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* Sets the learning rate if gradient descent algorithm is
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* selected for training
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*/
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public function setLearningRate(float $learningRate): void
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{
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$this->learningRate = $learningRate;
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}
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/**
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* Lambda (λ) parameter of regularization term. If 0 is given,
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* then the regularization term is cancelled
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*/
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public function setLambda(float $lambda): void
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{
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$this->lambda = $lambda;
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}
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/**
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* Adapts the weights with respect to given samples and targets
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* by use of selected solver
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*
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* @throws \Exception
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*/
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protected function runTraining(array $samples, array $targets): void
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{
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$callback = $this->getCostFunction();
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switch ($this->trainingType) {
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case self::BATCH_TRAINING:
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$this->runGradientDescent($samples, $targets, $callback, true);
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return;
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case self::ONLINE_TRAINING:
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$this->runGradientDescent($samples, $targets, $callback, false);
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return;
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case self::CONJUGATE_GRAD_TRAINING:
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$this->runConjugateGradient($samples, $targets, $callback);
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return;
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default:
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// Not reached
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throw new Exception(sprintf('Logistic regression has invalid training type: %d.', $this->trainingType));
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}
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}
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/**
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* Executes Conjugate Gradient method to optimize the weights of the LogReg model
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*/
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protected function runConjugateGradient(array $samples, array $targets, Closure $gradientFunc): void
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{
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if ($this->optimizer === null) {
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$this->optimizer = (new ConjugateGradient($this->featureCount))
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->setMaxIterations($this->maxIterations);
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}
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$this->weights = $this->optimizer->runOptimization($samples, $targets, $gradientFunc);
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$this->costValues = $this->optimizer->getCostValues();
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}
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/**
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* Returns the appropriate callback function for the selected cost function
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*
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* @throws \Exception
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*/
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protected function getCostFunction(): Closure
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{
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$penalty = 0;
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if ($this->penalty === 'L2') {
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$penalty = $this->lambda;
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}
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switch ($this->costFunction) {
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case 'log':
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/*
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* Negative of Log-likelihood cost function to be minimized:
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* J(x) = ∑( - y . log(h(x)) - (1 - y) . log(1 - h(x)))
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*
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* If regularization term is given, then it will be added to the cost:
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* for L2 : J(x) = J(x) + λ/m . w
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*
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* The gradient of the cost function to be used with gradient descent:
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* ∇J(x) = -(y - h(x)) = (h(x) - y)
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*/
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return function ($weights, $sample, $y) use ($penalty): array {
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$this->weights = $weights;
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$hX = $this->output($sample);
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// In cases where $hX = 1 or $hX = 0, the log-likelihood
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// value will give a NaN, so we fix these values
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if ($hX == 1) {
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$hX = 1 - 1e-10;
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}
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if ($hX == 0) {
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$hX = 1e-10;
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}
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$y = $y < 0 ? 0 : 1;
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$error = -$y * log($hX) - (1 - $y) * log(1 - $hX);
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$gradient = $hX - $y;
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return [$error, $gradient, $penalty];
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};
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case 'sse':
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/*
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* Sum of squared errors or least squared errors cost function:
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* J(x) = ∑ (y - h(x))^2
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*
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* If regularization term is given, then it will be added to the cost:
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* for L2 : J(x) = J(x) + λ/m . w
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*
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* The gradient of the cost function:
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* ∇J(x) = -(h(x) - y) . h(x) . (1 - h(x))
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*/
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return function ($weights, $sample, $y) use ($penalty): array {
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$this->weights = $weights;
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$hX = $this->output($sample);
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$y = $y < 0 ? 0 : 1;
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$error = (($y - $hX) ** 2);
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$gradient = -($y - $hX) * $hX * (1 - $hX);
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return [$error, $gradient, $penalty];
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};
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default:
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// Not reached
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throw new Exception(sprintf('Logistic regression has invalid cost function: %s.', $this->costFunction));
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}
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}
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/**
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* Returns the output of the network, a float value between 0.0 and 1.0
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*/
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protected function output(array $sample): float
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{
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$sum = parent::output($sample);
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return 1.0 / (1.0 + exp(-$sum));
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}
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/**
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* Returns the class value (either -1 or 1) for the given input
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*/
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protected function outputClass(array $sample): int
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{
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$output = $this->output($sample);
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if ($output > 0.5) {
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return 1;
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}
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return -1;
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}
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/**
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* Returns the probability of the sample of belonging to the given label.
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*
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* The probability is simply taken as the distance of the sample
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* to the decision plane.
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*
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* @param mixed $label
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*/
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protected function predictProbability(array $sample, $label): float
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{
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$sample = $this->checkNormalizedSample($sample);
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$probability = $this->output($sample);
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if (array_search($label, $this->labels, true) > 0) {
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return $probability;
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}
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return 1 - $probability;
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}
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}
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