/**
* @param Observations $observations
* @param array $coefficients
* @return array
*/
protected function calculateGradient(Observations $observations, array $coefficients) : array
{
$gradient = array_fill(0, count($observations->getObservation(0)->getFeatures()), 0.0);
$batchElementIndices = (array) array_rand(range(0, count($observations) - 1), $this->batchSize);
foreach ($batchElementIndices as $index) {
$observation = $observations->getObservation($index);
$observationGradient = $this->gradient->gradient($coefficients, $observation->getFeatures(), $observation->getOutcome());
foreach ($observationGradient as $i => $observationSlope) {
$gradient[$i] += $observationSlope / $this->batchSize;
}
}
return $gradient;
}
public function testGetObservation()
{
$observations = Observations::fromArray(static::$features, static::$outcomes);
$observation = $observations->getObservation(0);
static::assertEquals(static::$features[0], $observation->getFeatures());
static::assertEquals(static::$outcomes[0], $observation->getOutcome());
}
/**
* @return Observations
*/
private function getLogisticObservations()
{
// Data from http://statistics.ats.ucla.edu/stat/r/dae/logit.htm
$observations = new Observations();
$csv = fopen(__DIR__ . '/../../fixtures/logistic.csv', 'r');
fgetcsv($csv);
// Throw away headers.
while ($line = fgetcsv($csv)) {
// Split composite feature, since the school rank isn't actually an interval value.
$rank2 = $line[3] == 2 ? 1 : 0;
$rank3 = $line[3] == 3 ? 1 : 0;
$rank4 = $line[3] == 4 ? 1 : 0;
// Normalize the GRE score. This is critical to get convergence.
$gre = $line[1] / 100;
// [1, GRE, GPA, Rank2, Rank3, Rank4], Admitted
$observations->add([1, $gre, $line[2], $rank2, $rank3, $rank4], (double) $line[0]);
}
fclose($csv);
return $observations;
}
/**
* Calculates the standard error of each of the regression coefficients.
*
* @return array
*/
public function getStandardErrorCoefficients() : array
{
if (is_null($this->SCoefficients)) {
$design = new Matrix($this->observations->getFeatures());
$inverted = $design->transpose()->multiplyMatrix($design)->inverse();
$diagonalVector = [];
for ($i = 0, $size = $inverted->getRowCount(); $i < $size; $i++) {
$diagonalVector[] = $inverted->get($i, $i);
}
$this->SCoefficients = (new Matrix([$diagonalVector]))->multiplyScalar($this->getMeanSquaredError())->map(function ($element) {
return sqrt($element);
})->toArray()[0];
}
return $this->SCoefficients;
}
public function testStatistics()
{
$observations = Observations::fromArray($this->getFeatures(), $this->getOutcomes());
$coefficients = [1.0954970633022, 0.92451598868827];
$predictor = new LinearPredictor($coefficients);
$statisticsGatherer = new LinearStatisticsGatherer($observations, $coefficients, $predictor);
static::assertEquals(4, $statisticsGatherer->getDegreesOfFreedomTotal());
static::assertEquals(3, $statisticsGatherer->getDegreesOfFreedomError());
static::assertEquals(1, $statisticsGatherer->getDegreesOfFreedomModel());
static::assertEquals(1.94, round($statisticsGatherer->getFStatistic(), 2));
static::assertEquals(0.39, round($statisticsGatherer->getRSquared(), 2));
$stdErrorCoefficients = $statisticsGatherer->getStandardErrorCoefficients();
static::assertEquals(1.51, round($stdErrorCoefficients[0], 2));
static::assertEquals(0.66, round($stdErrorCoefficients[1], 2));
static::assertEquals(1.42, round($statisticsGatherer->getStandardError(), 2));
$tStatistics = $statisticsGatherer->getTStatistics();
static::assertEquals(0.73, round($tStatistics[0], 2));
static::assertEquals(1.39, round($tStatistics[1], 2));
}
/**
* @param Observations $observations
* @param array $coefficients
* @return array
*/
protected function calculateGradient(Observations $observations, array $coefficients) : array
{
$observation = $observations->getObservation(mt_rand(0, count($observations) - 1));
return $this->gradient->gradient($coefficients, $observation->getFeatures(), $observation->getOutcome());
}
public function testTooFewObservations()
{
static::setExpectedException('InvalidArgumentException');
$regression = new LeastSquares();
$regression->regress(Observations::fromArray([[1, 1]], [1]));
}
/**
* @param Observations $observations
* @return array
*/
public final function regress(Observations $observations) : array
{
$coefficients = array_fill(0, $observations->getFeatureCount(), 0.0);
do {
$gradient = $this->calculateGradient($observations, $coefficients);
$this->schedule->update($gradient);
$coefficients = $this->updateCoefficients($coefficients, $gradient);
} while (!$this->stoppingCriteria->converged($gradient, $coefficients));
return $coefficients;
}
/**
* @param Observations $observations
* @return array
* @throws InvalidArgumentException
*/
public function regress(Observations $observations) : array
{
$design = new Matrix($observations->getFeatures());
$observed = (new Matrix([$observations->getOutcomes()]))->transpose();
if ($design->getRowCount() < $design->getColumnCount()) {
throw new InvalidArgumentException('Not enough observations to perform regression. You need to have more observations than explanatory variables.');
}
$designTranspose = $design->transpose();
$prediction = $designTranspose->multiplyMatrix($design)->inverse()->multiplyMatrix($designTranspose->multiplyMatrix($observed));
return $prediction->transpose()->toArray()[0];
}
/**
* @param Observations $observations
* @param array $coefficients
* @return array
*/
protected function calculateGradient(Observations $observations, array $coefficients) : array
{
$gradient = array_fill(0, count($observations->getObservation(0)->getFeatures()), 0.0);
$batchSize = count($observations);
/** @var Observation $observation */
foreach ($observations as $observation) {
$observationGradient = $this->gradient->gradient($coefficients, $observation->getFeatures(), $observation->getOutcome());
foreach ($observationGradient as $i => $observationSlope) {
$gradient[$i] += $observationSlope / $batchSize;
}
}
return $gradient;
}
