/**
* Sends the factor-graph message with and returns the log-normalization constant.
*/
protected function sendMessageVariable(Message $message, Variable $variable)
{
$marginal = $variable->getValue();
$messageValue = $message->getValue();
$logZ = GaussianDistribution::logProductNormalization($marginal, $messageValue);
$variable->setValue(GaussianDistribution::multiply($marginal, $messageValue));
return $logZ;
}
public function testMultiplication()
{
// I verified this against the formula at http://www.tina-vision.net/tina-knoppix/tina-memo/2003-003.pdf
$standardNormal = new GaussianDistribution(0, 1);
$shiftedGaussian = new GaussianDistribution(2, 3);
$product = GaussianDistribution::multiply($standardNormal, $shiftedGaussian);
$this->assertEquals(0.2, $product->getMean(), '', GaussianDistributionTest::ERROR_TOLERANCE);
$this->assertEquals(3.0 / sqrt(10), $product->getStandardDeviation(), '', GaussianDistributionTest::ERROR_TOLERANCE);
$m4s5 = new GaussianDistribution(4, 5);
$m6s7 = new GaussianDistribution(6, 7);
$product2 = GaussianDistribution::multiply($m4s5, $m6s7);
$expectedMean = (4 * square(7) + 6 * square(5)) / (square(5) + square(7));
$this->assertEquals($expectedMean, $product2->getMean(), '', GaussianDistributionTest::ERROR_TOLERANCE);
$expectedSigma = sqrt(square(5) * square(7) / (square(5) + square(7)));
$this->assertEquals($expectedSigma, $product2->getStandardDeviation(), '', GaussianDistributionTest::ERROR_TOLERANCE);
}
private function updateHelper(Message $message1, Message $message2, Variable $variable1, Variable $variable2)
{
$message1Value = clone $message1->getValue();
$message2Value = clone $message2->getValue();
$marginal1 = clone $variable1->getValue();
$marginal2 = clone $variable2->getValue();
$a = $this->_precision / ($this->_precision + $marginal2->getPrecision() - $message2Value->getPrecision());
$newMessage = GaussianDistribution::fromPrecisionMean($a * ($marginal2->getPrecisionMean() - $message2Value->getPrecisionMean()), $a * ($marginal2->getPrecision() - $message2Value->getPrecision()));
$oldMarginalWithoutMessage = GaussianDistribution::divide($marginal1, $message1Value);
$newMarginal = GaussianDistribution::multiply($oldMarginalWithoutMessage, $newMessage);
// Update the message and marginal
$message1->setValue($newMessage);
$variable1->setValue($newMarginal);
// Return the difference in the new marginal
return GaussianDistribution::subtract($newMarginal, $marginal1);
}
protected function updateMessageVariable(Message &$message, Variable &$variable)
{
$oldMarginal = clone $variable->getValue();
$oldMessage = clone $message->getValue();
$messageFromVariable = GaussianDistribution::divide($oldMarginal, $oldMessage);
$c = $messageFromVariable->getPrecision();
$d = $messageFromVariable->getPrecisionMean();
$sqrtC = sqrt($c);
$dOnSqrtC = $d / $sqrtC;
$epsilonTimesSqrtC = $this->_epsilon * $sqrtC;
$d = $messageFromVariable->getPrecisionMean();
$denominator = 1.0 - TruncatedGaussianCorrectionFunctions::wWithinMargin($dOnSqrtC, $epsilonTimesSqrtC);
$newPrecision = $c / $denominator;
$newPrecisionMean = ($d + $sqrtC * TruncatedGaussianCorrectionFunctions::vWithinMargin($dOnSqrtC, $epsilonTimesSqrtC)) / $denominator;
$newMarginal = GaussianDistribution::fromPrecisionMean($newPrecisionMean, $newPrecision);
$newMessage = GaussianDistribution::divide(GaussianDistribution::multiply($oldMessage, $newMarginal), $oldMarginal);
// Update the message and marginal
$message->setValue($newMessage);
$variable->setValue($newMarginal);
// Return the difference in the new marginal
return GaussianDistribution::subtract($newMarginal, $oldMarginal);
}
private function updateHelper(array $weights, array $weightsSquared, array $messages, array $variables)
{
// Potentially look at http://mathworld.wolfram.com/NormalSumDistribution.html for clues as
// to what it's doing
$message0 = clone $messages[0]->getValue();
$marginal0 = clone $variables[0]->getValue();
// The math works out so that 1/newPrecision = sum of a_i^2 /marginalsWithoutMessages[i]
$inverseOfNewPrecisionSum = 0.0;
$anotherInverseOfNewPrecisionSum = 0.0;
$weightedMeanSum = 0.0;
$anotherWeightedMeanSum = 0.0;
$weightsSquaredLength = count($weightsSquared);
for ($i = 0; $i < $weightsSquaredLength; $i++) {
// These flow directly from the paper
$inverseOfNewPrecisionSum += $weightsSquared[$i] / ($variables[$i + 1]->getValue()->getPrecision() - $messages[$i + 1]->getValue()->getPrecision());
$diff = GaussianDistribution::divide($variables[$i + 1]->getValue(), $messages[$i + 1]->getValue());
$anotherInverseOfNewPrecisionSum += $weightsSquared[$i] / $diff->getPrecision();
$weightedMeanSum += $weights[$i] * ($variables[$i + 1]->getValue()->getPrecisionMean() - $messages[$i + 1]->getValue()->getPrecisionMean()) / ($variables[$i + 1]->getValue()->getPrecision() - $messages[$i + 1]->getValue()->getPrecision());
$anotherWeightedMeanSum += $weights[$i] * $diff->getPrecisionMean() / $diff->getPrecision();
}
$newPrecision = 1.0 / $inverseOfNewPrecisionSum;
$anotherNewPrecision = 1.0 / $anotherInverseOfNewPrecisionSum;
$newPrecisionMean = $newPrecision * $weightedMeanSum;
$anotherNewPrecisionMean = $anotherNewPrecision * $anotherWeightedMeanSum;
$newMessage = GaussianDistribution::fromPrecisionMean($newPrecisionMean, $newPrecision);
$oldMarginalWithoutMessage = GaussianDistribution::divide($marginal0, $message0);
$newMarginal = GaussianDistribution::multiply($oldMarginalWithoutMessage, $newMessage);
// Update the message and marginal
$messages[0]->setValue($newMessage);
$variables[0]->setValue($newMarginal);
// Return the difference in the new marginal
$finalDiff = GaussianDistribution::subtract($newMarginal, $marginal0);
return $finalDiff;
}
