protected function updateMessageVariable(Message $message, Variable $variable)
{
$oldMarginal = clone $variable->getValue();
$oldMessage = $message;
$newMarginal = GaussianDistribution::fromPrecisionMean($oldMarginal->getPrecisionMean() + $this->_newMessage->getPrecisionMean() - $oldMessage->getValue()->getPrecisionMean(), $oldMarginal->getPrecision() + $this->_newMessage->getPrecision() - $oldMessage->getValue()->getPrecision());
$variable->setValue($newMarginal);
$newMessage = $this->_newMessage;
$message->setValue($newMessage);
return GaussianDistribution::subtract($oldMarginal, $newMarginal);
}
public function __construct(GameInfo &$gameInfo, array &$teams, array $teamRanks)
{
$this->_priorLayer = new PlayerPriorValuesToSkillsLayer($this, $teams);
$this->_gameInfo = $gameInfo;
$newFactory = new VariableFactory(function () {
return GaussianDistribution::fromPrecisionMean(0, 0);
});
$this->setVariableFactory($newFactory);
$this->_layers = array($this->_priorLayer, new PlayerSkillsToPerformancesLayer($this), new PlayerPerformancesToTeamPerformancesLayer($this), new IteratedTeamDifferencesInnerLayer($this, new TeamPerformancesToTeamPerformanceDifferencesLayer($this), new TeamDifferencesComparisonLayer($this, $teamRanks)));
}
public function testAbsoluteDifference()
{
// Verified with Ralf Herbrich's F# implementation
$standardNormal = new GaussianDistribution(0, 1);
$absDiff = GaussianDistribution::absoluteDifference($standardNormal, $standardNormal);
$this->assertEquals(0.0, $absDiff, '', GaussianDistributionTest::ERROR_TOLERANCE);
$m1s2 = new GaussianDistribution(1, 2);
$m3s4 = new GaussianDistribution(3, 4);
$absDiff2 = GaussianDistribution::absoluteDifference($m1s2, $m3s4);
$this->assertEquals(0.4330127018922193, $absDiff2, '', GaussianDistributionTest::ERROR_TOLERANCE);
}
public static function getDrawMarginFromDrawProbability($drawProbability, $beta)
{
// Derived from TrueSkill technical report (MSR-TR-2006-80), page 6
// draw probability = 2 * CDF(margin/(sqrt(n1+n2)*beta)) -1
// implies
//
// margin = inversecdf((draw probability + 1)/2) * sqrt(n1+n2) * beta
// n1 and n2 are the number of players on each team
$margin = GaussianDistribution::inverseCumulativeTo(0.5 * ($drawProbability + 1), 0, 1) * sqrt(1 + 1) * $beta;
return $margin;
}
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);
}
public function createVariableToMessageBinding(Variable $variable)
{
$newDistribution = GaussianDistribution::fromPrecisionMean(0, 0);
$binding = parent::createVariableToMessageBindingWithMessage($variable, new Message($newDistribution, sprintf("message from %s to %s", $this, $variable)));
return $binding;
}
public function getPlayerWinProbability(GameInfo $gameInfo, $playerRating, $opponentRating)
{
$ratingDifference = $playerRating - $opponentRating;
// See equation 1.1 in the TrueSkill paper
return GaussianDistribution::cumulativeTo($ratingDifference / (sqrt(2) * $gameInfo->getBeta()));
}
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 $finalDiff;
}
public static function wWithinMargin($teamPerformanceDifference, $drawMargin)
{
$teamPerformanceDifferenceAbsoluteValue = abs($teamPerformanceDifference);
$denominator = GaussianDistribution::cumulativeTo($drawMargin - $teamPerformanceDifferenceAbsoluteValue) - GaussianDistribution::cumulativeTo(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue);
if ($denominator < 2.222758749E-162) {
return 1.0;
}
$vt = self::vWithinMargin($teamPerformanceDifferenceAbsoluteValue, $drawMargin);
return $vt * $vt + (($drawMargin - $teamPerformanceDifferenceAbsoluteValue) * GaussianDistribution::at($drawMargin - $teamPerformanceDifferenceAbsoluteValue) - (-$drawMargin - $teamPerformanceDifferenceAbsoluteValue) * GaussianDistribution::at(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue)) / $denominator;
}
