private double UpdateHelper(Message <GaussianDistribution> message1, Message <GaussianDistribution> message2,
Variable <GaussianDistribution> variable1, Variable <GaussianDistribution> variable2)
{
GaussianDistribution message1Value = message1.Value.Clone();
GaussianDistribution message2Value = message2.Value.Clone();
GaussianDistribution marginal1 = variable1.Value.Clone();
GaussianDistribution marginal2 = variable2.Value.Clone();
double a = _Precision / (_Precision + marginal2.Precision - message2Value.Precision);
GaussianDistribution newMessage = GaussianDistribution.FromPrecisionMean(
a * (marginal2.PrecisionMean - message2Value.PrecisionMean),
a * (marginal2.Precision - message2Value.Precision));
GaussianDistribution oldMarginalWithoutMessage = marginal1 / message1Value;
GaussianDistribution newMarginal = oldMarginalWithoutMessage * newMessage;
/// Update the message and marginal
message1.Value = newMessage;
variable1.Value = newMarginal;
/// Return the difference in the new marginal
return(newMarginal - marginal1);
}
protected override double UpdateMessage(Message <GaussianDistribution> message,
Variable <GaussianDistribution> variable)
{
GaussianDistribution oldMarginal = variable.Value.Clone();
GaussianDistribution oldMessage = message.Value.Clone();
GaussianDistribution messageFromVariable = oldMarginal / oldMessage;
double c = messageFromVariable.Precision;
double d = messageFromVariable.PrecisionMean;
double sqrtC = Math.Sqrt(c);
double dOnSqrtC = d / sqrtC;
double epsilonTimesSqrtC = _Epsilon * sqrtC;
d = messageFromVariable.PrecisionMean;
double denominator = 1.0 - TruncatedGaussianCorrectionFunctions.WWithinMargin(dOnSqrtC, epsilonTimesSqrtC);
double newPrecision = c / denominator;
double newPrecisionMean = (d +
sqrtC *
TruncatedGaussianCorrectionFunctions.VWithinMargin(dOnSqrtC, epsilonTimesSqrtC)) /
denominator;
GaussianDistribution newMarginal = GaussianDistribution.FromPrecisionMean(newPrecisionMean, newPrecision);
GaussianDistribution newMessage = oldMessage * newMarginal / oldMarginal;
/// Update the message and marginal
message.Value = newMessage;
variable.Value = newMarginal;
/// Return the difference in the new marginal
return(newMarginal - oldMarginal);
}
public GaussianPriorFactor(double mean, double variance, Variable <GaussianDistribution> variable)
: base(String.Format("Prior value going to {0}", variable))
{
_NewMessage = new GaussianDistribution(mean, Math.Sqrt(variance));
CreateVariableToMessageBinding(variable,
new Message <GaussianDistribution>(
GaussianDistribution.FromPrecisionMean(0, 0), "message from {0} to {1}",
this, variable));
}
private double UpdateHelper(double[] weights, double[] weightsSquared,
IList <Message <GaussianDistribution> > messages,
IList <Variable <GaussianDistribution> > variables)
{
// Potentially look at http://mathworld.wolfram.com/NormalSumDistribution.html for clues as
// to what it's doing
GaussianDistribution message0 = messages[0].Value.Clone();
GaussianDistribution marginal0 = variables[0].Value.Clone();
// The math works out so that 1/newPrecision = sum of a_i^2 /marginalsWithoutMessages[i]
double inverseOfNewPrecisionSum = 0.0;
double anotherInverseOfNewPrecisionSum = 0.0;
double weightedMeanSum = 0.0;
double anotherWeightedMeanSum = 0.0;
for (int i = 0; i < weightsSquared.Length; i++)
{
// These flow directly from the paper
inverseOfNewPrecisionSum += weightsSquared[i] /
(variables[i + 1].Value.Precision - messages[i + 1].Value.Precision);
GaussianDistribution diff = (variables[i + 1].Value / messages[i + 1].Value);
anotherInverseOfNewPrecisionSum += weightsSquared[i] / diff.Precision;
weightedMeanSum += weights[i]
*
(variables[i + 1].Value.PrecisionMean - messages[i + 1].Value.PrecisionMean)
/
(variables[i + 1].Value.Precision - messages[i + 1].Value.Precision);
anotherWeightedMeanSum += weights[i] * diff.PrecisionMean / diff.Precision;
}
double newPrecision = 1.0 / inverseOfNewPrecisionSum;
double anotherNewPrecision = 1.0 / anotherInverseOfNewPrecisionSum;
double newPrecisionMean = newPrecision * weightedMeanSum;
double anotherNewPrecisionMean = anotherNewPrecision * anotherWeightedMeanSum;
GaussianDistribution newMessage = GaussianDistribution.FromPrecisionMean(newPrecisionMean, newPrecision);
GaussianDistribution oldMarginalWithoutMessage = marginal0 / message0;
GaussianDistribution newMarginal = oldMarginalWithoutMessage * newMessage;
/// Update the message and marginal
messages[0].Value = newMessage;
variables[0].Value = newMarginal;
/// Return the difference in the new marginal
return(newMarginal - marginal0);
}
protected override double UpdateMessage(Message <GaussianDistribution> message,
Variable <GaussianDistribution> variable)
{
GaussianDistribution oldMarginal = variable.Value.Clone();
Message <GaussianDistribution> oldMessage = message;
GaussianDistribution newMarginal =
GaussianDistribution.FromPrecisionMean(
oldMarginal.PrecisionMean + _NewMessage.PrecisionMean - oldMessage.Value.PrecisionMean,
oldMarginal.Precision + _NewMessage.Precision - oldMessage.Value.Precision);
variable.Value = newMarginal;
message.Value = _NewMessage;
return(oldMarginal - newMarginal);
}
public TrueSkillFactorGraph(GameInfo gameInfo, IEnumerable <IDictionary <TPlayer, Rating> > teams, int[] teamRanks)
{
_PriorLayer = new PlayerPriorValuesToSkillsLayer <TPlayer>(this, teams);
GameInfo = gameInfo;
VariableFactory =
new VariableFactory <GaussianDistribution>(() => GaussianDistribution.FromPrecisionMean(0, 0));
_Layers = new List <FactorGraphLayerBase <GaussianDistribution> >
{
_PriorLayer,
new PlayerSkillsToPerformancesLayer <TPlayer>(this),
new PlayerPerformancesToTeamPerformancesLayer <TPlayer>(this),
new IteratedTeamDifferencesInnerLayer <TPlayer>(
this,
new TeamPerformancesToTeamPerformanceDifferencesLayer <TPlayer>(this),
new TeamDifferencesComparisonLayer <TPlayer>(this, teamRanks))
};
}
public static Rating GetPartialUpdate(Rating prior, Rating fullPosterior, double updatePercentage)
{
var priorGaussian = new GaussianDistribution(prior.Mean, prior.StandardDeviation);
var posteriorGaussian = new GaussianDistribution(fullPosterior.Mean, fullPosterior.StandardDeviation);
// From a clarification email from Ralf Herbrich:
// "the idea is to compute a linear interpolation between the prior and posterior skills of each player
// ... in the canonical space of parameters"
double precisionDifference = posteriorGaussian.Precision - priorGaussian.Precision;
double partialPrecisionDifference = updatePercentage * precisionDifference;
double precisionMeanDifference = posteriorGaussian.PrecisionMean - priorGaussian.PrecisionMean;
double partialPrecisionMeanDifference = updatePercentage * precisionMeanDifference;
GaussianDistribution partialPosteriorGaussion = GaussianDistribution.FromPrecisionMean(
priorGaussian.PrecisionMean + partialPrecisionMeanDifference,
priorGaussian.Precision + partialPrecisionDifference);
return(new Rating(partialPosteriorGaussion.Mean, partialPosteriorGaussion.StandardDeviation,
prior._ConservativeStandardDeviationMultiplier));
}