public GaussianPriorFactor(double mean, double variance, Variable <GaussianDistribution> variable)
: base(string.Format("Prior value going to {0}", variable))
{
mNewMessage = new GaussianDistribution(mean, Math.Sqrt(variance));
CreateVariableToMessageBinding(variable,
new Message <GaussianDistribution>(GaussianDistribution.FromPrecisionMean(0, 0), "message from {0} to {1}", this, variable));
}
protected override double UpdateMessage(Message <GaussianDistribution> message, Variable <GaussianDistribution> variable)
{
var oldMarginal = variable.Value.Clone();
var oldMessage = message.Value.Clone();
var messageFromVar = oldMarginal / oldMessage;
var c = messageFromVar.Precision;
var d = messageFromVar.PrecisionMean;
var sqrtC = Math.Sqrt(c);
var dOnSqrtC = d / sqrtC;
var epsilonTimesSqrtC = mEpsilon * sqrtC;
d = messageFromVar.PrecisionMean;
var denom = 1.0 - TruncatedGaussianCorrectionFunctions.WExceedsMargin(dOnSqrtC, epsilonTimesSqrtC);
var newPrecision = c / denom;
var newPrecisionMean = (d + sqrtC * TruncatedGaussianCorrectionFunctions.VExceedsMargin(dOnSqrtC, epsilonTimesSqrtC)) / denom;
var newMarginal = GaussianDistribution.FromPrecisionMean(newPrecisionMean, newPrecision);
var newMessage = oldMessage * newMarginal / oldMarginal;
message.Value = newMessage;
variable.Value = newMarginal;
return(newMarginal - oldMarginal);
}
protected override double UpdateMessage(Message <GaussianDistribution> message, Variable <GaussianDistribution> variable)
{
var oldMarginal = variable.Value.Clone();
var oldMessage = message;
var newMarginal = GaussianDistribution.FromPrecisionMean(
oldMarginal.PrecisionMean + mNewMessage.PrecisionMean - oldMessage.Value.PrecisionMean,
oldMarginal.Precision + mNewMessage.Precision - oldMessage.Value.Precision);
variable.Value = newMarginal;
message.Value = mNewMessage;
return(oldMarginal - newMarginal);
}
public TrueSkillFactorGraph(GameInfo gameInfo, IEnumerable <IDictionary <TPlayer, Rating> > teams, int[] teamRanks)
{
mPriorLayer = new PlayerPriorValuesToSkillsLayer <TPlayer>(this, teams);
GameInfo = gameInfo;
VariableFactory = new VariableFactory <GaussianDistribution>(() => GaussianDistribution.FromPrecisionMean(0, 0));
mLayers = new List <FactorGraphLayerBase <GaussianDistribution> >
{
mPriorLayer,
new PlayerSkillsToPerformancesLayer <TPlayer>(this),
new PlayerPerformancesToTeamPerformancesLayer <TPlayer>(this),
new IteratedTeamDifferencesInnerLayer <TPlayer>(
this,
new TeamPerformancesToTeamPerformanceDifferencesLayer <TPlayer>(this),
new TeamDifferencesComparisonLayer <TPlayer>(this, teamRanks))
};
}
/// <summary>
/// Get a partial update of a rating.
/// </summary>
/// <param name="prior">The rating before adjustment.</param>
/// <param name="fullPosterior">The rating after adjustment.</param>
/// <param name="updatePercentage">The percentage of the update to apply.</param>
/// <returns>The resulting rating after a partial update.</returns>
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);
var precisionDifference = posteriorGaussian.Precision - priorGaussian.Precision;
var partialPrecisionDifference = updatePercentage * precisionDifference;
var precisionMeanDifference = posteriorGaussian.PrecisionMean - priorGaussian.PrecisionMean;
double partialPrecisionMeanDifference = updatePercentage * precisionMeanDifference;
GaussianDistribution partialPosteriorGaussian = GaussianDistribution.FromPrecisionMean(
priorGaussian.PrecisionMean + partialPrecisionMeanDifference,
priorGaussian.Precision + partialPrecisionDifference);
return(new Rating(partialPosteriorGaussian.Mean, partialPosteriorGaussian.StandardDeviation,
prior.mConservativeStandardDeviationMultiplier));
}
private double UpdateHelper(double[] weights, double[] weightsSquared,
IList <Message <GaussianDistribution> > messages,
IList <Variable <GaussianDistribution> > variables)
{
var message0 = messages[0].Value.Clone();
var marginal0 = variables[0].Value.Clone();
var inverseOfNewPrecisionSum = 0.0;
var anotherInverseOfNewPrecisionSum = 0.0;
var weightedMeanSum = 0.0;
var anotherWeightedMeanSum = 0.0;
for (var i = 0; i < weightsSquared.Length; ++i)
{
inverseOfNewPrecisionSum += weightsSquared[i] /
(variables[i + 1].Value.Precision - messages[i + 1].Value.Precision);
var 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;
}
var newPrecision = 1.0 / inverseOfNewPrecisionSum;
var anotherNewPrecision = 1.0 / anotherInverseOfNewPrecisionSum;
var newPrecisionMean = newPrecision * weightedMeanSum;
var anotherNewPrecisionMean = anotherNewPrecision * anotherWeightedMeanSum;
var newMessage = GaussianDistribution.FromPrecisionMean(newPrecisionMean, newPrecision);
var oldMarginalWithoutMessage = marginal0 / message0;
var newMarginal = oldMarginalWithoutMessage * newMessage;
messages[0].Value = newMessage;
variables[0].Value = newMarginal;
return(newMarginal - marginal0);
}
private double UpdateHelper(Message <GaussianDistribution> message1, Message <GaussianDistribution> message2,
Variable <GaussianDistribution> variable1, Variable <GaussianDistribution> variable2)
{
var message1Value = message1.Value.Clone();
var message2Value = message2.Value.Clone();
var marginal1 = variable1.Value.Clone();
var marginal2 = variable2.Value.Clone();
var a = mPrecision / (mPrecision + marginal2.Precision - message2Value.Precision);
var newMessage = GaussianDistribution.FromPrecisionMean(
a * (marginal2.PrecisionMean - message2Value.PrecisionMean),
a * (marginal2.Precision - message2Value.Precision));
var oldMarginalWithoutMessage = marginal1 / message1Value;
var newMarginal = oldMarginalWithoutMessage * newMessage;
message1.Value = newMessage;
variable1.Value = newMarginal;
return(newMarginal - marginal1);
}
