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);
}
private static void UpdatePlayerRatings <TPlayer>(GameInfo gameInfo,
IDictionary <TPlayer, Rating> newPlayerRatings,
IDictionary <TPlayer, Rating> selfTeam,
IDictionary <TPlayer, Rating> otherTeam,
PairwiseComparison selfToOtherTeamComparison)
{
var drawMargin = DrawMargin.GetDrawMarginFromDrawProbability(gameInfo.DrawProbability, gameInfo.Beta);
var betaSquared = gameInfo.Beta * gameInfo.Beta;
var tauSquared = gameInfo.DynamicsFactor * gameInfo.DynamicsFactor;
var totalPlayers = selfTeam.Count() + otherTeam.Count();
var selfMeanSum = selfTeam.Values.Sum(r => r.Mean);
var otherTeamMeanSum = otherTeam.Values.Sum(r => r.Mean);
var c = Math.Sqrt(selfTeam.Values.Sum(r => r.StandardDeviation * r.StandardDeviation) +
otherTeam.Values.Sum(r => r.StandardDeviation * r.StandardDeviation) +
totalPlayers * betaSquared);
var winningMean = selfMeanSum;
var losingMean = otherTeamMeanSum;
if (selfToOtherTeamComparison == PairwiseComparison.Lose)
{
winningMean = otherTeamMeanSum;
losingMean = selfMeanSum;
}
var meanDelta = winningMean - losingMean;
double v, w, rankMultiplier;
if (selfToOtherTeamComparison != PairwiseComparison.Draw)
{
v = TruncatedGaussianCorrectionFunctions.VExceedsMargin(meanDelta, drawMargin, c);
w = TruncatedGaussianCorrectionFunctions.WExceedsMargin(meanDelta, drawMargin, c);
rankMultiplier = (int)selfToOtherTeamComparison;
}
else
{
v = TruncatedGaussianCorrectionFunctions.VWithinMargin(meanDelta, drawMargin, c);
w = TruncatedGaussianCorrectionFunctions.WWithinMargin(meanDelta, drawMargin, c);
rankMultiplier = 1;
}
foreach (var teamPlayerRatingPair in selfTeam)
{
Rating previousPlayerRating = teamPlayerRatingPair.Value;
var meanMultiplier = ((previousPlayerRating.StandardDeviation * previousPlayerRating.StandardDeviation) + tauSquared) / c;
var stdDevMultiplier = ((previousPlayerRating.StandardDeviation * previousPlayerRating.StandardDeviation) + tauSquared) / (c * c);
var playerMeanDelta = rankMultiplier * meanMultiplier * v;
var newMean = previousPlayerRating.Mean + playerMeanDelta;
var newStdDev = Math.Sqrt(((previousPlayerRating.StandardDeviation * previousPlayerRating.StandardDeviation) + tauSquared) * (1 - w * stdDevMultiplier));
newPlayerRatings[teamPlayerRatingPair.Key] = new Rating(newMean, newStdDev);
}
}
private static Rating CalculateNewRating(GameInfo gameInfo, Rating selfRating,
Rating opponentRating, PairwiseComparison comparison)
{
var drawMargin = DrawMargin.GetDrawMarginFromDrawProbability(gameInfo.DrawProbability, gameInfo.Beta);
var c = Math.Sqrt((selfRating.StandardDeviation * selfRating.StandardDeviation) +
(opponentRating.StandardDeviation * opponentRating.StandardDeviation) +
2 * (gameInfo.Beta * gameInfo.Beta));
var winningMean = selfRating.Mean;
var losingMean = opponentRating.Mean;
if (comparison == PairwiseComparison.Lose)
{
winningMean = opponentRating.Mean;
losingMean = selfRating.Mean;
}
var meanDelta = winningMean - losingMean;
double v;
double w;
double rankMultiplier;
if (comparison != PairwiseComparison.Draw)
{
v = TruncatedGaussianCorrectionFunctions.VExceedsMargin(meanDelta, drawMargin, c);
w = TruncatedGaussianCorrectionFunctions.WExceedsMargin(meanDelta, drawMargin, c);
rankMultiplier = (int)comparison;
}
else
{
v = TruncatedGaussianCorrectionFunctions.VWithinMargin(meanDelta, drawMargin, c);
w = TruncatedGaussianCorrectionFunctions.WWithinMargin(meanDelta, drawMargin, c);
rankMultiplier = 1;
}
var meanMultiplier = ((selfRating.StandardDeviation * selfRating.StandardDeviation) +
(gameInfo.DynamicsFactor * gameInfo.DynamicsFactor)) / c;
var varianceWithDynamics = (selfRating.StandardDeviation * selfRating.StandardDeviation) +
(gameInfo.DynamicsFactor * gameInfo.DynamicsFactor);
var stdDevMultiplier = varianceWithDynamics / (c * c);
var newMean = selfRating.Mean + (rankMultiplier * meanMultiplier * v);
var newStdDev = Math.Sqrt(varianceWithDynamics * (1 - w * stdDevMultiplier));
return(new Rating(newMean, newStdDev));
}
