/// <summary>
/// Gets the average row of a parameter matrix excluding the feature contribution.
/// </summary>
/// <param name="entityParameterVectors">
/// The matrix of parameters.
/// Each row of the matrix is expected to be the parameter vector of a given user or item.
/// </param>
/// <param name="weights">The feature weights.</param>
/// <param name="features">The feature values.</param>
/// <returns>The average user/item parameter vector excluding the feature contribution.</returns>
private static GaussianArray GetAverageParameterVectorExcludingFeatureContribution(
GaussianMatrix entityParameterVectors, GaussianMatrix weights, SparseFeatureMatrix features)
{
Debug.Assert(entityParameterVectors.Count > 0, "The number of entities must be positive.");
return(new GaussianArray(
entityParameterVectors[0].Count,
i => GetAverageParameterExcludingFeatureContribution(entityParameterVectors.Select(x => x[i]), weights[i], features)));
}
/// <summary>
/// Computes the average parameter of an array of user/item parameters
/// excluding the feature contribution for the users or items.
/// </summary>
/// <param name="entityParameters">The array of user/item parameters to get the average of.</param>
/// <param name="weights">The feature weights of each user/item.</param>
/// <param name="features">The feature values of each user/item.</param>
/// <returns>The average parameter distribution excluding feature contributions.</returns>
private static Gaussian GetAverageParameterExcludingFeatureContribution(
IEnumerable <Gaussian> entityParameters,
IList <Gaussian> weights,
SparseFeatureMatrix features)
{
var adjustedEntityParameters = entityParameters.Select((gaussian, i) =>
DoublePlusOp.AAverageConditional(gaussian, ComputeFeatureContribution(weights, features.NonZeroFeatureValues[i], features.NonZeroFeatureIndices[i])));
return(GetAverageParameter(adjustedEntityParameters));
}
/// <summary>
/// Gets the parameter distributions of the average item.
/// </summary>
/// <param name="parameterDistributions">The learned posterior parameter distributions.</param>
/// <param name="itemFeatures">The item features.</param>
/// <returns>The average item parameter distributions.</returns>
public static ItemParameterDistribution GetAverageItemParameters(
ParameterDistributions parameterDistributions, SparseFeatureMatrix itemFeatures)
{
GaussianArray traitDistribution;
Gaussian biasDistribution;
GetAverageTraitsAndBiases(
parameterDistributions.ItemTraitDistribution,
parameterDistributions.ItemBiasDistribution,
parameterDistributions.ItemFeature.TraitWeights,
parameterDistributions.ItemFeature.BiasWeights,
itemFeatures,
out traitDistribution,
out biasDistribution);
return(new ItemParameterDistribution(traitDistribution, biasDistribution));
}
/// <summary>
/// Gets the parameter distributions of the average user.
/// </summary>
/// <param name="parameterDistributions">The learned posterior parameter distributions.</param>
/// <param name="userFeatures">The user features.</param>
/// <returns>The average user parameter distributions.</returns>
public static UserParameterDistribution GetAverageUserParameters(
ParameterDistributions parameterDistributions, SparseFeatureMatrix userFeatures)
{
GaussianArray traitDistribution;
Gaussian biasDistribution;
GaussianArray thresholdDistribution = GetAverageParameterVector(parameterDistributions.UserThresholdDistribution);
GetAverageTraitsAndBiases(
parameterDistributions.UserTraitDistribution,
parameterDistributions.UserBiasDistribution,
parameterDistributions.UserFeature.TraitWeights,
parameterDistributions.UserFeature.BiasWeights,
userFeatures,
out traitDistribution,
out biasDistribution);
return(new UserParameterDistribution(traitDistribution, biasDistribution, thresholdDistribution));
}
/// <summary>
/// Gets the average traits and biases amongst all users or items.
/// </summary>
/// <param name="traits">The user/item traits.</param>
/// <param name="biases">The user/item biases.</param>
/// <param name="traitFeatureWeights">The feature weights for the traits.</param>
/// <param name="biasFeatureWeights">The feature weights for the biases.</param>
/// <param name="featureValues">The feature values of all users/items.</param>
/// <param name="averageTraits">The resulting average traits.</param>
/// <param name="averageBias">The resulting average bias.</param>
/// <remarks>
/// When features are used, this method will exclude the feature contribution when computing the average.
/// Therefore, the feature contribution for a given user/item has to be then added at prediction time.
/// </remarks>
private static void GetAverageTraitsAndBiases(
GaussianMatrix traits,
GaussianArray biases,
GaussianMatrix traitFeatureWeights,
GaussianArray biasFeatureWeights,
SparseFeatureMatrix featureValues,
out GaussianArray averageTraits,
out Gaussian averageBias)
{
if (featureValues.FeatureCount == 0)
{
averageTraits = GetAverageParameterVector(traits);
averageBias = GetAverageParameter(biases);
}
else
{
averageTraits = GetAverageParameterVectorExcludingFeatureContribution(traits, traitFeatureWeights, featureValues);
averageBias = GetAverageParameterExcludingFeatureContribution(biases, biasFeatureWeights, featureValues);
}
}