/// <summary>
/// Computes the expected component-wise product of a confusion matrix and a loss matrix.
/// </summary>
/// <param name="instanceSource">The instance source providing the ground truth (used to compute the expected confusion matrix).</param>
/// <param name="predictions">
/// A sparse users-by-items matrix of predicted rating distributions (used to compute the expected confusion matrix).
/// </param>
/// <param name="lossMatrix">The loss matrix.</param>
/// <param name="aggregationMethod">
/// A method specifying how metrics are aggregated over all instances (used to compute the expected confusion matrix).</param>
/// <returns>The computed expected weighted confusion.</returns>
public double ExpectedWeightedConfusion(
TInstanceSource instanceSource,
IDictionary <TUser, IDictionary <TItem, Discrete> > predictions,
RatingMatrix lossMatrix,
RecommenderMetricAggregationMethod aggregationMethod = RecommenderMetricAggregationMethod.Default)
{
RatingMatrix confusionMatrix = this.ExpectedConfusionMatrix(instanceSource, predictions, aggregationMethod);
return(RatingMatrix.ComponentwiseProduct(confusionMatrix, lossMatrix));
}
/// <summary>
/// Generates a loss matrix from a given loss function.
/// </summary>
/// <param name="minRating">The minimum rating.</param>
/// <param name="maxRating">The maximum rating.</param>
/// <param name="lossFunc">The loss function, which operates on index pairs.</param>
/// <returns>The generated loss matrix.</returns>
private static RatingMatrix LossMatrix(int minRating, int maxRating, Func <int, int, double> lossFunc)
{
var result = new RatingMatrix(minRating, maxRating);
for (int i = 1; i <= maxRating; ++i)
{
for (int j = 1; j <= maxRating; ++j)
{
result[i, j] = lossFunc(i, j);
}
}
return(result);
}
/// <summary>
/// Computes the component-wise products of two rating matrices.
/// </summary>
/// <param name="lhs">The left-hand side matrix.</param>
/// <param name="rhs">The right-hand side matrix.</param>
/// <returns>The sum of the products of the corresponding elements of the two matrices.</returns>
public static double ComponentwiseProduct(RatingMatrix lhs, RatingMatrix rhs)
{
if (lhs.MinRating != rhs.MinRating || lhs.MaxRating != rhs.MaxRating)
{
throw new ArgumentException("The given matrices are incompatible!");
}
double result = 0;
for (int i = lhs.MinRating; i <= lhs.MaxRating; ++i)
{
for (int j = lhs.MinRating; j <= lhs.MaxRating; ++j)
{
result += lhs[i, j] * rhs[i, j];
}
}
return(result);
}
/// <summary>
/// Computes the expected confusion matrix.
/// </summary>
/// <param name="instanceSource">The instance source providing the ground truth.</param>
/// <param name="predictions">A sparse users-by-items matrix of predicted rating distributions.</param>
/// <param name="aggregationMethod">A method specifying how metrics are aggregated over all instances.</param>
/// <returns>The computed expected confusion matrix.</returns>
public RatingMatrix ExpectedConfusionMatrix(
TInstanceSource instanceSource,
IDictionary <TUser, IDictionary <TItem, Discrete> > predictions,
RecommenderMetricAggregationMethod aggregationMethod = RecommenderMetricAggregationMethod.Default)
{
IStarRatingInfo <TGroundTruthRating> starRatingInfo = this.mapping.GetRatingInfo(instanceSource);
var result = new RatingMatrix(starRatingInfo.MinStarRating, starRatingInfo.MaxStarRating);
for (int predictedRating = starRatingInfo.MinStarRating; predictedRating <= starRatingInfo.MaxStarRating; ++predictedRating)
{
for (int trueRating = starRatingInfo.MinStarRating; trueRating <= starRatingInfo.MaxStarRating; ++trueRating)
{
result[predictedRating, trueRating] = this.ModelDomainRatingPredictionMetricExpectation(
instanceSource,
predictions,
(p, t) => p == predictedRating && t == trueRating ? 1.0 : 0.0,
aggregationMethod);
}
}
return(result);
}