/// <summary>
/// Tests that method
/// <see cref="RandomIndexPermutation.Next"/>
/// terminates successfully as expected.
/// </summary>
/// <param name="indexes">
/// The indexes to permute.
/// </param>
/// <param name="numberOfRandomPermutations">
/// The number of permutations to draw.
/// </param>
/// <param name="criticalValue">
/// A quantile of the chi-squared distribution with a number of
/// degrees of freedom equal to the <see cref="IndexCollection.Count"/>
/// of <paramref name="indexes"/>
/// minus <c>1</c>.
/// To serve as the critical value for the Pearson's
/// chi-squared test whose null hypothesis assume that the
/// the distinct possible permutations
/// are equiprobable.
/// </param>
/// <param name="delta">The required accuracy.
/// Defaults to <c>.01</c>.</param>
public static void Succeed(
IndexCollection indexes,
int numberOfRandomPermutations,
double criticalValue,
double delta = .01)
{
var randomPermutation = new RandomIndexPermutation(indexes);
// Generate permutations
var permutations = new IndexCollection[numberOfRandomPermutations];
for (int i = 0; i < numberOfRandomPermutations; i++)
{
permutations[i] = randomPermutation.Next();
}
// Check the number of distinct generated permutations
var permutationIdentifiers =
IndexCollection.Default(numberOfRandomPermutations - 1);
var actualDistinctPermutations =
IndexPartition.Create(
permutationIdentifiers,
(i) => { return(permutations[i]); });
int numberOfActualDistinctPermutations =
actualDistinctPermutations.Count;
Assert.AreEqual(
expected: SpecialFunctions.Factorial(indexes.Count),
actual: numberOfActualDistinctPermutations);
// Compute the actual permutation probabilities
DoubleMatrix actualPermutationProbabilities =
DoubleMatrix.Dense(
numberOfActualDistinctPermutations, 1);
int j = 0;
foreach (var identifier in actualDistinctPermutations.Identifiers)
{
actualPermutationProbabilities[j] =
(double)actualDistinctPermutations[identifier].Count
/
(double)numberOfRandomPermutations;
j++;
}
// Check that the Chebyshev Inequality holds true
// for each permutation probability
var expectedPermutationProbabilities =
DoubleMatrix.Dense(
numberOfActualDistinctPermutations,
1,
1.0
/
(double)numberOfActualDistinctPermutations);
for (int i = 0; i < numberOfActualDistinctPermutations; i++)
{
ProbabilityDistributionTest.CheckChebyshevInequality(
new BernoulliDistribution(expectedPermutationProbabilities[i]),
actualPermutationProbabilities[i],
numberOfRandomPermutations,
delta);
}
// Check how good the actual permutation probabilities fit
// the expected ones
ProbabilityDistributionTest.CheckGoodnessOfFit(
expectedPermutationProbabilities,
actualPermutationProbabilities,
criticalValue);
}
public void GetOptimalStateTest()
{
// valid input - random ties resolution
{
var context = new CategoricalEntailmentEnsembleOptimizationContext(
objectiveFunction:
(DoubleMatrix state) => { return(Double.PositiveInfinity); },
featureCategoryCounts: new List <int>(1)
{
6
},
numberOfResponseCategories: 4,
numberOfCategoricalEntailments: 1,
allowEntailmentPartialTruthValues: true,
probabilitySmoothingCoefficient: .9,
optimizationGoal: OptimizationGoal.Maximization,
minimumNumberOfIterations: 5,
maximumNumberOfIterations: 1000);
int numberOfEvaluations = 10000;
double delta = .01;
var parameter = DoubleMatrix.Dense(1, 10, new double[10] {
.5, .5, .5, .5, .5, .5, .25, .25, .25, .25
});
// Generate states
var states = new int[numberOfEvaluations];
var responseIndexes = IndexCollection.Range(6, 9);
for (int i = 0; i < numberOfEvaluations; i++)
{
var state = context.GetOptimalState(parameter);
states[i] = state.Vec(responseIndexes).FindNonzero()[0];
}
// Compute the actual inclusion probabilities
DoubleMatrix actualInclusionProbabilities =
DoubleMatrix.Dense(context.NumberOfResponseCategories, 1);
var stateIndexes = IndexCollection.Default(numberOfEvaluations - 1);
for (int j = 0; j < context.NumberOfResponseCategories; j++)
{
var samplesContainingCurrentUnit =
IndexPartition.Create(
stateIndexes,
(i) => { return(states[i] == j); });
actualInclusionProbabilities[j] =
(double)samplesContainingCurrentUnit[true].Count
/
(double)numberOfEvaluations;
}
// Check the number of distinct generated states
var distinctStates =
IndexPartition.Create(
states);
int numberOfDistinctStates =
distinctStates.Count;
Assert.AreEqual(
expected: context.NumberOfResponseCategories,
actual: numberOfDistinctStates);
// Check that the Chebyshev Inequality holds true
// for each inclusion probability
var expectedInclusionProbabilities =
DoubleMatrix.Dense(context.NumberOfResponseCategories, 1,
1.0 / context.NumberOfResponseCategories);
for (int j = 0; j < context.NumberOfResponseCategories; j++)
{
ProbabilityDistributionTest.CheckChebyshevInequality(
new BernoulliDistribution(expectedInclusionProbabilities[j]),
actualInclusionProbabilities[j],
numberOfEvaluations,
delta);
}
// Check how good the actual inclusion probabilities fit
// the expected ones
// The following assumes a number of response
// categories equal to 4.
//
// The quantile of order .9 for
// the chi-squared distribution having 4-1
// degrees of freedom is 6.251389
// (as from R function qchisq(.9, 3))
var goodnessOfFitCriticalValue = 6.251389;
ProbabilityDistributionTest.CheckGoodnessOfFit(
expectedInclusionProbabilities,
actualInclusionProbabilities,
goodnessOfFitCriticalValue);
}
}