public double[][] Estimate(AlphaBetaTransitionProbabiltyMatrixParameters <TDistribution> parameters)
{
if (_estimatedTransitionProbabilityMatrix != null)
{
return(_estimatedTransitionProbabilityMatrix);
}
var T = parameters.Observations.Length;
_estimatedTransitionProbabilityMatrix = new double[parameters.Model.N][];
for (var i = 0; i < parameters.Model.N; i++)
{
_estimatedTransitionProbabilityMatrix[i] = new double[parameters.Model.N];
for (var j = 0; j < parameters.Model.N; j++)
{
double nominator = (parameters.Normalized) ? double.NaN : 0.0d, denominator = (parameters.Normalized) ? double.NaN : 0.0d;
for (var t = 0; t < T - 1; t++)
{
var probability = parameters.Model.Emission[j].ProbabilityDensityFunction(parameters.Observations[t + 1]);
if (parameters.Normalized)
{
nominator = LogExtention.eLnSum(nominator, LogExtention.eLnProduct(parameters.Weights[t], LogExtention.eLnProduct(parameters.Alpha[t][i], LogExtention.eLnProduct(LogExtention.eLn(parameters.Model.TransitionProbabilityMatrix[i][j]), LogExtention.eLnProduct(LogExtention.eLn(probability), parameters.Beta[t + 1][j])))));
denominator = LogExtention.eLnSum(denominator, LogExtention.eLnProduct(parameters.Weights[t], LogExtention.eLnProduct(parameters.Alpha[t][i], parameters.Beta[t][j])));
}
else
{
nominator += parameters.Weights[t] * parameters.Alpha[t][i] * parameters.Model.TransitionProbabilityMatrix[i][j] * probability * parameters.Beta[t + 1][j];
denominator += parameters.Weights[t] * parameters.Alpha[t][i] * parameters.Beta[t][j];
}
}
_estimatedTransitionProbabilityMatrix[i][j] = CalculateTransitionProbabilityMatrixEntry(nominator, denominator, parameters.Normalized);
}
}
return(_estimatedTransitionProbabilityMatrix);
}
public void Estimate_AlphaBetaParameters_TransitionProbabilityMatrixCalculatedAndReturned()
{
const int numberOfStates = 2;
var util = new TestDataUtils();
var observations = util.GetSvcData(util.FTSEFilePath, new DateTime(2010, 12, 18), new DateTime(2011, 12, 18));
var model = HiddenMarkovModelStateFactory.GetState(new ModelCreationParameters <NormalDistribution>()
{
NumberOfStates = numberOfStates, Emissions = CreateEmissions(observations, numberOfStates)
});
model.Normalized = true;
var baseParameters = new BasicEstimationParameters <NormalDistribution> {
Model = model, Observations = Helper.Convert(observations), Normalized = model.Normalized
};
var alphaEstimator = new AlphaEstimator <NormalDistribution>();
var alpha = alphaEstimator.Estimate(baseParameters);
var betaEstimator = new BetaEstimator <NormalDistribution>();
var beta = betaEstimator.Estimate(baseParameters);
var weights = new double[observations.Length];
var estimator = new TransitionProbabilityEstimator <NormalDistribution>();
var parameters = new AlphaBetaTransitionProbabiltyMatrixParameters <NormalDistribution>
{
Alpha = alpha,
Beta = beta,
Model = model,
Observations = observations,
Normalized = model.Normalized,
Weights = weights
};
var estimatedTransitionProbabilityMatrix = estimator.Estimate(parameters);
Assert.AreEqual(1d, Math.Round(estimatedTransitionProbabilityMatrix[0][0] + estimatedTransitionProbabilityMatrix[0][1], 5));
Assert.AreEqual(1d, Math.Round(estimatedTransitionProbabilityMatrix[1][0] + estimatedTransitionProbabilityMatrix[1][1], 5));
}
public void Compare_AlphaBetaAndKsiGammaCalculation_EqualTransitionProbabilityMatrixes()
{
const int numberOfStates = 2;
var util = new TestDataUtils();
var observations = util.GetSvcData(util.FTSEFilePath, new DateTime(2010, 12, 18), new DateTime(2011, 12, 18));
var model = HiddenMarkovModelStateFactory.GetState(new ModelCreationParameters <NormalDistribution>()
{
NumberOfStates = numberOfStates, Emissions = CreateEmissions(observations, numberOfStates)
});
model.Normalized = true;
var observationsList = new List <IObservation>();
var weights = new double[observations.Length];
for (var i = 0; i < observations.Length; i++)
{
observationsList.Add(new Observation(observations[i], i.ToString()));
}
var baseParameters = new BasicEstimationParameters <NormalDistribution> {
Model = model, Observations = Helper.Convert(observations), Normalized = model.Normalized
};
var alphaEstimator = new AlphaEstimator <NormalDistribution>();
var alpha = alphaEstimator.Estimate(baseParameters);
var betaEstimator = new BetaEstimator <NormalDistribution>();
var beta = betaEstimator.Estimate(baseParameters);
var @params = new AdvancedEstimationParameters <NormalDistribution>
{
Alpha = alpha,
Beta = beta,
Observations = observationsList,
Model = model,
Normalized = model.Normalized
};
var gammaEstimator = new GammaEstimator <NormalDistribution>();
var ksiEstimator = new KsiEstimator <NormalDistribution>();
var estimatorKsiGamma = new TransitionProbabilityEstimator <NormalDistribution>();
var parametersKsiGamma = new KsiGammaTransitionProbabilityMatrixParameters <NormalDistribution>
{
Model = model,
Ksi = ksiEstimator.Estimate(@params),
Gamma = gammaEstimator.Estimate(@params),
T = observations.Length,
Normalized = model.Normalized
};
var estimatorAlphaBeta = new TransitionProbabilityEstimator <NormalDistribution>();
var parametersAlphaBeta = new AlphaBetaTransitionProbabiltyMatrixParameters <NormalDistribution>
{
Alpha = alpha,
Beta = beta,
Model = model,
Observations = observations,
Normalized = model.Normalized,
Weights = weights
};
var estimatedTransitionProbabilityMatrixKsiGamma = estimatorKsiGamma.Estimate(parametersKsiGamma);
var estimatedTransitionProbabilityMatrixAlphaBeta = estimatorAlphaBeta.Estimate(parametersAlphaBeta);
Assert.AreEqual(Math.Round(estimatedTransitionProbabilityMatrixKsiGamma[0][0], 5), Math.Round(estimatedTransitionProbabilityMatrixAlphaBeta[0][0], 5));
Assert.AreEqual(Math.Round(estimatedTransitionProbabilityMatrixKsiGamma[0][1], 5), Math.Round(estimatedTransitionProbabilityMatrixAlphaBeta[0][1], 5));
Assert.AreEqual(Math.Round(estimatedTransitionProbabilityMatrixKsiGamma[1][0], 5), Math.Round(estimatedTransitionProbabilityMatrixAlphaBeta[1][0], 5));
Assert.AreEqual(Math.Round(estimatedTransitionProbabilityMatrixKsiGamma[1][1], 5), Math.Round(estimatedTransitionProbabilityMatrixAlphaBeta[1][1], 5));
}
