public double[, ][,] Estimate(MixtureSigmaEstimationParameters <TDistribution> parameters)
{
if (_sigma != null)
{
return(_sigma);
}
try
{
_sigma = new double[parameters.Model.N, parameters.L][, ];
for (var i = 0; i < parameters.Model.N; i++)
{
for (var l = 0; l < parameters.L; l++)
{
var denominator = 0.0d;
var nominator = new double[parameters.Observations[0].Dimention, parameters.Observations[0].Dimention];
for (var t = 0; t < parameters.Observations.Count; t++)
{
// TODO : weights here
var weight = GetWeightValue(t, parameters.ObservationWeights);
var gammaComponents = (parameters.Model.Normalized) ? LogExtention.eExp(parameters.GammaComponents[t][i, l]) : parameters.GammaComponents[t][i, l];
var x = parameters.Observations[t].Value;
var z = x.Substruct(parameters.Mu[i, l]);
var m = z.OuterProduct(z);
m = m.Product(weight * gammaComponents);
denominator += weight * gammaComponents;
nominator = nominator.Add(m);
}
_sigma[i, l] = nominator.Product(1 / denominator);
var matrix = new Matrix(_sigma[i, l]);
if (!matrix.PositiviDefinite)
{
_sigma[i, l] = matrix.ConvertToPositiveDefinite();
Debug.WriteLine("HMM State [{0},{1}] Sigma is not Positive Definite. Converting.", i, l);
Debug.WriteLine("{0}", matrix);
}
}
}
}
catch (Exception)
{
for (var i = 0; i < parameters.Model.N; i++)
{
for (var l = 0; l < parameters.L; l++)
{
Debug.WriteLine("Mixture Sigma [{0},{1}] : {2}", i, l, new Matrix(_sigma[i, l]));
}
}
throw;
}
return(_sigma);
}
public void Sigma_RightLeftAndParametersAnnNotNormalized_SigmaCalculated()
{
var delta = 3;
var util = new TestDataUtils();
var observations = util.GetSvcData(util.FTSEFilePath, new DateTime(2011, 11, 18), new DateTime(2011, 12, 18));
var model = HiddenMarkovModelStateFactory.GetState(new ModelCreationParameters <Mixture <IMultivariateDistribution> >()
{
NumberOfStates = NumberOfStatesRightLeft, Delta = delta, Emissions = CreateEmissions(observations, NumberOfStatesRightLeft, NumberOfComponents)
}); //new HiddenMarkovModelState<Mixture<IMultivariateDistribution>>(NumberOfStatesRightLeft, delta, CreateEmissions(observations, NumberOfStatesRightLeft, NumberOfComponents)) { LogNormalized = false };
model.Normalized = false;
var baseParameters = new BasicEstimationParameters <Mixture <IMultivariateDistribution> > {
Model = model, Observations = Helper.Convert(observations), Normalized = model.Normalized
};
var alphaEstimator = new AlphaEstimator <Mixture <IMultivariateDistribution> >();
var alpha = alphaEstimator.Estimate(baseParameters);
var betaEstimator = new BetaEstimator <Mixture <IMultivariateDistribution> >();
var beta = betaEstimator.Estimate(baseParameters);
var parameters = new ParameterEstimations <Mixture <IMultivariateDistribution> >(model, Helper.Convert(observations), alpha, beta);
var sigma = new MixtureSigmaEstimator <Mixture <IMultivariateDistribution> >();
var mixtureGammaEstimator = new MixtureGammaEstimator <Mixture <IMultivariateDistribution> >();
var mixtureMuEstimator = new MixtureMuEstimator <Mixture <IMultivariateDistribution> >();
var @params = new MixtureSigmaEstimationParameters <Mixture <IMultivariateDistribution> >
{
Model = model,
Normalized = model.Normalized,
Alpha = alpha,
Beta = beta,
Observations = Helper.Convert(observations),
L = model.Emission[0].Components.Length
};
var gamma = mixtureGammaEstimator.Estimate(@params as AdvancedEstimationParameters <Mixture <IMultivariateDistribution> >);
var gammaComponens = mixtureGammaEstimator.Estimate(@params);
@params.Gamma = gamma;
@params.GammaComponents = gammaComponens;
@params.Mu = mixtureMuEstimator.Estimate(@params);
for (int i = 0; i < NumberOfStatesRightLeft; i++)
{
for (int l = 0; l < NumberOfComponents; l++)
{
for (int rows = 0; rows < parameters.Observation[0].Dimention; rows++)
{
for (int cols = 0; cols < parameters.Observation[0].Dimention; cols++)
{
Assert.IsTrue(sigma.Estimate(@params)[i, l][rows, cols] > 0, string.Format("Failed Sigma {0}", sigma.Estimate(@params)[i, l][rows, cols]));
}
}
}
}
}
public IHiddenMarkovModel <Mixture <IMultivariateDistribution> > Run(int maxIterations, double likelihoodTolerance)
{
// Initialize responce object
var forwardBackward = new ForwardBackward(Normalized);
do
{
maxIterations--;
if (!_estimatedModel.Likelihood.EqualsTo(0))
{
_currentModel = HiddenMarkovModelStateFactory.GetState(new ModelCreationParameters <Mixture <IMultivariateDistribution> > {
Pi = _estimatedPi, TransitionProbabilityMatrix = _estimatedTransitionProbabilityMatrix, Emissions = _estimatedEmissions
}); //new HiddenMarkovModelState<Mixture<IMultivariateDistribution>>(_estimatedPi, _estimatedTransitionProbabilityMatrix, _estimatedEmissions) { LogNormalized = _estimatedModel.LogNormalized };
_currentModel.Normalized = Normalized;
_currentModel.Likelihood = _estimatedModel.Likelihood;
}
// Run Forward-Backward procedure
forwardBackward.RunForward(_observations, _currentModel);
forwardBackward.RunBackward(_observations, _currentModel);
// Calculate Gamma and Xi
var @params = new MixtureSigmaEstimationParameters <Mixture <IMultivariateDistribution> >
{
Alpha = forwardBackward.Alpha,
Beta = forwardBackward.Beta,
Observations = _observations,
Model = _currentModel,
Normalized = _currentModel.Normalized,
L = _currentModel.Emission[0].Components.Length
};
_gammaEstimator = new GammaEstimator <Mixture <IMultivariateDistribution> >();
_ksiEstimator = new KsiEstimator <Mixture <IMultivariateDistribution> >();
var mixtureCoefficientsEstimator = new MixtureCoefficientsEstimator <Mixture <IMultivariateDistribution> >();
var mixtureMuEstimator = new MixtureMuEstimator <Mixture <IMultivariateDistribution> >(); // Mean
var mixtureSigmaEstimator = new MixtureSigmaEstimator <Mixture <IMultivariateDistribution> >(); // Covariance
var mixtureGammaEstimator = new MixtureGammaEstimator <Mixture <IMultivariateDistribution> >();
@params.Gamma = _gammaEstimator.Estimate(@params);
@params.GammaComponents = mixtureGammaEstimator.Estimate(@params);
EstimatePi(_gammaEstimator.Estimate(@params));
EstimateTransitionProbabilityMatrix(_gammaEstimator.Estimate(@params), _ksiEstimator.Estimate(@params), null, _observations.Count);
for (var n = 0; n < _currentModel.N; n++)
{
var mixturesComponents = _currentModel.Emission[n].Coefficients.Length;
var distributions = new IMultivariateDistribution[mixturesComponents];
// Calculate coefficients for state n
var coefficients = mixtureCoefficientsEstimator.Estimate(@params)[n];
if (Normalized)
{
mixtureCoefficientsEstimator.Denormalize();
}
@params.Mu = mixtureMuEstimator.Estimate(@params);
for (var l = 0; l < mixturesComponents; l++)
{
distributions[l] = new NormalDistribution(mixtureMuEstimator.Estimate(@params)[n, l], mixtureSigmaEstimator.Estimate(@params)[n, l]);
}
_estimatedEmissions[n] = new Mixture <IMultivariateDistribution>(coefficients, distributions);
}
_estimatedModel = HiddenMarkovModelStateFactory.GetState(new ModelCreationParameters <Mixture <IMultivariateDistribution> > {
Pi = _estimatedPi, TransitionProbabilityMatrix = _estimatedTransitionProbabilityMatrix, Emissions = _estimatedEmissions
});
_estimatedModel.Normalized = Normalized;
_estimatedModel.Likelihood = forwardBackward.RunForward(_observations, _estimatedModel);
_likelihoodDelta = Math.Abs(Math.Abs(_currentModel.Likelihood) - Math.Abs(_estimatedModel.Likelihood));
Debug.WriteLine("Iteration {3} , Current {0}, Estimate {1} Likelihood delta {2}", _currentModel.Likelihood, _estimatedModel.Likelihood, _likelihoodDelta, maxIterations);
}while (_currentModel != _estimatedModel && maxIterations > 0 && _likelihoodDelta > likelihoodTolerance);
return(_estimatedModel);
}
