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); }