/// <summary>
/// Computes Forward probabilities for a given hidden Markov model and a set of observations.
/// </summary>
public static double[,] Forward(ContinuousHiddenMarkovModel model, double[][] observations, out double[] scaling)
{
int states = model.States;
double[,] A = model.Transitions;
IDistribution[] B = model.Emissions;
double[] pi = model.Probabilities;
int T = observations.Length;
var fwd = new double[T, states];
scaling = new double[T];
// 1. Initialization
for (int i = 0; i < states; i++)
{
scaling[0] += fwd[0, i] = pi[i] * B[i].ProbabilityFunction(observations[0]);
}
if (scaling[0] != 0) // Scaling
{
for (int i = 0; i < states; i++)
{
fwd[0, i] /= scaling[0];
}
}
// 2. Induction
for (int t = 1; t < T; t++)
{
double[] obs = observations[t];
for (int i = 0; i < states; i++)
{
double sum = 0.0;
for (int j = 0; j < states; j++)
{
sum += fwd[t - 1, j] * A[j, i];
}
fwd[t, i] = sum * B[i].ProbabilityFunction(obs);
scaling[t] += fwd[t, i]; // scaling coefficient
}
if (scaling[t] != 0) // Scaling
{
for (int i = 0; i < states; i++)
{
fwd[t, i] /= scaling[t];
}
}
}
return(fwd);
}
public void TestErrorRateDecreasesAfterEachIteration()
{
var hmm = new ContinuousHiddenMarkovModel(States, Symbols);
var testSequence = new double[] {YesUmbrella, YesUmbrella, NoUmbrella};
var initialError = 1 - hmm.Evaluate(testSequence);
var trainedHmm = TrainHelper(new[] {testSequence});
var errorAfterTraining = 1 - trainedHmm.Evaluate(testSequence);
Assert.IsTrue(errorAfterTraining <= initialError);
}
public static void AssertHMMAreEqual(ContinuousHiddenMarkovModel expected,
ContinuousHiddenMarkovModel actual)
{
// ensure all parameters are still the same
// including Dimension, number of states,
// starting-state probabilities and transition matrix.
Assert.AreEqual(expected.Dimension, actual.Dimension);
Assert.AreEqual(expected.States, actual.States);
AssertVectorsAreEqual(expected.Probabilities, actual.Probabilities);
AssertMatricesAreEqual(expected.Transitions, actual.Transitions, expected.States);
}
/// <summary>
/// Computes Forward probabilities for a given hidden Markov model and a set of observations.
/// </summary>
public static double[,] Forward(ContinuousHiddenMarkovModel model, double[][] observations,
out double logLikelihood)
{
double[] coefficients;
double[,] fwd = Forward(model, observations, out coefficients);
logLikelihood = 0;
for (int i = 0; i < coefficients.Length; i++)
{
logLikelihood += System.Math.Log(coefficients[i]);
}
return(fwd);
}
private static ContinuousHiddenMarkovModel TrainHelper(double[][] sequences)
{
var hmm = new ContinuousHiddenMarkovModel(States, Symbols);
var learner = new ContinuousBaumWelchLearning(hmm)
{
Tolerance = MinTolerance,
Iterations = MaxIterations,
FittingOptions = new NormalOptions()
{
Regularization = RegularisationFactor
}
};
learner.Run(sequences);
return hmm;
}
public void TestDeserialisationUndoesSerialisation()
{
const int states = 3;
var origHMM = new ContinuousHiddenMarkovModel(states, new NormalDistribution(4));
// change the model slightly.
// i.e. make state 1 twice as likely, make state 0 not a starting state.
origHMM.Probabilities[1] += origHMM.Probabilities[0];
origHMM.Probabilities[0] = 0;
// save then load the model
string path = Path.GetTempFileName();
(new HMM(origHMM)).SaveToFile(path);
var newHMM = HMM.CreateFromFile(path).CHMM;
File.Delete(path);
AssertHMMAreEqual(origHMM, newHMM);
}
/// <summary>
/// Computes Backward probabilities for a given hidden Markov model and a set of observations.
/// </summary>
public static double[,] Backward(ContinuousHiddenMarkovModel model, double[][] observations, double[] scaling)
{
int states = model.States;
double[,] A = model.Transitions;
IDistribution[] B = model.Emissions;
double[] pi = model.Probabilities;
int T = observations.Length;
var bwd = new double[T, states];
// For backward variables, we use the same scale factors
// for each time t as were used for forward variables.
// 1. Initialization
for (int i = 0; i < states; i++)
{
bwd[T - 1, i] = 1.0 / scaling[T - 1];
}
// 2. Induction
for (int t = T - 2; t >= 0; t--)
{
for (int i = 0; i < states; i++)
{
double sum = 0;
for (int j = 0; j < states; j++)
{
sum += A[i, j] * B[j].ProbabilityFunction(observations[t + 1]) * bwd[t + 1, j];
}
bwd[t, i] += sum / scaling[t];
}
}
return(bwd);
}
/// <summary>
/// Computes Forward probabilities for a given hidden Markov model and a set of observations.
/// </summary>
public static double[,] Forward(ContinuousHiddenMarkovModel model, double[][] observations, out double[] scaling)
{
int states = model.States;
double[,] A = model.Transitions;
IDistribution[] B = model.Emissions;
double[] pi = model.Probabilities;
int T = observations.Length;
var fwd = new double[T,states];
scaling = new double[T];
// 1. Initialization
for (int i = 0; i < states; i++)
scaling[0] += fwd[0, i] = pi[i]*B[i].ProbabilityFunction(observations[0]);
if (scaling[0] != 0) // Scaling
{
for (int i = 0; i < states; i++)
fwd[0, i] /= scaling[0];
}
// 2. Induction
for (int t = 1; t < T; t++)
{
double[] obs = observations[t];
for (int i = 0; i < states; i++)
{
double sum = 0.0;
for (int j = 0; j < states; j++)
sum += fwd[t - 1, j]*A[j, i];
fwd[t, i] = sum*B[i].ProbabilityFunction(obs);
scaling[t] += fwd[t, i]; // scaling coefficient
}
if (scaling[t] != 0) // Scaling
{
for (int i = 0; i < states; i++)
fwd[t, i] /= scaling[t];
}
}
return fwd;
}
/// <summary>
/// Computes Backward probabilities for a given hidden Markov model and a set of observations.
/// </summary>
public static double[,] Backward(ContinuousHiddenMarkovModel model, double[][] observations, double[] scaling)
{
int states = model.States;
double[,] A = model.Transitions;
IDistribution[] B = model.Emissions;
double[] pi = model.Probabilities;
int T = observations.Length;
var bwd = new double[T,states];
// For backward variables, we use the same scale factors
// for each time t as were used for forward variables.
// 1. Initialization
for (int i = 0; i < states; i++)
bwd[T - 1, i] = 1.0/scaling[T - 1];
// 2. Induction
for (int t = T - 2; t >= 0; t--)
{
for (int i = 0; i < states; i++)
{
double sum = 0;
for (int j = 0; j < states; j++)
sum += A[i, j]*B[j].ProbabilityFunction(observations[t + 1])*bwd[t + 1, j];
bwd[t, i] += sum/scaling[t];
}
}
return bwd;
}
/// <summary>
/// Computes Forward probabilities for a given hidden Markov model and a set of observations.
/// </summary>
public static double[,] Forward(ContinuousHiddenMarkovModel model, double[][] observations,
out double logLikelihood)
{
double[] coefficients;
double[,] fwd = Forward(model, observations, out coefficients);
logLikelihood = 0;
for (int i = 0; i < coefficients.Length; i++)
logLikelihood += System.Math.Log(coefficients[i]);
return fwd;
}
public HMM(ContinuousHiddenMarkovModel signHMM)
{
CHMM = signHMM;
}
