/// <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;
var A = model.Transitions;
var B = model.Emissions;
var pi = model.Probabilities;
int T = observations.Length;
double[,] 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 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 = ForwardBackwardAlgorithm.Forward(model, observations, out coefficients);
logLikelihood = 0;
for (int i = 0; i < coefficients.Length; i++)
{
logLikelihood += System.Math.Log(coefficients[i]);
}
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;
var A = model.Transitions;
var B = model.Emissions;
var pi = model.Probabilities;
int T = observations.Length;
double[,] 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>
/// Creates a new instance of the Baum-Welch learning algorithm.
/// </summary>
public ContinuousBaumWelchLearning(ContinuousHiddenMarkovModel model)
: base(model)
{
this.model = model;
}
/// <summary>
/// Creates a new instance of the Baum-Welch learning algorithm.
/// </summary>
public ContinuousBaumWelchLearning(ContinuousHiddenMarkovModel model)
: base(model)
{
this.model = model;
}
