public void LearnTest6()
{
// Continuous Markov Models can operate using any
// probability distribution, including discrete ones.
// In the following example, we will try to create a
// Continuous Hidden Markov Model using a discrete
// distribution to detect if a given sequence starts
// with a zero and has any number of ones after that.
double[][] sequences = new double[][]
{
new double[] { 0,1,1,1,1,0,1,1,1,1 },
new double[] { 0,1,1,1,0,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1,1,1,1 },
};
// Create a new Hidden Markov Model with 3 states and
// a generic discrete distribution with two symbols
var hmm = HiddenMarkovModel.CreateGeneric(3, 2);
// Try to fit the model to the data until the difference in
// the average log-likelihood changes only by as little as 0.0001
var teacher = new BaumWelchLearning<GeneralDiscreteDistribution>(hmm)
{
Tolerance = 0.0001,
Iterations = 0
};
double ll = Math.Exp(teacher.Run(sequences));
// Calculate the probability that the given
// sequences originated from the model
double l1 = Math.Exp(hmm.Evaluate(new double[] { 0, 1 })); // 0.999
double l2 = Math.Exp(hmm.Evaluate(new double[] { 0, 1, 1, 1 })); // 0.916
// Sequences which do not start with zero have much lesser probability.
double l3 = Math.Exp(hmm.Evaluate(new double[] { 1, 1 })); // 0.000
double l4 = Math.Exp(hmm.Evaluate(new double[] { 1, 0, 0, 0 })); // 0.000
// Sequences which contains few errors have higher probability
// than the ones which do not start with zero. This shows some
// of the temporal elasticity and error tolerance of the HMMs.
double l5 = Math.Exp(hmm.Evaluate(new double[] { 0, 1, 0, 1, 1, 1, 1, 1, 1 })); // 0.034
double l6 = Math.Exp(hmm.Evaluate(new double[] { 0, 1, 1, 1, 1, 1, 1, 0, 1 })); // 0.034
Assert.AreEqual(1.2114235662225716, ll, 1e-4);
Assert.AreEqual(0.99996863060890995, l1, 1e-4);
Assert.AreEqual(0.91667240076011669, l2, 1e-4);
Assert.AreEqual(0.00002335133758386, l3, 1e-4);
Assert.AreEqual(0.00000000000000012, l4, 1e-4);
Assert.AreEqual(0.03423723144322685, l5, 1e-4);
Assert.AreEqual(0.03423719592053246, l6, 1e-4);
Assert.IsFalse(Double.IsNaN(ll));
Assert.IsFalse(Double.IsNaN(l1));
Assert.IsFalse(Double.IsNaN(l2));
Assert.IsFalse(Double.IsNaN(l3));
Assert.IsFalse(Double.IsNaN(l4));
Assert.IsFalse(Double.IsNaN(l5));
Assert.IsFalse(Double.IsNaN(l6));
Assert.IsTrue(l1 > l3 && l1 > l4);
Assert.IsTrue(l2 > l3 && l2 > l4);
}
