public void HiddenMarkovModelFunctionConstructorTest()
{
HiddenMarkovModel model = CreateModel1();
DiscreteMarkovModelFunction target = new DiscreteMarkovModelFunction(model);
var features = target.Features;
double[] weights = target.Weights;
Assert.AreEqual(features.Length, 12);
Assert.AreEqual(weights.Length, 12);
int k = 0;
for (int i = 0; i < model.States; i++)
{
Assert.AreEqual(model.Probabilities[i], weights[k++]);
}
for (int i = 0; i < model.States; i++)
{
for (int j = 0; j < model.States; j++)
{
Assert.AreEqual(model.Transitions[i, j], weights[k++]);
}
}
for (int i = 0; i < model.States; i++)
{
for (int j = 0; j < model.Symbols; j++)
{
Assert.AreEqual(model.Emissions[i, j], weights[k++]);
}
}
}
public void ConditionalRandomFieldConstructorTest()
{
HiddenMarkovModel hmm = createHMM();
int states = 2;
var function = new DiscreteMarkovModelFunction(hmm);
var target = new ConditionalRandomField<int>(states, function);
Assert.AreEqual(function, target.Function);
Assert.AreEqual(2, target.States);
}
public void BackwardTest()
{
HiddenMarkovModel hmm = Accord.Tests.Statistics.Models.Markov.
ForwardBackwardAlgorithmTest.CreateModel2();
DiscreteMarkovModelFunction function = new DiscreteMarkovModelFunction(hmm);
// A B B A
int[] observations = { 0, 1, 1, 0 };
double logLikelihood;
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Backward(function.Factors[0], observations, 0, out logLikelihood);
var A = Matrix.Exp(hmm.Transitions);
var B = Matrix.Exp(hmm.Emissions);
var P = Matrix.Exp(hmm.Probabilities);
double a30 = 1;
double a31 = 1;
double a20 = A[0, 0] * B[0, 0] * a30 + A[0, 1] * B[1, 0] * a31;
double a21 = A[1, 0] * B[0, 0] * a30 + A[1, 1] * B[1, 0] * a31;
double a10 = A[0, 0] * B[0, 1] * a20 + A[0, 1] * B[1, 1] * a21;
double a11 = A[1, 0] * B[0, 1] * a20 + A[1, 1] * B[1, 1] * a21;
double a00 = A[0, 0] * B[0, 1] * a10 + A[0, 1] * B[1, 1] * a11;
double a01 = A[1, 0] * B[0, 1] * a10 + A[1, 1] * B[1, 1] * a11;
Assert.AreEqual(actual[0, 0], a00, 1e-10);
Assert.AreEqual(actual[0, 1], a01, 1e-10);
Assert.AreEqual(actual[1, 0], a10, 1e-10);
Assert.AreEqual(actual[1, 1], a11, 1e-10);
Assert.AreEqual(actual[2, 0], a20, 1e-10);
Assert.AreEqual(actual[2, 1], a21, 1e-10);
Assert.AreEqual(actual[3, 0], a30, 1e-10);
Assert.AreEqual(actual[3, 1], a31, 1e-10);
foreach (double e in actual)
{
Assert.IsFalse(double.IsNaN(e));
}
double p = 0;
for (int i = 0; i < hmm.States; i++)
{
p += actual[0, i] * P[i] * B[i, observations[0]];
}
Assert.AreEqual(0.054814695, p, 1e-8);
Assert.IsFalse(double.IsNaN(p));
p = System.Math.Exp(logLikelihood);
Assert.AreEqual(0.054814695, p, 1e-8);
Assert.IsFalse(double.IsNaN(p));
}
public void ForwardScalingTest()
{
HiddenMarkovModel hmm = Accord.Tests.Statistics.Models.Markov.
ForwardBackwardAlgorithmTest.CreateModel1();
DiscreteMarkovModelFunction function = new DiscreteMarkovModelFunction(hmm);
// G G C A
int[] observations = { 2, 2, 1, 0 };
double[] scaling;
double logLikelihood;
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Forward(function.Factors[0], observations, 0, out scaling, out logLikelihood);
double[] P = Matrix.Exp(hmm.Probabilities);
double[,] B = Matrix.Exp(hmm.Emissions);
double[,] A = Matrix.Exp(hmm.Transitions);
double a00 = P[0] * B[0, 2];
double a01 = P[1] * B[1, 2];
double t0 = a00 + a01;
a00 /= t0;
a01 /= t0;
double a10 = (a00 * A[0, 0] + a01 * A[1, 0]) * B[0, 2];
double a11 = (a01 * A[1, 1] + a00 * A[0, 1]) * B[1, 2];
double t1 = a10 + a11;
a10 /= t1;
a11 /= t1;
double a20 = (a10 * A[0, 0] + a11 * A[1, 0]) * B[0, 1];
double a21 = (a11 * A[1, 1] + a10 * A[0, 1]) * B[1, 1];
double t2 = a20 + a21;
a20 /= t2;
a21 /= t2;
double a30 = (a20 * A[0, 0] + a21 * A[1, 0]) * B[0, 0];
double a31 = (a21 * A[1, 1] + a20 * A[0, 1]) * B[1, 0];
double t3 = a30 + a31;
a30 /= t3;
a31 /= t3;
Assert.AreEqual(a00, actual[0, 0], 1e-10);
Assert.AreEqual(a01, actual[0, 1], 1e-10);
Assert.AreEqual(a10, actual[1, 0], 1e-10);
Assert.AreEqual(a11, actual[1, 1], 1e-10);
Assert.AreEqual(a20, actual[2, 0], 1e-10);
Assert.AreEqual(a21, actual[2, 1], 1e-10);
Assert.AreEqual(a30, actual[3, 0], 1e-10);
Assert.AreEqual(a31, actual[3, 1], 1e-10);
foreach (double e in actual)
{
Assert.IsFalse(double.IsNaN(e));
}
double p = System.Math.Exp(logLikelihood);
Assert.AreEqual(0.00384315, p, 1e-8);
Assert.IsFalse(double.IsNaN(p));
}
public void RunTest()
{
int nstates = 3;
int symbols = 3;
int[][] sequences = new int[][]
{
new int[] { 0, 1, 1, 1, 2 },
new int[] { 0, 1, 1, 1, 2, 2, 2 },
new int[] { 0, 0, 1, 1, 2, 2 },
new int[] { 0, 1, 1, 1, 2, 2, 2 },
new int[] { 0, 1, 1, 1, 2, 2 },
new int[] { 0, 1, 1, 2, 2 },
new int[] { 0, 0, 1, 1, 1, 2, 2 },
new int[] { 0, 0, 0, 1, 1, 1, 2, 2 },
new int[] { 0, 1, 1, 2, 2, 2 },
};
var function = new DiscreteMarkovModelFunction(nstates, symbols);
var model = new ConditionalRandomField<int>(nstates, function);
for (int i = 0; i < sequences.Length; i++)
{
double p;
int[] s = sequences[i];
int[] r = model.Compute(s, out p);
Assert.IsFalse(s.IsEqual(r));
}
var target = new QuasiNewtonLearning<int>(model);
int[][] labels = sequences;
int[][] observations = sequences;
double ll0 = model.LogLikelihood(observations, labels);
double actual = target.Run(observations, labels);
double ll1 = model.LogLikelihood(observations, labels);
Assert.IsTrue(ll1 > ll0);
Assert.AreEqual(-0.01205815673780819, actual, 1e-10);
for (int i = 0; i < sequences.Length; i++)
{
double p;
int[] s = sequences[i];
int[] r = model.Compute(s, out p);
Assert.IsTrue(s.IsEqual(r));
}
}
public void ComputeTest()
{
HiddenMarkovModel model = CreateModel1();
DiscreteMarkovModelFunction target = new DiscreteMarkovModelFunction(model);
double actual;
double expected;
int[] x = { 0, 1 };
for (int i = 0; i < model.States; i++)
{
// Check initial state transitions
expected = Math.Exp(model.Probabilities[i]) * Math.Exp(model.Emissions[i, x[0]]);
actual = Math.Exp(target.Factors[0].Compute(-1, i, x, 0));
Assert.AreEqual(expected, actual, 1e-6);
}
for (int t = 0; t < x.Length; t++)
{
for (int i = 0; i < model.States; i++)
{
// Check initial state transitions
expected = Math.Exp(model.Probabilities[i]) * Math.Exp(model.Emissions[i, x[0]]);
actual = Math.Exp(target.Factors[0].Compute(-1, i, x, 0));
Assert.AreEqual(expected, actual, 1e-6);
// Check normal state transitions
for (int j = 0; j < model.States; j++)
{
expected = Math.Exp(model.Transitions[i, j]) * Math.Exp(model.Emissions[j, x[t]]);
actual = Math.Exp(target.Factors[0].Compute(i, j, x, t));
Assert.AreEqual(expected, actual, 1e-6);
}
}
}
}
public void BackwardTest()
{
HiddenMarkovModel hmm = Accord.Tests.Statistics.Models.Markov.
ForwardBackwardAlgorithmTest.CreateModel2();
DiscreteMarkovModelFunction function = new DiscreteMarkovModelFunction(hmm);
// A B B A
int[] observations = { 0, 1, 1, 0 };
double logLikelihood;
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Backward(function.Factors[0], observations, 0, out logLikelihood);
var A = Matrix.Exp(hmm.Transitions);
var B = Matrix.Exp(hmm.Emissions);
var P = Matrix.Exp(hmm.Probabilities);
double a30 = 1;
double a31 = 1;
double a20 = A[0, 0] * B[0, 0] * a30 + A[0, 1] * B[1, 0] * a31;
double a21 = A[1, 0] * B[0, 0] * a30 + A[1, 1] * B[1, 0] * a31;
double a10 = A[0, 0] * B[0, 1] * a20 + A[0, 1] * B[1, 1] * a21;
double a11 = A[1, 0] * B[0, 1] * a20 + A[1, 1] * B[1, 1] * a21;
double a00 = A[0, 0] * B[0, 1] * a10 + A[0, 1] * B[1, 1] * a11;
double a01 = A[1, 0] * B[0, 1] * a10 + A[1, 1] * B[1, 1] * a11;
Assert.AreEqual(actual[0, 0], a00, 1e-10);
Assert.AreEqual(actual[0, 1], a01, 1e-10);
Assert.AreEqual(actual[1, 0], a10, 1e-10);
Assert.AreEqual(actual[1, 1], a11, 1e-10);
Assert.AreEqual(actual[2, 0], a20, 1e-10);
Assert.AreEqual(actual[2, 1], a21, 1e-10);
Assert.AreEqual(actual[3, 0], a30, 1e-10);
Assert.AreEqual(actual[3, 1], a31, 1e-10);
foreach (double e in actual)
Assert.IsFalse(double.IsNaN(e));
double p = 0;
for (int i = 0; i < hmm.States; i++)
p += actual[0, i] * P[i] * B[i, observations[0]];
Assert.AreEqual(0.054814695, p, 1e-8);
Assert.IsFalse(double.IsNaN(p));
p = System.Math.Exp(logLikelihood);
Assert.AreEqual(0.054814695, p, 1e-8);
Assert.IsFalse(double.IsNaN(p));
}
public void LogBackwardTest2()
{
HiddenMarkovModel hmm = Accord.Tests.Statistics.Models.Markov.
ForwardBackwardAlgorithmTest.CreateModel3();
DiscreteMarkovModelFunction function = new DiscreteMarkovModelFunction(hmm);
int[] observations = { 0, 0, 1, 1 };
double[,] expected = Matrix.Log(Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Backward(function.Factors[0], observations, 0));
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.LogBackward(function.Factors[0], observations, 0);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
foreach (double p in actual)
Assert.IsFalse(double.IsNaN(p));
}
public void LogForwardTest2()
{
HiddenMarkovModel hmm = Accord.Tests.Statistics.Models.Markov.
ForwardBackwardAlgorithmTest.CreateModel2();
DiscreteMarkovModelFunction function = new DiscreteMarkovModelFunction(hmm);
int[] observations = { 0, 1, 1, 0 };
double[,] expected = Matrix.Log(Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Forward(function.Factors[0], observations, 0));
double logLikelihood;
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.LogForward(function.Factors[0], observations, 0, out logLikelihood);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
double p = 0;
for (int i = 0; i < hmm.States; i++)
p += Math.Exp(actual[observations.Length - 1, i]);
Assert.AreEqual(0.054814695, p, 1e-8);
Assert.AreEqual(0.054814695, Math.Exp(logLikelihood), 1e-8);
Assert.IsFalse(double.IsNaN(p));
}
public void ForwardScalingTest()
{
HiddenMarkovModel hmm = Accord.Tests.Statistics.Models.Markov.
ForwardBackwardAlgorithmTest.CreateModel1();
DiscreteMarkovModelFunction function = new DiscreteMarkovModelFunction(hmm);
// G G C A
int[] observations = { 2, 2, 1, 0 };
double[] scaling;
double logLikelihood;
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Forward(function.Factors[0], observations, 0, out scaling, out logLikelihood);
double[] P = Matrix.Exp(hmm.Probabilities);
double[,] B = Matrix.Exp(hmm.Emissions);
double[,] A = Matrix.Exp(hmm.Transitions);
double a00 = P[0] * B[0, 2];
double a01 = P[1] * B[1, 2];
double t0 = a00 + a01;
a00 /= t0;
a01 /= t0;
double a10 = (a00 * A[0, 0] + a01 * A[1, 0]) * B[0, 2];
double a11 = (a01 * A[1, 1] + a00 * A[0, 1]) * B[1, 2];
double t1 = a10 + a11;
a10 /= t1;
a11 /= t1;
double a20 = (a10 * A[0, 0] + a11 * A[1, 0]) * B[0, 1];
double a21 = (a11 * A[1, 1] + a10 * A[0, 1]) * B[1, 1];
double t2 = a20 + a21;
a20 /= t2;
a21 /= t2;
double a30 = (a20 * A[0, 0] + a21 * A[1, 0]) * B[0, 0];
double a31 = (a21 * A[1, 1] + a20 * A[0, 1]) * B[1, 0];
double t3 = a30 + a31;
a30 /= t3;
a31 /= t3;
Assert.AreEqual(a00, actual[0, 0], 1e-10);
Assert.AreEqual(a01, actual[0, 1], 1e-10);
Assert.AreEqual(a10, actual[1, 0], 1e-10);
Assert.AreEqual(a11, actual[1, 1], 1e-10);
Assert.AreEqual(a20, actual[2, 0], 1e-10);
Assert.AreEqual(a21, actual[2, 1], 1e-10);
Assert.AreEqual(a30, actual[3, 0], 1e-10);
Assert.AreEqual(a31, actual[3, 1], 1e-10);
foreach (double e in actual)
Assert.IsFalse(double.IsNaN(e));
double p = System.Math.Exp(logLikelihood);
Assert.AreEqual(0.00384315, p, 1e-8);
Assert.IsFalse(double.IsNaN(p));
}
public void ForwardScalingTest2()
{
HiddenMarkovModel hmm = Accord.Tests.Statistics.Models.Markov.
ForwardBackwardAlgorithmTest.CreateModel2();
DiscreteMarkovModelFunction function = new DiscreteMarkovModelFunction(hmm);
// A B B A
int[] observations = { 0, 1, 1, 0 };
double[] scaling;
double logLikelihood;
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Forward(function.Factors[0], observations, 0, out scaling, out logLikelihood);
double p = System.Math.Exp(logLikelihood);
Assert.AreEqual(0.054814695, p, 1e-7);
Assert.IsFalse(double.IsNaN(p));
}
public void ForwardTest3()
{
HiddenMarkovModel hmm = Accord.Tests.Statistics.Models.Markov.
ForwardBackwardAlgorithmTest.CreateModel3();
DiscreteMarkovModelFunction function = new DiscreteMarkovModelFunction(hmm);
// L L R R
int[] observations = { 0, 0, 1, 1 };
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Forward(function.Factors[0], observations);
// Forward matrices from R's HMM package are
// transposed in relation to the framework's:
Assert.AreEqual(4, actual.GetLength(0));
Assert.AreEqual(2, actual.GetLength(1));
Assert.AreEqual(0.675, actual[0, 0], 1e-10);
Assert.AreEqual(0.011, actual[0, 1], 1e-10);
Assert.AreEqual(0.407475, actual[1, 0], 1e-10);
Assert.AreEqual(0.015697, actual[1, 1], 1e-10);
Assert.AreEqual(0.08267228, actual[2, 0], 1e-8);
Assert.AreEqual(0.08138495, actual[2, 1], 1e-8);
Assert.AreEqual(0.02263833, actual[3, 0], 1e-8);
Assert.AreEqual(0.06468345, actual[3, 1], 1e-8);
foreach (double p in actual)
Assert.IsFalse(double.IsNaN(p));
}
public void ForwardTest2()
{
HiddenMarkovModel hmm = Accord.Tests.Statistics.Models.Markov.
ForwardBackwardAlgorithmTest.CreateModel2();
DiscreteMarkovModelFunction function = new DiscreteMarkovModelFunction(hmm);
// A B B A
int[] observations = { 0, 1, 1, 0 };
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Forward(function.Factors[0], observations);
var A = Matrix.Exp(hmm.Transitions);
var B = Matrix.Exp(hmm.Emissions);
var P = Matrix.Exp(hmm.Probabilities);
double a00 = P[0] * B[0, 0];
double a01 = P[1] * B[1, 0];
double a10 = (a00 * A[0, 0] + a01 * A[1, 0]) * B[0, 1];
double a11 = (a01 * A[1, 1] + a00 * A[0, 1]) * B[1, 1];
double a20 = (a10 * A[0, 0] + a11 * A[1, 0]) * B[0, 1];
double a21 = (a11 * A[1, 1] + a10 * A[0, 1]) * B[1, 1];
double a30 = (a20 * A[0, 0] + a21 * A[1, 0]) * B[0, 0];
double a31 = (a21 * A[1, 1] + a20 * A[0, 1]) * B[1, 0];
Assert.AreEqual(a00, actual[0, 0], 1e-10);
Assert.AreEqual(a01, actual[0, 1], 1e-10);
Assert.AreEqual(a10, actual[1, 0], 1e-10);
Assert.AreEqual(a11, actual[1, 1], 1e-10);
Assert.AreEqual(a20, actual[2, 0], 1e-10);
Assert.AreEqual(a21, actual[2, 1], 1e-10);
Assert.AreEqual(a30, actual[3, 0], 1e-10);
Assert.AreEqual(a31, actual[3, 1], 1e-10);
foreach (double e in actual)
Assert.IsFalse(double.IsNaN(e));
double p = 0;
for (int i = 0; i < hmm.States; i++)
p += actual[observations.Length - 1, i];
Assert.AreEqual(0.054814695, p, 1e-8);
Assert.IsFalse(double.IsNaN(p));
}
public void BackwardTest2()
{
HiddenMarkovModel hmm = Accord.Tests.Statistics.Models.Markov.
ForwardBackwardAlgorithmTest.CreateModel3();
DiscreteMarkovModelFunction function = new DiscreteMarkovModelFunction(hmm);
// L L R R
int[] observations = { 0, 0, 1, 1 };
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Backward(function.Factors[0], observations);
// Backward matrices from R's HMM package are
// transposed in relation to the framework's:
Assert.AreEqual(4, actual.GetLength(0));
Assert.AreEqual(2, actual.GetLength(1));
Assert.AreEqual(0.128074432, actual[0, 0], 1e-10);
Assert.AreEqual(0.07923051, actual[0, 1], 1e-8);
Assert.AreEqual(0.196816, actual[1, 0]);
Assert.AreEqual(0.453856, actual[1, 1]);
Assert.AreEqual(0.376, actual[2, 0]);
Assert.AreEqual(0.691, actual[2, 1]);
Assert.AreEqual(1, actual[3, 0]);
Assert.AreEqual(1, actual[3, 1]);
foreach (double p in actual)
Assert.IsFalse(double.IsNaN(p));
}
public void ComputeTest()
{
HiddenMarkovModel hmm = HiddenMarkovModelFunctionTest.CreateModel2();
int states = hmm.States;
var function = new DiscreteMarkovModelFunction(hmm);
var target = new ConditionalRandomField<int>(states, function);
double p1, p2;
int[] observations, expected, actual;
observations = new int[] { 0, 0, 1, 1, 1, 2 };
expected = hmm.Decode(observations, out p1);
actual = target.Compute(observations, out p2);
Assert.IsTrue(expected.IsEqual(actual));
Assert.AreEqual(p1, p2, 1e-6);
observations = new int[] { 0, 1, 2, 2, 2 };
expected = hmm.Decode(observations, out p1);
actual = target.Compute(observations, out p2);
Assert.IsTrue(expected.IsEqual(actual));
Assert.AreEqual(p1, p2, 1e-6);
}
public void LogForwardBackwardTest()
{
HiddenMarkovModel hmm = Accord.Tests.Statistics.Models.Markov.
ForwardBackwardAlgorithmTest.CreateModel1();
DiscreteMarkovModelFunction function = new DiscreteMarkovModelFunction(hmm);
// G G C A
int[] observations = { 2, 2, 1, 0 };
double fwdLogLikelihood;
double[,] fwd = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.LogForward(function.Factors[0], observations, 0, out fwdLogLikelihood);
double bwdLogLikelihood;
double[,] bwd = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.LogBackward(function.Factors[0], observations, 0, out bwdLogLikelihood);
Assert.AreEqual(fwdLogLikelihood, bwdLogLikelihood, 1e-10); // -5.5614629361549142
Assert.AreEqual(-5.5614629361549142, fwdLogLikelihood, 1e-10);
Assert.IsFalse(double.IsNaN(fwdLogLikelihood));
}
public void LikelihoodTest()
{
HiddenMarkovModel hmm = HiddenMarkovModelFunctionTest.CreateModel2();
int states = hmm.States;
int symbols = hmm.Symbols;
var function1 = new DiscreteMarkovModelFunction(hmm);
var target1 = new ConditionalRandomField<int>(states, function1);
var function2 = new DiscreteMarkovModelFunction(states, symbols);
var target2 = new ConditionalRandomField<int>(states, function2);
int[] observations;
double a, b, la, lb;
observations = new int[] { 0, 0, 1, 1, 1, 2 };
a = target1.LogLikelihood(observations, observations);
b = target2.LogLikelihood(observations, observations);
Assert.IsTrue(a > b);
observations = new int[] { 0, 0, 1, 1, 1, 2 };
la = target1.LogLikelihood(observations, observations);
lb = target2.LogLikelihood(observations, observations);
Assert.IsTrue(la > lb);
double lla = System.Math.Log(a);
double llb = System.Math.Log(b);
Assert.AreEqual(lla, la, 1e-6);
Assert.AreEqual(llb, lb, 1e-6);
}
public void HiddenMarkovModelFunctionConstructorTest()
{
HiddenMarkovModel model = CreateModel1();
DiscreteMarkovModelFunction target = new DiscreteMarkovModelFunction(model);
var features = target.Features;
double[] weights = target.Weights;
Assert.AreEqual(features.Length, 12);
Assert.AreEqual(weights.Length, 12);
int k = 0;
for (int i = 0; i < model.States; i++)
Assert.AreEqual(model.Probabilities[i], weights[k++]);
for (int i = 0; i < model.States; i++)
for (int j = 0; j < model.States; j++)
Assert.AreEqual(model.Transitions[i, j], weights[k++]);
for (int i = 0; i < model.States; i++)
for (int j = 0; j < model.Symbols; j++)
Assert.AreEqual(model.Emissions[i, j], weights[k++]);
}