public void GradientTest3()
{
double[][][] sequences2;
int[] labels2;
var hmm = CreateModel3(out sequences2, out labels2);
var function = new MarkovMultivariateFunction(hmm);
var model = new HiddenConditionalRandomField <double[]>(function);
var target = new ForwardBackwardGradient <double[]>(model);
target.Regularization = 2;
var inputs = sequences2;
var outputs = labels2;
FiniteDifferences diff = new FiniteDifferences(function.Weights.Length);
diff.Function = parameters => func(model, parameters, inputs, outputs, target.Regularization);
double[] expected = diff.Compute(function.Weights);
double[] actual = target.Gradient(function.Weights, inputs, outputs);
for (int i = 0; i < actual.Length; i++)
{
double e = expected[i];
double a = actual[i];
Assert.AreEqual(e, a, 1e-3);
Assert.IsFalse(double.IsNaN(actual[i]));
Assert.IsFalse(double.IsNaN(expected[i]));
}
}
public void GradientTest4()
{
var hmm = IndependentMarkovClassifierPotentialFunctionTest.CreateModel2();
var function = new MarkovMultivariateFunction(hmm);
var model = new HiddenConditionalRandomField <double[]>(function);
var target = new ForwardBackwardGradient <double[]>(model);
target.Regularization = 0;
FiniteDifferences diff = new FiniteDifferences(function.Weights.Length);
diff.Function = parameters => func(model, parameters,
IndependentMarkovClassifierPotentialFunctionTest.sequences,
IndependentMarkovClassifierPotentialFunctionTest.labels);
double[] expected = diff.Compute(function.Weights);
double[] actual = target.Gradient(function.Weights,
IndependentMarkovClassifierPotentialFunctionTest.sequences,
IndependentMarkovClassifierPotentialFunctionTest.labels);
for (int i = 0; i < actual.Length; i++)
{
if (double.IsNaN(expected[i]))
{
continue;
}
Assert.AreEqual(expected[i], actual[i], 1e-5);
Assert.IsFalse(double.IsNaN(actual[i]));
}
}
public void GradientTest_MarkovIndependentNormal_NoPriors()
{
double[][][] observations;
int[] labels;
HiddenMarkovClassifier <Independent <NormalDistribution> > hmm =
IndependentMarkovFunctionTest.CreateModel4(out observations, out labels, usePriors: false);
var function = new MarkovMultivariateFunction(hmm);
var model = new HiddenConditionalRandomField <double[]>(function);
var target = new ForwardBackwardGradient <double[]>(model);
target.Regularization = 0;
FiniteDifferences diff = new FiniteDifferences(function.Weights.Length);
diff.Function = parameters => func(model, parameters,
observations,
labels);
double[] expected = diff.Compute(function.Weights);
double[] actual = target.Gradient(function.Weights, observations, labels);
for (int i = 0; i < actual.Length; i++)
{
if (double.IsNaN(expected[i]))
{
continue;
}
Assert.AreEqual(expected[i], actual[i], 1e-5);
Assert.IsFalse(double.IsNaN(actual[i]));
}
}
public void LogBackwardTest2()
{
HiddenMarkovClassifier <Independent> hmm = IndependentMarkovClassifierPotentialFunctionTest
.CreateModel3();
MarkovMultivariateFunction function = new MarkovMultivariateFunction(hmm);
double[][][] observations = IndependentMarkovClassifierPotentialFunctionTest.sequences2;
int[] labels = IndependentMarkovClassifierPotentialFunctionTest.labels2;
foreach (double[][] x in observations)
{
foreach (int y in labels)
{
double[,] actual = new double[x.Length, 5];
Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.LogBackward(function.Factors[y], x, y, actual);
double[,] expected = new double[x.Length, 5];
Accord.Statistics.Models.Markov.
ForwardBackwardAlgorithm.LogBackward(hmm.Models[y], x, expected);
for (int i = 0; i < actual.GetLength(0); i++)
{
for (int j = 0; j < actual.GetLength(1); j++)
{
Assert.AreEqual(expected[i, j], actual[i, j], 1e-10);
Assert.IsFalse(Double.IsNaN(actual[i, j]));
}
}
}
}
}
public void LogForwardTest4()
{
var hmmc = Accord.Tests.Statistics.Models.Fields.
MultivariateNormalHiddenMarkovClassifierPotentialFunctionTest.CreateModel3();
for (int c = 0; c < hmmc.Classes; c++)
{
var hmm = hmmc[c];
var function = new MarkovMultivariateFunction(hmm);
var sequences = Accord.Tests.Statistics.Models.Fields.
MultivariateNormalHiddenMarkovClassifierPotentialFunctionTest.inputTest;
for (int i = 0; i < sequences.Length; i++)
{
var observations = sequences[i];
double expectedLogLikelihood;
double[,] expected = Accord.Statistics.Models.Markov
.ForwardBackwardAlgorithm.LogForward(hmm, observations, out expectedLogLikelihood);
double actualLogLikelihood;
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.LogForward(function.Factors[0], observations, 0, out actualLogLikelihood);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
Assert.AreEqual(expectedLogLikelihood, actualLogLikelihood, 1e-6);
Assert.IsFalse(Double.IsNaN(actualLogLikelihood));
}
}
}
public void LogForwardTest()
{
double[][][] observations;
int[] labels;
var hmm = IndependentMarkovFunctionTest.CreateModel2(out observations, out labels);
MarkovMultivariateFunction function = new MarkovMultivariateFunction(hmm, includePriors: false);
foreach (double[][] x in observations)
{
foreach (int y in labels)
{
double[,] actual = new double[5, 2];
Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.LogForward(function.Factors[y], x, y, actual);
double[,] expected = new double[5, 2];
Accord.Statistics.Models.Markov.
ForwardBackwardAlgorithm.LogForward(hmm.Models[y], x, expected);
for (int i = 0; i < actual.GetLength(0); i++)
{
for (int j = 0; j < actual.GetLength(1); j++)
{
Assert.AreEqual(expected[i, j], actual[i, j], 1e-10);
}
}
}
}
}
public void NumberOfFeaturesTest()
{
Independent initial = new Independent(
new GeneralDiscreteDistribution(46), // output,
new NormalDistribution(0, 1), // headAngle,
new NormalDistribution(0, 1), // handAngle,
new NormalDistribution(0, 1), // relHandX,
new NormalDistribution(0, 1) // relHandY,
);
var model = new HiddenMarkovClassifier <Independent>(
classes: 13, topology: new Forward(5), initial: initial);
var function = new MarkovMultivariateFunction(model);
var field = new HiddenConditionalRandomField <double[]>(function);
int discreteDistributions = 1;
int continuousDistributions = 4;
int symbols = 46;
int states = 5;
int classes = 13;
int expected = classes *
(1 + states + states * states +
states * discreteDistributions * symbols +
states * continuousDistributions * 3);
Assert.AreEqual(expected, field.Function.Features.Length);
Assert.AreEqual(expected, field.Function.Weights.Length);
Assert.AreEqual(4173, expected);
}
public void ForwardTest4()
{
var hmmc = Accord.Tests.Statistics.Models.Fields.
MultivariateMarkovFunctionTest.CreateModel3();
var hmm = hmmc[0];
var function = new MarkovMultivariateFunction(hmm);
var observations = Accord.Tests.Statistics.Models.Fields.
MultivariateMarkovFunctionTest.inputTest[3];
double expectedLogLikelihood;
double[,] expected = Accord.Statistics.Models.Markov
.ForwardBackwardAlgorithm.Forward(hmm, observations, out expectedLogLikelihood);
double actualLogLikelihood;
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Forward(function.Factors[0], observations, 0, out actualLogLikelihood);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
Assert.AreEqual(expectedLogLikelihood, actualLogLikelihood, 1e-6);
Assert.IsFalse(Double.IsNaN(actualLogLikelihood));
}
public void GradientTest3()
{
var hmm = MultivariateNormalHiddenMarkovClassifierPotentialFunctionTest.CreateModel1();
var function = new MarkovMultivariateFunction(hmm);
var model = new HiddenConditionalRandomField <double[]>(function);
var target = new ForwardBackwardGradient <double[]>(model);
target.Regularization = 2;
var inputs = inputs1;
var outputs = outputs1;
FiniteDifferences diff = new FiniteDifferences(function.Weights.Length);
diff.Function = parameters => func(model, parameters, inputs, outputs, target.Regularization);
double[] expected = diff.Compute(function.Weights);
double[] actual = target.Gradient(function.Weights, inputs, outputs);
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 1e-3);
Assert.IsFalse(double.IsNaN(actual[i]));
Assert.IsFalse(double.IsNaN(expected[i]));
}
}
public void LogForwardGesturesDeoptimizedTest()
{
int[] labels;
double[][][] words;
var classifier = IndependentMarkovFunctionTest.CreateModel4(out words, out labels, false);
var function = new MarkovMultivariateFunction(classifier);
function.Deoptimize();
var target = new HiddenConditionalRandomField <double[]>(function);
foreach (var word in words)
{
for (int c = 0; c < 3; c++)
{
var actual = Accord.Statistics.Models.Fields.ForwardBackwardAlgorithm.LogForward(
target.Function.Factors[c], word, c);
var expected = Accord.Statistics.Models.Markov.ForwardBackwardAlgorithm.LogForward(
classifier[c], word);
for (int i = 0; i < actual.GetLength(0); i++)
{
for (int j = 0; j < actual.GetLength(1); j++)
{
double a = actual[i, j];
double e = expected[i, j];
Assert.IsTrue(e.IsRelativelyEqual(a, 0.1));
}
}
}
}
}
public void GradientDeoptimizeTest2()
{
double[][][] sequences2;
int[] labels2;
var hmm = CreateModel3(out sequences2, out labels2);
var function = new MarkovMultivariateFunction(hmm);
#pragma warning disable 0618
function.Deoptimize();
#pragma warning restore 0618
var model = new HiddenConditionalRandomField <double[]>(function);
var target = new ForwardBackwardGradient <double[]>(model);
var inputs = sequences2;
var outputs = labels2;
double[] actual = target.Gradient(function.Weights, inputs, outputs);
FiniteDifferences diff = new FiniteDifferences(function.Weights.Length);
diff.Function = parameters => func(model, parameters, inputs, outputs);
double[] expected = diff.Compute(function.Weights);
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 1e-3);
Assert.IsFalse(double.IsNaN(actual[i]));
Assert.IsFalse(double.IsNaN(expected[i]));
}
}
public void RunTest()
{
var hmm = MultivariateNormalHiddenMarkovClassifierPotentialFunctionTest.CreateModel1();
var function = new MarkovMultivariateFunction(hmm);
var model = new HiddenConditionalRandomField <double[]>(function);
var target = new HiddenQuasiNewtonLearning <double[]>(model);
var inputs = inputs1;
var outputs = outputs1;
double[] actual = new double[inputs.Length];
double[] expected = new double[inputs.Length];
for (int i = 0; i < inputs.Length; i++)
{
actual[i] = model.Compute(inputs[i]);
expected[i] = outputs[i];
}
for (int i = 0; i < inputs.Length; i++)
{
Assert.AreEqual(expected[i], actual[i]);
}
double llm = hmm.LogLikelihood(inputs, outputs);
double ll0 = model.LogLikelihood(inputs, outputs);
Assert.AreEqual(llm, ll0, 1e-10);
Assert.IsFalse(double.IsNaN(llm));
Assert.IsFalse(double.IsNaN(ll0));
double error = target.Run(inputs, outputs);
double ll1 = model.LogLikelihood(inputs, outputs);
Assert.AreEqual(-ll1, error, 1e-10);
Assert.IsFalse(double.IsNaN(ll1));
Assert.IsFalse(double.IsNaN(error));
for (int i = 0; i < inputs.Length; i++)
{
actual[i] = model.Compute(inputs[i]);
expected[i] = outputs[i];
}
Assert.AreEqual(-0.0000041736023117522336, ll0, 1e-10);
Assert.AreEqual(error, -ll1);
Assert.IsFalse(Double.IsNaN(ll0));
Assert.IsFalse(Double.IsNaN(error));
for (int i = 0; i < inputs.Length; i++)
{
Assert.AreEqual(expected[i], actual[i]);
}
Assert.IsTrue(ll1 > ll0);
}
public void ComputeTest3()
{
var hmm = MultivariateMarkovFunctionTest.CreateModel1();
var owner = new MarkovMultivariateFunction(hmm);
double[][] x =
{
new double[] { 0 },
new double[] { 1 },
new double[] { 3 },
new double[] { 1 },
new double[] { 2 },
new double[] { 8 },
new double[] { 0 },
new double[] { 10 },
new double[] { System.Math.PI },
};
foreach (var factor in owner.Factors)
{
for (int y = 0; y < owner.Outputs; y++)
{
double[,] fwd = Accord.Statistics.Models.Fields
.ForwardBackwardAlgorithm.Forward(factor, x, y);
double[,] bwd = Accord.Statistics.Models.Fields
.ForwardBackwardAlgorithm.Backward(factor, x, y);
double[,] lnfwd = Accord.Statistics.Models.Fields
.ForwardBackwardAlgorithm.LogForward(factor, x, y);
double[,] lnbwd = Accord.Statistics.Models.Fields
.ForwardBackwardAlgorithm.LogBackward(factor, x, y);
for (int i = 0; i < fwd.GetLength(0); i++)
for (int j = 0; j < fwd.GetLength(1); j++)
Assert.AreEqual(System.Math.Log(fwd[i, j]), lnfwd[i, j], 1e-10);
for (int i = 0; i < bwd.GetLength(0); i++)
for (int j = 0; j < bwd.GetLength(1); j++)
Assert.AreEqual(System.Math.Log(bwd[i, j]), lnbwd[i, j], 1e-10);
foreach (var feature in factor)
{
double expected = System.Math.Log(feature.Marginal(fwd, bwd, x, y));
double actual = feature.LogMarginal(lnfwd, lnbwd, x, y);
Assert.AreEqual(expected, actual, 1e-10);
Assert.IsFalse(Double.IsNaN(actual));
}
}
}
}
public void ComputeTestPriors4()
{
int[] labels;
double[][][] words;
var model = CreateModel4(out words, out labels, true);
var target = new MarkovMultivariateFunction(model);
var hcrf = new HiddenConditionalRandomField <double[]>(target);
double actual;
double expected;
foreach (var x in words)
{
for (int c = 0; c < model.Classes; c++)
{
for (int i = 0; i < model[c].States; i++)
{
// Check initial state transitions
double xa = model.Priors[c];
double xb = Math.Exp(model[c].Probabilities[i]);
double xc = model[c].Emissions[i].ProbabilityDensityFunction(x[0]);
expected = xa * xb * xc;
actual = Math.Exp(target.Factors[c].Compute(-1, i, x, 0, c));
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-5));
Assert.IsFalse(double.IsNaN(actual));
}
for (int t = 1; t < x.Length; t++)
{
// Check normal state transitions
for (int i = 0; i < model[c].States; i++)
{
for (int j = 0; j < model[c].States; j++)
{
double xb = Math.Exp(model[c].Transitions[i, j]);
double xc = model[c].Emissions[j].ProbabilityDensityFunction(x[t]);
expected = xb * xc;
actual = Math.Exp(target.Factors[c].Compute(i, j, x, t, c));
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-6));
Assert.IsFalse(double.IsNaN(actual));
}
}
}
actual = Math.Exp(model.LogLikelihood(x, c));
expected = Math.Exp(hcrf.LogLikelihood(x, c));
Assert.AreEqual(expected, actual, 1e-10);
Assert.IsFalse(double.IsNaN(actual));
actual = model.Compute(x);
expected = hcrf.Compute(x);
Assert.AreEqual(expected, actual);
Assert.IsFalse(double.IsNaN(actual));
}
}
}
public void RunTest()
{
var hmm = MultivariateNormalHiddenMarkovClassifierPotentialFunctionTest.CreateModel1();
var function = new MarkovMultivariateFunction(hmm);
var model = new HiddenConditionalRandomField<double[]>(function);
var target = new HiddenQuasiNewtonLearning<double[]>(model);
var inputs = inputs1;
var outputs = outputs1;
double[] actual = new double[inputs.Length];
double[] expected = new double[inputs.Length];
for (int i = 0; i < inputs.Length; i++)
{
actual[i] = model.Compute(inputs[i]);
expected[i] = outputs[i];
}
for (int i = 0; i < inputs.Length; i++)
Assert.AreEqual(expected[i], actual[i]);
double llm = hmm.LogLikelihood(inputs, outputs);
double ll0 = model.LogLikelihood(inputs, outputs);
Assert.AreEqual(llm, ll0, 1e-10);
Assert.IsFalse(double.IsNaN(llm));
Assert.IsFalse(double.IsNaN(ll0));
double error = target.Run(inputs, outputs);
double ll1 = model.LogLikelihood(inputs, outputs);
Assert.AreEqual(-ll1, error, 1e-10);
Assert.IsFalse(double.IsNaN(ll1));
Assert.IsFalse(double.IsNaN(error));
for (int i = 0; i < inputs.Length; i++)
{
actual[i] = model.Compute(inputs[i]);
expected[i] = outputs[i];
}
Assert.AreEqual(-0.0000041736023117522336, ll0, 1e-10);
Assert.AreEqual(error, -ll1);
Assert.IsFalse(Double.IsNaN(ll0));
Assert.IsFalse(Double.IsNaN(error));
for (int i = 0; i < inputs.Length; i++)
Assert.AreEqual(expected[i], actual[i]);
Assert.IsTrue(ll1 > ll0);
}
public void learn_test()
{
double[][][] sequences;
int[] labels;
HiddenMarkovClassifier <Independent, double[]> model =
CreateModel2_learn(out sequences, out labels);
var target = new MarkovMultivariateFunction(model);
var hcrf = new HiddenConditionalRandomField <double[]>(target);
double actual;
double expected;
double[][] x = { new double[] { 0, 1.7 }, new double[] { 2, 2.1 } };
for (int c = 0; c < model.Classes; c++)
{
for (int i = 0; i < model[c].States; i++)
{
// Check initial state transitions
expected = model.Priors[c] * Math.Exp(model[c].LogInitial[i]) * model[c].Emissions[i].ProbabilityDensityFunction(x[0]);
actual = Math.Exp(target.Factors[c].Compute(-1, i, x, 0, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
for (int t = 1; t < x.Length; t++)
{
// Check normal state transitions
for (int i = 0; i < model[c].States; i++)
{
for (int j = 0; j < model[c].States; j++)
{
double xb = Math.Exp(model[c].LogTransitions[i][j]);
double xc = model[c].Emissions[j].ProbabilityDensityFunction(x[t]);
expected = xb * xc;
actual = Math.Exp(target.Factors[c].Compute(i, j, x, t, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
}
}
actual = model.LogLikelihood(x, c);
expected = hcrf.LogLikelihood(x, c);
Assert.AreEqual(expected, actual);
Assert.IsFalse(double.IsNaN(actual));
}
}
public void ComputeTest()
{
var model = CreateModel1();
var target = new MarkovMultivariateFunction(model);
var hcrf = new HiddenConditionalRandomField <double[]>(target);
double actual;
double expected;
double[][] x = { new double[] { 0 }, new double[] { 1 } };
for (int c = 0; c < model.Classes; c++)
{
for (int i = 0; i < model[c].States; i++)
{
// Check initial state transitions
expected = model.Priors[c] * Math.Exp(model[c].Probabilities[i]) * model[c].Emissions[i].ProbabilityDensityFunction(x[0]);
actual = Math.Exp(target.Factors[c].Compute(-1, i, x, 0, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
for (int t = 1; t < x.Length; t++)
{
// Check normal state transitions
for (int i = 0; i < model[c].States; i++)
{
for (int j = 0; j < model[c].States; j++)
{
double xb = Math.Exp(model[c].Transitions[i, j]);
double xc = model[c].Emissions[j].ProbabilityDensityFunction(x[t]);
expected = xb * xc;
actual = Math.Exp(target.Factors[c].Compute(i, j, x, t, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
}
}
actual = model.LogLikelihood(x, c);
expected = hcrf.LogLikelihood(x, c);
Assert.AreEqual(expected, actual, 1e-8);
Assert.IsFalse(double.IsNaN(actual));
}
}
public void ForwardTest2()
{
double[][][] observations;
int[] labels;
var hmm = IndependentMarkovFunctionTest.CreateModel3(out observations, out labels);
var function = new MarkovMultivariateFunction(hmm, includePriors: false);
foreach (double[][] x in observations)
{
foreach (int y in labels)
{
double[] scaling1;
double logLikelihood1;
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Forward(function.Factors[y], x, y, out scaling1, out logLikelihood1);
double[] scaling2;
double logLikelihood2;
double[,] expected = Accord.Statistics.Models.Markov.
ForwardBackwardAlgorithm.Forward(hmm.Models[y], x, out scaling2, out logLikelihood2);
for (int i = 0; i < actual.GetLength(0); i++)
{
for (int j = 0; j < actual.GetLength(1); j++)
{
Assert.AreEqual(expected[i, j], actual[i, j], 1e-10);
Assert.IsFalse(Double.IsNaN(actual[i, j]));
}
}
Assert.AreEqual(logLikelihood1, logLikelihood2, 1e-10);
for (int i = 0; i < scaling1.Length; i++)
{
Assert.IsTrue(scaling1[i].IsRelativelyEqual(scaling2[i], 1e-10));
Assert.IsFalse(Double.IsNaN(scaling1[i]));
Assert.IsFalse(Double.IsNaN(scaling2[i]));
}
}
}
}
public void ComputeTest4()
{
int[] labels;
double[][][] words;
HiddenMarkovClassifier <Independent <NormalDistribution> > model =
CreateModel4(out words, out labels, false);
var target = new MarkovMultivariateFunction(model);
var hcrf = new HiddenConditionalRandomField <double[]>(target);
Assert.AreEqual(3, model.Priors.Length);
Assert.AreEqual(1 / 3.0, model.Priors[0]);
Assert.AreEqual(1 / 3.0, model.Priors[1]);
Assert.AreEqual(1 / 3.0, model.Priors[2]);
check4(words, model, target, hcrf);
}
public void GradientTest_MarkovMultivariate()
{
// Creates a sequence classifier containing 2 hidden Markov Models
// with 2 states and an underlying Normal distribution as density.
MultivariateNormalDistribution density = new MultivariateNormalDistribution(3);
var hmm = new HiddenMarkovClassifier <MultivariateNormalDistribution>(2, new Ergodic(2), density);
double[][][] inputs =
{
new [] { new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 } },
new [] { new double[] { 1, 6, 2 }, new double[] { 2, 1, 6 }, new double[] { 1, 1, 0 } },
new [] { new double[] { 9, 1, 0 }, new double[] { 0, 1, 5 }, new double[] { 0, 0, 0 } },
};
int[] outputs =
{
0, 0, 1
};
var function = new MarkovMultivariateFunction(hmm);
var model = new HiddenConditionalRandomField <double[]>(function);
var target = new ForwardBackwardGradient <double[]>(model);
FiniteDifferences diff = new FiniteDifferences(function.Weights.Length)
{
StepSize = 1e-5
};
diff.Function = parameters => func(model, parameters, inputs, outputs);
double[] expected = diff.Compute(function.Weights);
double[] actual = target.Gradient(function.Weights, inputs, outputs);
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 0.05);
Assert.IsFalse(double.IsNaN(actual[i]));
Assert.IsFalse(double.IsNaN(expected[i]));
}
}
public void LogForwardTest3()
{
MultivariateNormalDistribution density = new MultivariateNormalDistribution(3);
var hmm = new HiddenMarkovClassifier <MultivariateNormalDistribution>(2, new Ergodic(2), density);
double[][][] inputs =
{
new [] { new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 } },
new [] { new double[] { 1, 6, 2 }, new double[] { 2, 1, 6 }, new double[] { 1, 1, 0 } },
new [] { new double[] { 9, 1, 0 }, new double[] { 0, 1, 5 }, new double[] { 0, 0, 0 } },
};
int[] outputs =
{
0, 0, 1
};
var function = new MarkovMultivariateFunction(hmm);
var observations = inputs[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[0].States; i++)
{
p += Math.Exp(actual[observations.Length - 1, i]);
}
Assert.AreEqual(Math.Exp(logLikelihood), p, 1e-8);
Assert.IsFalse(double.IsNaN(p));
}
public void ComputeDeoptimizeTest3()
{
double[][][] sequences;
int[] labels;
var model = CreateModel3(out sequences, out labels);
var target = new MarkovMultivariateFunction(model);
#pragma warning disable 0618
target.Deoptimize();
#pragma warning restore 0618
var hcrf = new HiddenConditionalRandomField <double[]>(target);
Assert.AreEqual(2, model.Priors.Length);
Assert.AreEqual(1 / 2.0, model.Priors[0]);
Assert.AreEqual(1 / 2.0, model.Priors[1]);
check4(sequences, model, target, hcrf);
}
public void ComputeDeoptimizeTest4()
{
int[] labels;
double[][][] words;
var model = CreateModel4(out words, out labels, false);
var target = new MarkovMultivariateFunction(model);
#pragma warning disable 0618
target.Deoptimize();
#pragma warning restore 0618
var hcrf = new HiddenConditionalRandomField <double[]>(target);
Assert.AreEqual(3, model.Priors.Length);
Assert.AreEqual(1 / 3.0, model.Priors[0]);
Assert.AreEqual(1 / 3.0, model.Priors[1]);
Assert.AreEqual(1 / 3.0, model.Priors[2]);
check4(words, model, target, hcrf);
}
public void ForwardTest()
{
double[][][] observations;
int[] labels;
var hmm = IndependentMarkovFunctionTest.CreateModel2(out observations, out labels);
var function = new MarkovMultivariateFunction(hmm, includePriors: false);
foreach (double[][] x in observations)
{
foreach (int y in labels)
{
double[] scaling1;
double logLikelihood1;
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Forward(function.Factors[y], x, y, out scaling1, out logLikelihood1);
double[] scaling2;
double logLikelihood2;
double[,] expected = Accord.Statistics.Models.Markov.
ForwardBackwardAlgorithm.Forward(hmm.Models[y], x, out scaling2, out logLikelihood2);
for (int i = 0; i < actual.GetLength(0); i++)
for (int j = 0; j < actual.GetLength(1); j++)
{
Assert.AreEqual(expected[i, j], actual[i, j], 1e-10);
Assert.IsFalse(Double.IsNaN(actual[i, j]));
}
Assert.AreEqual(logLikelihood1, logLikelihood2, 1e-10);
for (int i = 0; i < scaling1.Length; i++)
Assert.AreEqual(scaling1[i], scaling2[i], 1e-10);
}
}
}
public void LogForwardTest4()
{
var hmmc = Accord.Tests.Statistics.Models.Fields.
MultivariateMarkovFunctionTest.CreateModel3();
for (int c = 0; c < hmmc.Classes; c++)
{
var hmm = hmmc[c];
var function = new MarkovMultivariateFunction(hmm);
var sequences = Accord.Tests.Statistics.Models.Fields.
MultivariateMarkovFunctionTest.inputTest;
for (int i = 0; i < sequences.Length; i++)
{
var observations = sequences[i];
double expectedLogLikelihood;
double[,] expected = Accord.Statistics.Models.Markov
.ForwardBackwardAlgorithm.LogForward(hmm, observations, out expectedLogLikelihood);
double actualLogLikelihood;
double[,] actual = Accord.Statistics.Models.Fields
.ForwardBackwardAlgorithm.LogForward(function.Factors[0], observations, 0, out actualLogLikelihood);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
Assert.AreEqual(expectedLogLikelihood, actualLogLikelihood, 1e-6);
Assert.IsFalse(Double.IsNaN(actualLogLikelihood));
}
}
}
public void ForwardTest4()
{
var hmmc = Accord.Tests.Statistics.Models.Fields.
MultivariateMarkovFunctionTest.CreateModel3();
var hmm = hmmc[0];
var function = new MarkovMultivariateFunction(hmm);
var observations = Accord.Tests.Statistics.Models.Fields.
MultivariateMarkovFunctionTest.inputTest[3];
double expectedLogLikelihood;
double[,] expected = Accord.Statistics.Models.Markov
.ForwardBackwardAlgorithm.Forward(hmm, observations, out expectedLogLikelihood);
double actualLogLikelihood;
double[,] actual = Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.Forward(function.Factors[0], observations, 0, out actualLogLikelihood);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
Assert.AreEqual(expectedLogLikelihood, actualLogLikelihood, 1e-6);
Assert.IsFalse(Double.IsNaN(actualLogLikelihood));
}
public void LogForwardTest3()
{
MultivariateNormalDistribution density = new MultivariateNormalDistribution(3);
var hmm = new HiddenMarkovClassifier<MultivariateNormalDistribution>(2, new Ergodic(2), density);
double[][][] inputs =
{
new [] { new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 } },
new [] { new double[] { 1, 6, 2 }, new double[] { 2, 1, 6 }, new double[] { 1, 1, 0 } },
new [] { new double[] { 9, 1, 0 }, new double[] { 0, 1, 5 }, new double[] { 0, 0, 0 } },
};
int[] outputs =
{
0, 0, 1
};
var function = new MarkovMultivariateFunction(hmm);
var observations = inputs[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[0].States; i++)
p += Math.Exp(actual[observations.Length - 1, i]);
Assert.AreEqual(Math.Exp(logLikelihood), p, 1e-8);
Assert.IsFalse(double.IsNaN(p));
}
public void SimpleGestureRecognitionTest()
{
// Let's say we would like to do a very simple mechanism for
// gesture recognition. In this example, we will be trying to
// create a classifier that can distinguish between the words
// "hello", "car", and "wardrobe".
// Let's say we decided to acquire some data, and we asked some
// people to perform those words in front of a Kinect camera, and,
// using Microsoft's SDK, we were able to captured the x and y
// coordinates of each hand while the word was being performed.
// Let's say we decided to represent our frames as:
//
// double[] frame = { leftHandX, leftHandY, rightHandX, rightHandY };
//
// Since we captured words, this means we captured sequences of
// frames as we described above. Let's write some of those as
// rough examples to explain how gesture recognition can be done:
double[][] hello =
{
new double[] { 1.0, 0.1, 0.0, 0.0 }, // let's say the word
new double[] { 0.0, 1.0, 0.1, 0.1 }, // hello took 6 frames
new double[] { 0.0, 1.0, 0.1, 0.1 }, // to be recorded.
new double[] { 0.0, 0.0, 1.0, 0.0 },
new double[] { 0.0, 0.0, 1.0, 0.0 },
new double[] { 0.0, 0.0, 0.1, 1.1 },
};
double[][] car =
{
new double[] { 0.0, 0.0, 0.0, 1.0 }, // the car word
new double[] { 0.1, 0.0, 1.0, 0.1 }, // took only 4.
new double[] { 0.0, 0.0, 0.1, 0.0 },
new double[] { 1.0, 0.0, 0.0, 0.0 },
};
double[][] wardrobe =
{
new double[] { 0.0, 0.0, 1.0, 0.0 }, // same for the
new double[] { 0.1, 0.0, 1.0, 0.1 }, // wardrobe word.
new double[] { 0.0, 0.1, 1.0, 0.0 },
new double[] { 0.1, 0.0, 1.0, 0.1 },
};
// Here, please note that a real-world example would involve *lots*
// of samples for each word. Here, we are considering just one from
// each class which is clearly sub-optimal and should _never_ be done
// on practice. For example purposes, however, please disregard this.
// Those are the words we have in our vocabulary:
//
double[][][] words = { hello, car, wardrobe };
// Now, let's associate integer labels with them. This is needed
// for the case where there are multiple samples for each word.
//
int[] labels = { 0, 1, 2 };
// We will create our classifiers assuming an independent
// Gaussian distribution for each component in our feature
// vectors (like assuming a Naive Bayes assumption).
var initial = new Independent <NormalDistribution>
(
new NormalDistribution(0, 1),
new NormalDistribution(0, 1),
new NormalDistribution(0, 1),
new NormalDistribution(0, 1)
);
// Now, we can proceed and create our classifier.
//
int numberOfWords = 3; // we are trying to distinguish between 3 words
int numberOfStates = 5; // this value can be found by trial-and-error
var hmm = new HiddenMarkovClassifier <Independent <NormalDistribution> >
(
classes: numberOfWords,
topology: new Forward(numberOfStates), // word classifiers should use a forward topology
initial: initial
);
// Create a new learning algorithm to train the sequence classifier
var teacher = new HiddenMarkovClassifierLearning <Independent <NormalDistribution> >(hmm,
// Train each model until the log-likelihood changes less than 0.001
modelIndex => new BaumWelchLearning <Independent <NormalDistribution> >(hmm.Models[modelIndex])
{
Tolerance = 0.001,
Iterations = 100,
// This is necessary so the code doesn't blow up when it realize
// there is only one sample per word class. But this could also be
// needed in normal situations as well.
//
FittingOptions = new IndependentOptions()
{
InnerOption = new NormalOptions()
{
Regularization = 1e-5
}
}
}
);
// Finally, we can run the learning algorithm!
double logLikelihood = teacher.Run(words, labels);
// At this point, the classifier should be successfully
// able to distinguish between our three word classes:
//
int tc1 = hmm.Compute(hello);
int tc2 = hmm.Compute(car);
int tc3 = hmm.Compute(wardrobe);
Assert.AreEqual(0, tc1);
Assert.AreEqual(1, tc2);
Assert.AreEqual(2, tc3);
// Now, we can use the Markov classifier to initialize a HCRF
var function = new MarkovMultivariateFunction(hmm);
var hcrf = new HiddenConditionalRandomField <double[]>(function);
// We can check that both are equivalent, although they have
// formulations that can be learned with different methods
//
for (int i = 0; i < words.Length; i++)
{
// Should be the same
int expected = hmm.Compute(words[i]);
int actual = hcrf.Compute(words[i]);
// Should be the same
double h0 = hmm.LogLikelihood(words[i], 0);
double c0 = hcrf.LogLikelihood(words[i], 0);
double h1 = hmm.LogLikelihood(words[i], 1);
double c1 = hcrf.LogLikelihood(words[i], 1);
double h2 = hmm.LogLikelihood(words[i], 2);
double c2 = hcrf.LogLikelihood(words[i], 2);
Assert.AreEqual(expected, actual);
Assert.AreEqual(h0, c0, 1e-10);
Assert.IsTrue(h1.IsRelativelyEqual(c1, 1e-10));
Assert.IsTrue(h2.IsRelativelyEqual(c2, 1e-10));
Assert.IsFalse(double.IsNaN(c0));
Assert.IsFalse(double.IsNaN(c1));
Assert.IsFalse(double.IsNaN(c2));
}
// Now we can learn the HCRF using one of the best learning
// algorithms available, Resilient Backpropagation learning:
// Create a learning algorithm
var rprop = new HiddenResilientGradientLearning <double[]>(hcrf)
{
Iterations = 50,
Tolerance = 1e-5
};
// Run the algorithm and learn the models
double error = rprop.Run(words, labels);
// At this point, the HCRF should be successfully
// able to distinguish between our three word classes:
//
int hc1 = hcrf.Compute(hello);
int hc2 = hcrf.Compute(car);
int hc3 = hcrf.Compute(wardrobe);
Assert.AreEqual(0, hc1);
Assert.AreEqual(1, hc2);
Assert.AreEqual(2, hc3);
}
public void GradientTest3()
{
var hmm = MultivariateNormalHiddenMarkovClassifierPotentialFunctionTest.CreateModel1();
var function = new MarkovMultivariateFunction(hmm);
var model = new HiddenConditionalRandomField<double[]>(function);
var target = new ForwardBackwardGradient<double[]>(model);
target.Regularization = 2;
var inputs = inputs1;
var outputs = outputs1;
FiniteDifferences diff = new FiniteDifferences(function.Weights.Length);
diff.Function = parameters => func(model, parameters, inputs, outputs, target.Regularization);
double[] expected = diff.Compute(function.Weights);
double[] actual = target.Gradient(function.Weights, inputs, outputs);
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 1e-3);
Assert.IsFalse(double.IsNaN(actual[i]));
Assert.IsFalse(double.IsNaN(expected[i]));
}
}
private static void check4(double[][][] words, HiddenMarkovClassifier<Independent> model, MarkovMultivariateFunction target, HiddenConditionalRandomField<double[]> hcrf)
{
double actual;
double expected;
foreach (var x in words)
{
for (int c = 0; c < model.Classes; c++)
{
for (int i = 0; i < model[c].States; i++)
{
// Check initial state transitions
double xa = model.Priors[c];
double xb = Math.Exp(model[c].Probabilities[i]);
double xc = model[c].Emissions[i].ProbabilityDensityFunction(x[0]);
expected = xa * xb * xc;
actual = Math.Exp(target.Factors[c].Compute(-1, i, x, 0, c));
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-10));
Assert.IsFalse(double.IsNaN(actual));
}
for (int t = 1; t < x.Length; t++)
{
// Check normal state transitions
for (int i = 0; i < model[c].States; i++)
{
for (int j = 0; j < model[c].States; j++)
{
double xb = Math.Exp(model[c].Transitions[i, j]);
double xc = model[c].Emissions[j].ProbabilityDensityFunction(x[t]);
expected = xb * xc;
actual = Math.Exp(target.Factors[c].Compute(i, j, x, t, c));
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-10));
Assert.IsFalse(double.IsNaN(actual));
}
}
}
actual = Math.Exp(model.LogLikelihood(x, c));
expected = Math.Exp(hcrf.LogLikelihood(x, c));
Assert.AreEqual(expected, actual, 1e-10);
Assert.IsFalse(double.IsNaN(actual));
actual = model.Compute(x);
expected = hcrf.Compute(x);
Assert.AreEqual(expected, actual);
Assert.IsFalse(double.IsNaN(actual));
}
}
}
public void SaveLoadTest()
{
double[][] hello =
{
new double[] { 1.0, 0.1, 0.0, 0.0 }, // let's say the word
new double[] { 0.0, 1.0, 0.1, 0.1 }, // hello took 6 frames
new double[] { 0.0, 1.0, 0.1, 0.1 }, // to be recorded.
new double[] { 0.0, 0.0, 1.0, 0.0 },
new double[] { 0.0, 0.0, 1.0, 0.0 },
new double[] { 0.0, 0.0, 0.1, 1.1 },
};
double[][] car =
{
new double[] { 0.0, 0.0, 0.0, 1.0 }, // the car word
new double[] { 0.1, 0.0, 1.0, 0.1 }, // took only 4.
new double[] { 0.0, 0.0, 0.1, 0.0 },
new double[] { 1.0, 0.0, 0.0, 0.0 },
};
double[][] wardrobe =
{
new double[] { 0.0, 0.0, 1.0, 0.0 }, // same for the
new double[] { 0.1, 0.0, 1.0, 0.1 }, // wardrobe word.
new double[] { 0.0, 0.1, 1.0, 0.0 },
new double[] { 0.1, 0.0, 1.0, 0.1 },
};
double[][][] words = { hello, car, wardrobe };
int[] labels = { 0, 1, 2 };
var initial = new Independent
(
new NormalDistribution(0, 1),
new NormalDistribution(0, 1),
new NormalDistribution(0, 1),
new NormalDistribution(0, 1)
);
int numberOfWords = 3;
int numberOfStates = 5;
var classifier = new HiddenMarkovClassifier <Independent>
(
classes: numberOfWords,
topology: new Forward(numberOfStates),
initial: initial
);
var teacher = new HiddenMarkovClassifierLearning <Independent>(classifier,
modelIndex => new BaumWelchLearning <Independent>(classifier.Models[modelIndex])
{
Tolerance = 0.001,
Iterations = 100,
FittingOptions = new IndependentOptions()
{
InnerOption = new NormalOptions()
{
Regularization = 1e-5
}
}
}
);
double logLikelihood = teacher.Run(words, labels);
var function = new MarkovMultivariateFunction(classifier);
var hcrf = new HiddenConditionalRandomField <double[]>(function);
MemoryStream stream = new MemoryStream();
hcrf.Save(stream);
stream.Seek(0, SeekOrigin.Begin);
var target = HiddenConditionalRandomField <double[]> .Load(stream);
Assert.AreEqual(hcrf.Function.Factors.Length, target.Function.Factors.Length);
for (int i = 0; i < hcrf.Function.Factors.Length; i++)
{
var e = hcrf.Function.Factors[i];
var a = target.Function.Factors[i];
Assert.AreEqual(e.Index, target.Function.Factors[i].Index);
Assert.AreEqual(e.States, target.Function.Factors[i].States);
Assert.AreEqual(e.EdgeParameters.Count, a.EdgeParameters.Count);
Assert.AreEqual(e.EdgeParameters.Offset, a.EdgeParameters.Offset);
Assert.AreEqual(e.FactorParameters.Count, a.FactorParameters.Count);
Assert.AreEqual(e.FactorParameters.Offset, a.FactorParameters.Offset);
Assert.AreEqual(e.OutputParameters.Count, a.OutputParameters.Count);
Assert.AreEqual(e.OutputParameters.Offset, a.OutputParameters.Offset);
Assert.AreEqual(e.StateParameters.Count, a.StateParameters.Count);
Assert.AreEqual(e.StateParameters.Offset, a.StateParameters.Offset);
Assert.AreEqual(target.Function, a.Owner);
Assert.AreEqual(hcrf.Function, e.Owner);
}
Assert.AreEqual(hcrf.Function.Features.Length, target.Function.Features.Length);
for (int i = 0; i < hcrf.Function.Factors.Length; i++)
{
Assert.AreEqual(hcrf.Function.Features[i].GetType(), target.Function.Features[i].GetType());
}
Assert.AreEqual(hcrf.Function.Outputs, target.Function.Outputs);
for (int i = 0; i < hcrf.Function.Weights.Length; i++)
{
Assert.AreEqual(hcrf.Function.Weights[i], target.Function.Weights[i]);
}
}
public void ComputeTest3()
{
var model = CreateModel3();
var target = new MarkovMultivariateFunction(model);
var hcrf = new HiddenConditionalRandomField<double[]>(target);
double actual;
double expected;
for (int k = 0; k < 5; k++)
{
foreach (var x in sequences2)
{
for (int c = 0; c < model.Classes; c++)
{
for (int i = 0; i < model[c].States; i++)
{
// Check initial state transitions
double xa = model.Priors[c];
double xb = Math.Exp(model[c].Probabilities[i]);
double xc = model[c].Emissions[i].ProbabilityDensityFunction(x[0]);
expected = xa * xb * xc;
actual = Math.Exp(target.Factors[c].Compute(-1, i, x, 0, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
for (int t = 1; t < x.Length; t++)
{
// Check normal state transitions
for (int i = 0; i < model[c].States; i++)
{
for (int j = 0; j < model[c].States; j++)
{
expected = Math.Exp(model[c].Transitions[i, j]) * model[c].Emissions[j].ProbabilityDensityFunction(x[t]);
actual = Math.Exp(target.Factors[c].Compute(i, j, x, t, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
}
}
actual = Math.Exp(model.LogLikelihood(x, c));
expected = Math.Exp(hcrf.LogLikelihood(x, c));
Assert.AreEqual(expected, actual, 1e-10);
Assert.IsFalse(double.IsNaN(actual));
actual = model.Compute(x);
expected = hcrf.Compute(x);
Assert.AreEqual(expected, actual);
Assert.IsFalse(double.IsNaN(actual));
}
}
}
}
public void ComputeTest5()
{
var model = CreateModel3(states: 7);
var target = new MarkovMultivariateFunction(model);
double actual;
double expected;
double[][] x = { new double[] { 0, 1 }, new double[] { 3, 2 } };
for (int c = 0; c < model.Classes; c++)
{
for (int i = 0; i < model[c].States; i++)
{
// Check initial state transitions
expected = model.Priors[c] * Math.Exp(model[c].Probabilities[i]) * model[c].Emissions[i].ProbabilityDensityFunction(x[0]);
actual = Math.Exp(target.Factors[c].Compute(-1, i, x, 0, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
for (int t = 1; t < x.Length; t++)
{
// Check normal state transitions
for (int i = 0; i < model[c].States; i++)
{
for (int j = 0; j < model[c].States; j++)
{
expected = Math.Exp(model[c].Transitions[i, j]) * model[c].Emissions[j].ProbabilityDensityFunction(x[t]);
actual = Math.Exp(target.Factors[c].Compute(i, j, x, t, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
}
}
}
var hcrf = new HiddenConditionalRandomField<double[]>(target);
for (int i = 0; i < inputTest.Length; i++)
{
int h = model.Compute(inputTest[i]);
int c = hcrf.Compute(inputTest[i]);
Assert.AreEqual(h, c);
}
}
public void HiddenMarkovHiddenPotentialFunctionConstructorTest2()
{
var model = CreateModel2();
var target = new MarkovMultivariateFunction(model);
var features = target.Features;
double[] weights = target.Weights;
Assert.AreEqual(38, features.Length);
Assert.AreEqual(38, weights.Length);
int k = 0;
for (int c = 0; c < model.Classes; c++)
{
Assert.AreEqual(Math.Log(model.Priors[c]), weights[k++]);
for (int i = 0; i < model[c].States; i++)
Assert.AreEqual(model[c].Probabilities[i], weights[k++]);
for (int i = 0; i < model[c].States; i++)
for (int j = 0; j < model[c].States; j++)
Assert.AreEqual(model[c].Transitions[i, j], weights[k++]);
for (int i = 0; i < model[c].States; i++)
for (int j = 0; j < model[c].Dimension; j++)
{
double mean = model[c].Emissions[i].Mean[j];
double var = model[c].Emissions[i].Variance[j];
double l2ps = System.Math.Log(2 * System.Math.PI * var);
Assert.AreEqual(-0.5 * (l2ps + (mean * mean) / var), weights[k++]);
Assert.AreEqual(mean / var, weights[k++]);
Assert.AreEqual(-1.0 / (2 * var), weights[k++]);
}
}
}
private static void check4(double[][][] words, HiddenMarkovClassifier <Independent> model, MarkovMultivariateFunction target, HiddenConditionalRandomField <double[]> hcrf)
{
double actual;
double expected;
foreach (var x in words)
{
for (int c = 0; c < model.Classes; c++)
{
for (int i = 0; i < model[c].States; i++)
{
// Check initial state transitions
double xa = model.Priors[c];
double xb = Math.Exp(model[c].Probabilities[i]);
double xc = model[c].Emissions[i].ProbabilityDensityFunction(x[0]);
expected = xa * xb * xc;
actual = Math.Exp(target.Factors[c].Compute(-1, i, x, 0, c));
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-10));
Assert.IsFalse(double.IsNaN(actual));
}
for (int t = 1; t < x.Length; t++)
{
// Check normal state transitions
for (int i = 0; i < model[c].States; i++)
{
for (int j = 0; j < model[c].States; j++)
{
double xb = Math.Exp(model[c].Transitions[i, j]);
double xc = model[c].Emissions[j].ProbabilityDensityFunction(x[t]);
expected = xb * xc;
actual = Math.Exp(target.Factors[c].Compute(i, j, x, t, c));
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-10));
Assert.IsFalse(double.IsNaN(actual));
}
}
}
actual = Math.Exp(model.LogLikelihood(x, c));
expected = Math.Exp(hcrf.LogLikelihood(x, c));
Assert.AreEqual(expected, actual, 1e-10);
Assert.IsFalse(double.IsNaN(actual));
actual = model.Compute(x);
expected = hcrf.Compute(x);
Assert.AreEqual(expected, actual);
Assert.IsFalse(double.IsNaN(actual));
}
}
}
public void GradientDeoptimizeTest3()
{
double[][][] sequences2;
int[] labels2;
var hmm = CreateModel3(out sequences2, out labels2);
var function = new MarkovMultivariateFunction(hmm);
#pragma warning disable 0618
function.Deoptimize();
#pragma warning restore 0618
var model = new HiddenConditionalRandomField<double[]>(function);
var target = new ForwardBackwardGradient<double[]>(model);
target.Regularization = 2;
var inputs = sequences2;
var outputs = labels2;
FiniteDifferences diff = new FiniteDifferences(function.Weights.Length);
diff.Function = parameters => func(model, parameters, inputs, outputs, target.Regularization);
double[] expected = diff.Compute(function.Weights);
double[] actual = target.Gradient(function.Weights, inputs, outputs);
for (int i = 0; i < actual.Length; i++)
{
double e = expected[i];
double a = actual[i];
Assert.AreEqual(e, a, 1e-3);
Assert.IsFalse(double.IsNaN(actual[i]));
Assert.IsFalse(double.IsNaN(expected[i]));
}
}
public void ComputeTest2()
{
double[][][] sequences;
int[] labels;
var model = CreateModel2(out sequences, out labels);
var target = new MarkovMultivariateFunction(model);
var hcrf = new HiddenConditionalRandomField<double[]>(target);
double actual;
double expected;
double[][] x = { new double[] { 0, 1.7 }, new double[] { 2, 2.1 } };
for (int c = 0; c < model.Classes; c++)
{
for (int i = 0; i < model[c].States; i++)
{
// Check initial state transitions
expected = model.Priors[c] * Math.Exp(model[c].Probabilities[i]) * model[c].Emissions[i].ProbabilityDensityFunction(x[0]);
actual = Math.Exp(target.Factors[c].Compute(-1, i, x, 0, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
for (int t = 1; t < x.Length; t++)
{
// Check normal state transitions
for (int i = 0; i < model[c].States; i++)
{
for (int j = 0; j < model[c].States; j++)
{
double xb = Math.Exp(model[c].Transitions[i, j]);
double xc = model[c].Emissions[j].ProbabilityDensityFunction(x[t]);
expected = xb * xc;
actual = Math.Exp(target.Factors[c].Compute(i, j, x, t, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
}
}
actual = model.LogLikelihood(x, c);
expected = hcrf.LogLikelihood(x, c);
Assert.AreEqual(expected, actual);
Assert.IsFalse(double.IsNaN(actual));
}
}
public void LogBackwardTest2()
{
HiddenMarkovClassifier<Independent> hmm = IndependentMarkovClassifierPotentialFunctionTest
.CreateModel3();
MarkovMultivariateFunction function = new MarkovMultivariateFunction(hmm);
double[][][] observations = IndependentMarkovClassifierPotentialFunctionTest.sequences2;
int[] labels = IndependentMarkovClassifierPotentialFunctionTest.labels2;
foreach (double[][] x in observations)
{
foreach (int y in labels)
{
double[,] actual = new double[x.Length, 5];
Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.LogBackward(function.Factors[y], x, y, actual);
double[,] expected = new double[x.Length, 5];
Accord.Statistics.Models.Markov.
ForwardBackwardAlgorithm.LogBackward(hmm.Models[y], x, expected);
for (int i = 0; i < actual.GetLength(0); i++)
for (int j = 0; j < actual.GetLength(1); j++)
{
Assert.AreEqual(expected[i, j], actual[i, j], 1e-10);
Assert.IsFalse(Double.IsNaN(actual[i, j]));
}
}
}
}
public void GradientTest()
{
// Creates a sequence classifier containing 2 hidden Markov Models
// with 2 states and an underlying Normal distribution as density.
MultivariateNormalDistribution density = new MultivariateNormalDistribution(3);
var hmm = new HiddenMarkovClassifier<MultivariateNormalDistribution>(2, new Ergodic(2), density);
double[][][] inputs =
{
new [] { new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 }, new double[] { 0, 1, 0 } },
new [] { new double[] { 1, 6, 2 }, new double[] { 2, 1, 6 }, new double[] { 1, 1, 0 } },
new [] { new double[] { 9, 1, 0 }, new double[] { 0, 1, 5 }, new double[] { 0, 0, 0 } },
};
int[] outputs =
{
0, 0, 1
};
var function = new MarkovMultivariateFunction(hmm);
var model = new HiddenConditionalRandomField<double[]>(function);
var target = new ForwardBackwardGradient<double[]>(model);
FiniteDifferences diff = new FiniteDifferences(function.Weights.Length);
diff.Function = parameters => func(model, parameters, inputs, outputs);
double[] expected = diff.Compute(function.Weights);
double[] actual = target.Gradient(function.Weights, inputs, outputs);
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 0.05);
Assert.IsFalse(double.IsNaN(actual[i]));
Assert.IsFalse(double.IsNaN(expected[i]));
}
}
public void ComputeDeoptimizeTest3()
{
double[][][] sequences;
int[] labels;
var model = CreateModel3(out sequences, out labels);
var target = new MarkovMultivariateFunction(model);
#pragma warning disable 0618
target.Deoptimize();
#pragma warning restore 0618
var hcrf = new HiddenConditionalRandomField<double[]>(target);
Assert.AreEqual(2, model.Priors.Length);
Assert.AreEqual(1 / 2.0, model.Priors[0]);
Assert.AreEqual(1 / 2.0, model.Priors[1]);
check4(sequences, model, target, hcrf);
}
public void ComputeDeoptimizeTest4()
{
int[] labels;
double[][][] words;
var model = CreateModel4(out words, out labels, false);
var target = new MarkovMultivariateFunction(model);
#pragma warning disable 0618
target.Deoptimize();
#pragma warning restore 0618
var hcrf = new HiddenConditionalRandomField<double[]>(target);
Assert.AreEqual(3, model.Priors.Length);
Assert.AreEqual(1 / 3.0, model.Priors[0]);
Assert.AreEqual(1 / 3.0, model.Priors[1]);
Assert.AreEqual(1 / 3.0, model.Priors[2]);
check4(words, model, target, hcrf);
}
public void LogForwardTest()
{
double[][][] observations;
int[] labels;
var hmm = IndependentMarkovFunctionTest.CreateModel2(out observations, out labels);
MarkovMultivariateFunction function = new MarkovMultivariateFunction(hmm, includePriors: false);
foreach (double[][] x in observations)
{
foreach (int y in labels)
{
double[,] actual = new double[5, 2];
Accord.Statistics.Models.Fields.
ForwardBackwardAlgorithm.LogForward(function.Factors[y], x, y, actual);
double[,] expected = new double[5, 2];
Accord.Statistics.Models.Markov.
ForwardBackwardAlgorithm.LogForward(hmm.Models[y], x, expected);
for (int i = 0; i < actual.GetLength(0); i++)
for (int j = 0; j < actual.GetLength(1); j++)
Assert.AreEqual(expected[i, j], actual[i, j], 1e-10);
}
}
}
public void GradientTest4()
{
var hmm = IndependentMarkovClassifierPotentialFunctionTest.CreateModel2();
var function = new MarkovMultivariateFunction(hmm);
var model = new HiddenConditionalRandomField<double[]>(function);
var target = new ForwardBackwardGradient<double[]>(model);
target.Regularization = 0;
FiniteDifferences diff = new FiniteDifferences(function.Weights.Length);
diff.Function = parameters => func(model, parameters,
IndependentMarkovClassifierPotentialFunctionTest.sequences,
IndependentMarkovClassifierPotentialFunctionTest.labels);
double[] expected = diff.Compute(function.Weights);
double[] actual = target.Gradient(function.Weights,
IndependentMarkovClassifierPotentialFunctionTest.sequences,
IndependentMarkovClassifierPotentialFunctionTest.labels);
for (int i = 0; i < actual.Length; i++)
{
if (double.IsNaN(expected[i]))
continue;
Assert.AreEqual(expected[i], actual[i], 1e-5);
Assert.IsFalse(double.IsNaN(actual[i]));
}
}
public void GradientTest2()
{
var hmm = CreateModel3();
var function = new MarkovMultivariateFunction(hmm);
var model = new HiddenConditionalRandomField<double[]>(function);
var target = new ForwardBackwardGradient<double[]>(model);
var inputs = sequences2;
var outputs = labels2;
double[] actual = target.Gradient(function.Weights, inputs, outputs);
FiniteDifferences diff = new FiniteDifferences(function.Weights.Length);
diff.Function = parameters => func(model, parameters, inputs, outputs);
double[] expected = diff.Compute(function.Weights);
for (int i = 0; i < actual.Length; i++)
{
Assert.AreEqual(expected[i], actual[i], 1e-3);
Assert.IsFalse(double.IsNaN(actual[i]));
Assert.IsFalse(double.IsNaN(expected[i]));
}
}
public void ComputeTest3()
{
var hmm = MultivariateMarkovFunctionTest.CreateModel1();
var owner = new MarkovMultivariateFunction(hmm);
double[][] x =
{
new double[] { 0 },
new double[] { 1 },
new double[] { 3 },
new double[] { 1 },
new double[] { 2 },
new double[] { 8 },
new double[] { 0 },
new double[] { 10 },
new double[] { System.Math.PI },
};
foreach (var factor in owner.Factors)
{
for (int y = 0; y < owner.Outputs; y++)
{
double[,] fwd = Accord.Statistics.Models.Fields
.ForwardBackwardAlgorithm.Forward(factor, x, y);
double[,] bwd = Accord.Statistics.Models.Fields
.ForwardBackwardAlgorithm.Backward(factor, x, y);
double[,] lnfwd = Accord.Statistics.Models.Fields
.ForwardBackwardAlgorithm.LogForward(factor, x, y);
double[,] lnbwd = Accord.Statistics.Models.Fields
.ForwardBackwardAlgorithm.LogBackward(factor, x, y);
for (int i = 0; i < fwd.GetLength(0); i++)
for (int j = 0; j < fwd.GetLength(1); j++)
Assert.AreEqual(System.Math.Log(fwd[i, j]), lnfwd[i, j], 1e-10);
for (int i = 0; i < bwd.GetLength(0); i++)
for (int j = 0; j < bwd.GetLength(1); j++)
Assert.AreEqual(System.Math.Log(bwd[i, j]), lnbwd[i, j], 1e-10);
foreach (var feature in factor)
{
double expected = System.Math.Log(feature.Marginal(fwd, bwd, x, y));
double actual = feature.LogMarginal(lnfwd, lnbwd, x, y);
Assert.AreEqual(expected, actual, 1e-10);
Assert.IsFalse(Double.IsNaN(actual));
}
}
}
}
public void LogForwardGesturesPriorsTest()
{
int[] labels;
double[][][] words;
var classifier = IndependentMarkovFunctionTest.CreateModel4(out words, out labels, true);
var function = new MarkovMultivariateFunction(classifier);
var target = new HiddenConditionalRandomField<double[]>(function);
foreach (var word in words)
{
for (int c = 0; c < 3; c++)
{
var actual = Accord.Statistics.Models.Fields.ForwardBackwardAlgorithm.LogForward(
target.Function.Factors[c], word, c);
var expected = Accord.Statistics.Models.Markov.ForwardBackwardAlgorithm.LogForward(
classifier[c], word);
for (int i = 0; i < actual.GetLength(0); i++)
{
for (int j = 0; j < actual.GetLength(1); j++)
{
double a = actual[i, j];
double e = expected[i, j];
// TODO: Verify if is possible to reduce this tolerance
Assert.IsTrue(e.IsRelativelyEqual(a, 0.1));
}
}
}
}
}
public void LogForwardGesturesPriorsDeoptimizedTest()
{
int[] labels;
double[][][] words;
var classifier = IndependentMarkovFunctionTest.CreateModel4(out words, out labels, true);
var deopFun = new MarkovMultivariateFunction(classifier);
deopFun.Deoptimize();
var target1 = new HiddenConditionalRandomField<double[]>(deopFun);
var function = new MarkovMultivariateFunction(classifier);
var target2 = new HiddenConditionalRandomField<double[]>(function);
foreach (var word in words)
{
for (int c = 0; c < 3; c++)
{
for (int y = 0; y < 3; y++)
{
var actual = Accord.Statistics.Models.Fields.ForwardBackwardAlgorithm
.LogForward(target1.Function.Factors[c], word, y);
var expected = Accord.Statistics.Models.Fields.ForwardBackwardAlgorithm
.LogForward(target2.Function.Factors[c], word, y);
for (int i = 0; i < actual.GetLength(0); i++)
{
for (int j = 0; j < actual.GetLength(1); j++)
{
double a = actual[i, j];
double e = expected[i, j];
Assert.IsTrue(e.IsRelativelyEqual(a, 0.1));
}
}
}
}
}
}
public void ComputeTest4()
{
int[] labels;
double[][][] words;
HiddenMarkovClassifier<Independent<NormalDistribution>> model =
CreateModel4(out words, out labels, false);
var target = new MarkovMultivariateFunction(model);
var hcrf = new HiddenConditionalRandomField<double[]>(target);
Assert.AreEqual(3, model.Priors.Length);
Assert.AreEqual(1 / 3.0, model.Priors[0]);
Assert.AreEqual(1 / 3.0, model.Priors[1]);
Assert.AreEqual(1 / 3.0, model.Priors[2]);
check4(words, model, target, hcrf);
}
public void ComputeTest()
{
var model = CreateModel1();
var target = new MarkovMultivariateFunction(model);
double actual;
double expected;
double[][] x = { new double[] { 0 }, new double[] { 1 } };
for (int c = 0; c < model.Classes; c++)
{
for (int i = 0; i < model[c].States; i++)
{
// Check initial state transitions
expected = model.Priors[c] * Math.Exp(model[c].Probabilities[i]) * model[c].Emissions[i].ProbabilityDensityFunction(x[0]);
actual = Math.Exp(target.Factors[c].Compute(-1, i, x, 0, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
for (int t = 1; t < x.Length; t++)
{
// Check normal state transitions
for (int i = 0; i < model[c].States; i++)
{
for (int j = 0; j < model[c].States; j++)
{
expected = Math.Exp(model[c].Transitions[i, j]) * model[c].Emissions[j].ProbabilityDensityFunction(x[t]);
actual = Math.Exp(target.Factors[c].Compute(i, j, x, t, c));
Assert.AreEqual(expected, actual, 1e-6);
Assert.IsFalse(double.IsNaN(actual));
}
}
}
}
}
public void SaveLoadTest()
{
double[][] hello =
{
new double[] { 1.0, 0.1, 0.0, 0.0 }, // let's say the word
new double[] { 0.0, 1.0, 0.1, 0.1 }, // hello took 6 frames
new double[] { 0.0, 1.0, 0.1, 0.1 }, // to be recorded.
new double[] { 0.0, 0.0, 1.0, 0.0 },
new double[] { 0.0, 0.0, 1.0, 0.0 },
new double[] { 0.0, 0.0, 0.1, 1.1 },
};
double[][] car =
{
new double[] { 0.0, 0.0, 0.0, 1.0 }, // the car word
new double[] { 0.1, 0.0, 1.0, 0.1 }, // took only 4.
new double[] { 0.0, 0.0, 0.1, 0.0 },
new double[] { 1.0, 0.0, 0.0, 0.0 },
};
double[][] wardrobe =
{
new double[] { 0.0, 0.0, 1.0, 0.0 }, // same for the
new double[] { 0.1, 0.0, 1.0, 0.1 }, // wardrobe word.
new double[] { 0.0, 0.1, 1.0, 0.0 },
new double[] { 0.1, 0.0, 1.0, 0.1 },
};
double[][][] words = { hello, car, wardrobe };
int[] labels = { 0, 1, 2 };
var initial = new Independent
(
new NormalDistribution(0, 1),
new NormalDistribution(0, 1),
new NormalDistribution(0, 1),
new NormalDistribution(0, 1)
);
int numberOfWords = 3;
int numberOfStates = 5;
var classifier = new HiddenMarkovClassifier<Independent>
(
classes: numberOfWords,
topology: new Forward(numberOfStates),
initial: initial
);
var teacher = new HiddenMarkovClassifierLearning<Independent>(classifier,
modelIndex => new BaumWelchLearning<Independent>(classifier.Models[modelIndex])
{
Tolerance = 0.001,
Iterations = 100,
FittingOptions = new IndependentOptions()
{
InnerOption = new NormalOptions() { Regularization = 1e-5 }
}
}
);
double logLikelihood = teacher.Run(words, labels);
var function = new MarkovMultivariateFunction(classifier);
var hcrf = new HiddenConditionalRandomField<double[]>(function);
MemoryStream stream = new MemoryStream();
hcrf.Save(stream);
stream.Seek(0, SeekOrigin.Begin);
var target = HiddenConditionalRandomField<double[]>.Load(stream);
Assert.AreEqual(hcrf.Function.Factors.Length, target.Function.Factors.Length);
for (int i = 0; i < hcrf.Function.Factors.Length; i++)
{
var e = hcrf.Function.Factors[i];
var a = target.Function.Factors[i];
Assert.AreEqual(e.Index, target.Function.Factors[i].Index);
Assert.AreEqual(e.States, target.Function.Factors[i].States);
Assert.AreEqual(e.EdgeParameters.Count, a.EdgeParameters.Count);
Assert.AreEqual(e.EdgeParameters.Offset, a.EdgeParameters.Offset);
Assert.AreEqual(e.FactorParameters.Count, a.FactorParameters.Count);
Assert.AreEqual(e.FactorParameters.Offset, a.FactorParameters.Offset);
Assert.AreEqual(e.OutputParameters.Count, a.OutputParameters.Count);
Assert.AreEqual(e.OutputParameters.Offset, a.OutputParameters.Offset);
Assert.AreEqual(e.StateParameters.Count, a.StateParameters.Count);
Assert.AreEqual(e.StateParameters.Offset, a.StateParameters.Offset);
Assert.AreEqual(target.Function, a.Owner);
Assert.AreEqual(hcrf.Function, e.Owner);
}
Assert.AreEqual(hcrf.Function.Features.Length, target.Function.Features.Length);
for (int i = 0; i < hcrf.Function.Factors.Length; i++)
Assert.AreEqual(hcrf.Function.Features[i].GetType(), target.Function.Features[i].GetType());
Assert.AreEqual(hcrf.Function.Outputs, target.Function.Outputs);
for (int i = 0; i < hcrf.Function.Weights.Length; i++)
Assert.AreEqual(hcrf.Function.Weights[i], target.Function.Weights[i]);
}
public void SimpleGestureRecognitionTest()
{
// Let's say we would like to do a very simple mechanism for
// gesture recognition. In this example, we will be trying to
// create a classifier that can distinguish between the words
// "hello", "car", and "wardrobe".
// Let's say we decided to acquire some data, and we asked some
// people to perform those words in front of a Kinect camera, and,
// using Microsoft's SDK, we were able to captured the x and y
// coordinates of each hand while the word was being performed.
// Let's say we decided to represent our frames as:
//
// double[] frame = { leftHandX, leftHandY, rightHandX, rightHandY };
//
// Since we captured words, this means we captured sequences of
// frames as we described above. Let's write some of those as
// rough examples to explain how gesture recognition can be done:
double[][] hello =
{
new double[] { 1.0, 0.1, 0.0, 0.0 }, // let's say the word
new double[] { 0.0, 1.0, 0.1, 0.1 }, // hello took 6 frames
new double[] { 0.0, 1.0, 0.1, 0.1 }, // to be recorded.
new double[] { 0.0, 0.0, 1.0, 0.0 },
new double[] { 0.0, 0.0, 1.0, 0.0 },
new double[] { 0.0, 0.0, 0.1, 1.1 },
};
double[][] car =
{
new double[] { 0.0, 0.0, 0.0, 1.0 }, // the car word
new double[] { 0.1, 0.0, 1.0, 0.1 }, // took only 4.
new double[] { 0.0, 0.0, 0.1, 0.0 },
new double[] { 1.0, 0.0, 0.0, 0.0 },
};
double[][] wardrobe =
{
new double[] { 0.0, 0.0, 1.0, 0.0 }, // same for the
new double[] { 0.1, 0.0, 1.0, 0.1 }, // wardrobe word.
new double[] { 0.0, 0.1, 1.0, 0.0 },
new double[] { 0.1, 0.0, 1.0, 0.1 },
};
// Here, please note that a real-world example would involve *lots*
// of samples for each word. Here, we are considering just one from
// each class which is clearly sub-optimal and should _never_ be done
// on practice. For example purposes, however, please disregard this.
// Those are the words we have in our vocabulary:
//
double[][][] words = { hello, car, wardrobe };
// Now, let's associate integer labels with them. This is needed
// for the case where there are multiple samples for each word.
//
int[] labels = { 0, 1, 2 };
// We will create our classifiers assuming an independent
// Gaussian distribution for each component in our feature
// vectors (like assuming a Naive Bayes assumption).
var initial = new Independent<NormalDistribution>
(
new NormalDistribution(0, 1),
new NormalDistribution(0, 1),
new NormalDistribution(0, 1),
new NormalDistribution(0, 1)
);
// Now, we can proceed and create our classifier.
//
int numberOfWords = 3; // we are trying to distinguish between 3 words
int numberOfStates = 5; // this value can be found by trial-and-error
var hmm = new HiddenMarkovClassifier<Independent<NormalDistribution>>
(
classes: numberOfWords,
topology: new Forward(numberOfStates), // word classifiers should use a forward topology
initial: initial
);
// Create a new learning algorithm to train the sequence classifier
var teacher = new HiddenMarkovClassifierLearning<Independent<NormalDistribution>>(hmm,
// Train each model until the log-likelihood changes less than 0.001
modelIndex => new BaumWelchLearning<Independent<NormalDistribution>>(hmm.Models[modelIndex])
{
Tolerance = 0.001,
Iterations = 100,
// This is necessary so the code doesn't blow up when it realize
// there is only one sample per word class. But this could also be
// needed in normal situations as well.
//
FittingOptions = new IndependentOptions()
{
InnerOption = new NormalOptions() { Regularization = 1e-5 }
}
}
);
// Finally, we can run the learning algorithm!
double logLikelihood = teacher.Run(words, labels);
// At this point, the classifier should be successfully
// able to distinguish between our three word classes:
//
int tc1 = hmm.Compute(hello);
int tc2 = hmm.Compute(car);
int tc3 = hmm.Compute(wardrobe);
Assert.AreEqual(0, tc1);
Assert.AreEqual(1, tc2);
Assert.AreEqual(2, tc3);
// Now, we can use the Markov classifier to initialize a HCRF
var function = new MarkovMultivariateFunction(hmm);
var hcrf = new HiddenConditionalRandomField<double[]>(function);
// We can check that both are equivalent, although they have
// formulations that can be learned with different methods
//
for (int i = 0; i < words.Length; i++)
{
// Should be the same
int expected = hmm.Compute(words[i]);
int actual = hcrf.Compute(words[i]);
// Should be the same
double h0 = hmm.LogLikelihood(words[i], 0);
double c0 = hcrf.LogLikelihood(words[i], 0);
double h1 = hmm.LogLikelihood(words[i], 1);
double c1 = hcrf.LogLikelihood(words[i], 1);
double h2 = hmm.LogLikelihood(words[i], 2);
double c2 = hcrf.LogLikelihood(words[i], 2);
Assert.AreEqual(expected, actual);
Assert.AreEqual(h0, c0, 1e-10);
Assert.IsTrue(h1.IsRelativelyEqual(c1, 1e-10));
Assert.IsTrue(h2.IsRelativelyEqual(c2, 1e-10));
Assert.IsFalse(double.IsNaN(c0));
Assert.IsFalse(double.IsNaN(c1));
Assert.IsFalse(double.IsNaN(c2));
}
// Now we can learn the HCRF using one of the best learning
// algorithms available, Resilient Backpropagation learning:
// Create a learning algorithm
var rprop = new HiddenResilientGradientLearning<double[]>(hcrf)
{
Iterations = 50,
Tolerance = 1e-5
};
// Run the algorithm and learn the models
double error = rprop.Run(words, labels);
// At this point, the HCRF should be successfully
// able to distinguish between our three word classes:
//
int hc1 = hcrf.Compute(hello);
int hc2 = hcrf.Compute(car);
int hc3 = hcrf.Compute(wardrobe);
Assert.AreEqual(0, hc1);
Assert.AreEqual(1, hc2);
Assert.AreEqual(2, hc3);
}
public void NumberOfFeaturesTest()
{
Independent initial = new Independent(
new GeneralDiscreteDistribution(46), // output,
new NormalDistribution(0, 1), // headAngle,
new NormalDistribution(0, 1), // handAngle,
new NormalDistribution(0, 1), // relHandX,
new NormalDistribution(0, 1) // relHandY,
);
var model = new HiddenMarkovClassifier<Independent>(
classes: 13, topology: new Forward(5), initial: initial);
var function = new MarkovMultivariateFunction(model);
var field = new HiddenConditionalRandomField<double[]>(function);
int discreteDistributions = 1;
int continuousDistributions = 4;
int symbols = 46;
int states = 5;
int classes = 13;
int expected = classes *
(1 + states + states * states +
states * discreteDistributions * symbols +
states * continuousDistributions * 3);
Assert.AreEqual(expected, field.Function.Features.Length);
Assert.AreEqual(expected, field.Function.Weights.Length);
Assert.AreEqual(4173, expected);
}