public void DualLinearRegressionWithResidualSumOfSquares()
{
// obtain the test data
var trainingSet = new List <DataPoint <double> >
{
new DataPoint <double>(-1, new [] { -1.5, -1.0 }),
new DataPoint <double>(0, new [] { 0.5, 1.0 }),
new DataPoint <double>(1, new [] { 2.5, 3.0 }),
new DataPoint <double>(2, new [] { 4.5, 5.0 }),
new DataPoint <double>(3, new [] { 6.5, 6.0 })
};
// assume a hypothesis
var hypothesis = new DualLinearHypothesis(1);
var initialCoefficients = Vector <double> .Build.Random(2);
// cost function is sum of squared errors
var costFunction = new ResidualSumOfSquaresCostFunction(hypothesis, trainingSet);
// define the optimization problem
var problem = new OptimizationProblem <double, IDifferentiableCostFunction <double> >(costFunction, initialCoefficients);
// optimize!
var gd = new ResilientErrorGD
{
ErrorTolerance = 0.0D
};
var result = gd.Minimize(problem);
// assert!
var coefficients = result.Coefficients;
coefficients[0].Should().BeApproximately(0.5, 1E-6D, "because that's the underlying system's intercept");
coefficients[1].Should().BeApproximately(2, 1E-6D, "because that's the underlying system's slope");
}
public void DualLinearRegressionWithResidualSumOfSquares()
{
// obtain the test data
var trainingSet = new List<DataPoint<double>>
{
new DataPoint<double>(-1, new [] {-1.5 , -1.0 }),
new DataPoint<double>(0, new [] {0.5, 1.0}),
new DataPoint<double>(1, new [] {2.5, 3.0}),
new DataPoint<double>(2, new [] {4.5, 5.0}),
new DataPoint<double>(3, new [] {6.5, 6.0})
};
// assume a hypothesis
var hypothesis = new DualLinearHypothesis(1);
var initialCoefficients = Vector<double>.Build.Random(2);
// cost function is sum of squared errors
var costFunction = new ResidualSumOfSquaresCostFunction(hypothesis, trainingSet);
// define the optimization problem
var problem = new OptimizationProblem<double, IDifferentiableCostFunction<double>>(costFunction, initialCoefficients);
// optimize!
var gd = new ResilientErrorGD
{
ErrorTolerance = 0.0D
};
var result = gd.Minimize(problem);
// assert!
var coefficients = result.Coefficients;
coefficients[0].Should().BeApproximately(0.5, 1E-6D, "because that's the underlying system's intercept");
coefficients[1].Should().BeApproximately(2, 1E-6D, "because that's the underlying system's slope");
}
public void Rosenbrock()
{
// starting point for search is somewhere
var initialTheta = Vector <double> .Build.DenseOfArray(new[] { -1D, 1D });
// define the hypothesis with default parameter
var rosenbrockParameter = Vector <double> .Build.DenseOfArray(new[] { 1D, 100D });
var hypothesis = new RosenbrockHypothesis();
// cost function is sum of squared errors
var costFunction = new FunctionValueOptimization <double>(hypothesis, rosenbrockParameter);
// define the optimization problem
var problem = new OptimizationProblem <double, IDifferentiableCostFunction <double> >(costFunction, initialTheta);
// optimize!
var gd = new ResilientErrorGD
{
MaxIterations = 50000,
ErrorTolerance = 1E-20D
};
var result = gd.Minimize(problem);
// assert!
var coefficients = result.Coefficients;
coefficients[0].Should().BeApproximately(rosenbrockParameter[0], 1E-5D, "because the Rosenbrock function has a minimum at x={0}, y={1}", rosenbrockParameter[0], Math.Sqrt(rosenbrockParameter[0]));
coefficients[1].Should().BeApproximately(Math.Sqrt(rosenbrockParameter[0]), 1E-5D, "because the Rosenbrock function has a minimum at x={0}, y={1}", rosenbrockParameter[0], Math.Sqrt(rosenbrockParameter[0]));
}
public void RosenbrockParameterFitWithResidualSumOfSquares()
{
// parameter is default Rosenbrock
var realTheta = Vector <double> .Build.DenseOfArray(new [] { 1D, 105D });
var initialTheta = Vector <double> .Build.DenseOfArray(new [] { 2D, 200D });
// define the hypothesis
var hypothesis = new RosenbrockHypothesis();
// define a probability distribution
var distribution = new ContinuousUniform(-10D, 10D);
// obtain the test data
const int dataPoints = 10;
var trainingSet = new List <DataPoint <double> >(dataPoints);
for (int i = 0; i < dataPoints; ++i)
{
var inputs = Vector <double> .Build.Random(2, distribution);
var output = hypothesis.Evaluate(realTheta, inputs);
trainingSet.Add(new DataPoint <double>(inputs, output));
}
;
// cost function is sum of squared errors
var costFunction = new ResidualSumOfSquaresCostFunction(hypothesis, trainingSet);
// define the optimization problem
var problem = new OptimizationProblem <double, IDifferentiableCostFunction <double> >(costFunction, initialTheta);
// optimize!
var gd = new ResilientErrorGD
{
ErrorTolerance = 0.0D // TODO: actually use it
};
var result = gd.Minimize(problem);
// assert!
var coefficients = result.Coefficients;
coefficients[0].Should().BeApproximately(realTheta[0], 1D, "because that's the functions [a] parameter");
coefficients[1].Should().BeApproximately(realTheta[1], 1D, "because that's the functions [b] parameter");
}
public void UnivariateExponentialRegressionWithResidualSumOfSquares()
{
var theta = Vector <double> .Build.DenseOfArray(new[] { 0D, 13500D, -1.7D });
var initialTheta = Vector <double> .Build.DenseOfArray(new[] { 0D, 10000D, -1D });
// define the hypothesis
var hypothesis = new UnivariateExponentialHypothesis();
// define a probability distribution
var distribution = new ContinuousUniform(0D, 1000D);
// obtain the test data
const int dataPoints = 100;
var trainingSet = new List <DataPoint <double> >(dataPoints);
for (int i = 0; i < dataPoints; ++i)
{
var inputs = Vector <double> .Build.Random(1, distribution);
var output = hypothesis.Evaluate(theta, inputs);
trainingSet.Add(new DataPoint <double>(inputs, output));
}
;
// cost function is sum of squared errors
var costFunction = new ResidualSumOfSquaresCostFunction(hypothesis, trainingSet);
// define the optimization problem
var problem = new OptimizationProblem <double, IDifferentiableCostFunction <double> >(costFunction, initialTheta);
// optimize!
var gd = new ResilientErrorGD();
var result = gd.Minimize(problem);
// assert!
var coefficients = result.Coefficients;
coefficients[1].Should().BeApproximately(theta[1], 1000D, "because that's the underlying system's [a] parameter");
coefficients[2].Should().BeApproximately(theta[2], 1E-2D, "because that's the underlying system's [b] parameter");
coefficients[0].Should().BeApproximately(theta[0], 1E-5D, "because that's the underlying system's offset");
}
public void Rosenbrock()
{
// starting point for search is somewhere
var initialTheta = Vector<double>.Build.DenseOfArray(new[] { -1D, 1D });
// define the hypothesis with default parameter
var rosenbrockParameter = Vector<double>.Build.DenseOfArray(new[] { 1D, 100D });
var hypothesis = new RosenbrockHypothesis();
// cost function is sum of squared errors
var costFunction = new FunctionValueOptimization<double>(hypothesis, rosenbrockParameter);
// define the optimization problem
var problem = new OptimizationProblem<double, IDifferentiableCostFunction<double>>(costFunction, initialTheta);
// optimize!
var gd = new ResilientErrorGD
{
MaxIterations = 50000,
ErrorTolerance = 1E-20D
};
var result = gd.Minimize(problem);
// assert!
var coefficients = result.Coefficients;
coefficients[0].Should().BeApproximately(rosenbrockParameter[0], 1E-5D, "because the Rosenbrock function has a minimum at x={0}, y={1}", rosenbrockParameter[0], Math.Sqrt(rosenbrockParameter[0]));
coefficients[1].Should().BeApproximately(Math.Sqrt(rosenbrockParameter[0]), 1E-5D, "because the Rosenbrock function has a minimum at x={0}, y={1}", rosenbrockParameter[0], Math.Sqrt(rosenbrockParameter[0]));
}
public void UnivariateExponentialRegressionWithResidualSumOfSquares()
{
var theta = Vector<double>.Build.DenseOfArray(new[] { 0D, 13500D, -1.7D });
var initialTheta = Vector<double>.Build.DenseOfArray(new[] { 0D, 10000D, -1D });
// define the hypothesis
var hypothesis = new UnivariateExponentialHypothesis();
// define a probability distribution
var distribution = new ContinuousUniform(0D, 1000D);
// obtain the test data
const int dataPoints = 100;
var trainingSet = new List<DataPoint<double>>(dataPoints);
for (int i = 0; i < dataPoints; ++i)
{
var inputs = Vector<double>.Build.Random(1, distribution);
var output = hypothesis.Evaluate(theta, inputs);
trainingSet.Add(new DataPoint<double>(inputs, output));
};
// cost function is sum of squared errors
var costFunction = new ResidualSumOfSquaresCostFunction(hypothesis, trainingSet);
// define the optimization problem
var problem = new OptimizationProblem<double, IDifferentiableCostFunction<double>>(costFunction, initialTheta);
// optimize!
var gd = new ResilientErrorGD();
var result = gd.Minimize(problem);
// assert!
var coefficients = result.Coefficients;
coefficients[1].Should().BeApproximately(theta[1], 1000D, "because that's the underlying system's [a] parameter");
coefficients[2].Should().BeApproximately(theta[2], 1E-2D, "because that's the underlying system's [b] parameter");
coefficients[0].Should().BeApproximately(theta[0], 1E-5D, "because that's the underlying system's offset");
}
public void RosenbrockParameterFitWithResidualSumOfSquares()
{
// parameter is default Rosenbrock
var realTheta = Vector<double>.Build.DenseOfArray(new []{1D, 105D});
var initialTheta = Vector<double>.Build.DenseOfArray(new []{2D, 200D});
// define the hypothesis
var hypothesis = new RosenbrockHypothesis();
// define a probability distribution
var distribution = new ContinuousUniform(-10D, 10D);
// obtain the test data
const int dataPoints = 10;
var trainingSet = new List<DataPoint<double>>(dataPoints);
for (int i = 0; i < dataPoints; ++i)
{
var inputs = Vector<double>.Build.Random(2, distribution);
var output = hypothesis.Evaluate(realTheta, inputs);
trainingSet.Add(new DataPoint<double>(inputs, output));
};
// cost function is sum of squared errors
var costFunction = new ResidualSumOfSquaresCostFunction(hypothesis, trainingSet);
// define the optimization problem
var problem = new OptimizationProblem<double, IDifferentiableCostFunction<double>>(costFunction, initialTheta);
// optimize!
var gd = new ResilientErrorGD
{
ErrorTolerance = 0.0D // TODO: actually use it
};
var result = gd.Minimize(problem);
// assert!
var coefficients = result.Coefficients;
coefficients[0].Should().BeApproximately(realTheta[0], 1D, "because that's the functions [a] parameter");
coefficients[1].Should().BeApproximately(realTheta[1], 1D, "because that's the functions [b] parameter");
}