public void LinearRegressionWithResidualSumOfSquares()
{
// obtain the test data
var trainingSet = new List<DataPoint<double>>
{
new DataPoint<double>(-1, -1.5),
new DataPoint<double>(0, 0.5),
new DataPoint<double>(1, 2.5),
new DataPoint<double>(2, 4.5),
new DataPoint<double>(3, 6.5)
};
// assume a hypothesis
var hypothesis = new LinearHypothesis(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 LinearRegressionWithResidualSumOfSquares()
{
// obtain the test data
var trainingSet = new List <DataPoint <double> >
{
new DataPoint <double>(-1, -1.5),
new DataPoint <double>(0, 0.5),
new DataPoint <double>(1, 2.5),
new DataPoint <double>(2, 4.5),
new DataPoint <double>(3, 6.5)
};
// assume a hypothesis
var hypothesis = new LinearHypothesis(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 TrivialLinearHypothesisIsIdentity([Random(5)] double value)
{
var h = new LinearHypothesis(1);
var theta = Vector<double>.Build.Dense(new[] {0D, 1D});
var inputs = Vector<double>.Build.Dense(1, value);
var outputs = h.Evaluate(theta, inputs);
outputs.Count.Should().Be(1, "because one output is expected");
outputs.Single().Should().BeApproximately(value, 1E-5D, "because the function is linear");
var derivative = h.CoefficientJacobian(theta, inputs, outputs);
derivative.Count.Should().Be(2, "because two coefficients are evaluated");
// ReSharper disable once CompareOfFloatsByEqualityOperator
derivative[0].Should().Be(1D, "because the offset is independent of the inmput");
derivative[1].Should().Be(value, "because the coefficient's derivative is the input");
}
public void TrivialLinearHypothesisIsIdentity([Random(5)] double value)
{
var h = new LinearHypothesis(1);
var theta = Vector <double> .Build.Dense(new[] { 0D, 1D });
var inputs = Vector <double> .Build.Dense(1, value);
var outputs = h.Evaluate(theta, inputs);
outputs.Count.Should().Be(1, "because one output is expected");
outputs.Single().Should().BeApproximately(value, 1E-5D, "because the function is linear");
var derivative = h.CoefficientJacobian(theta, inputs, outputs);
derivative.Count.Should().Be(2, "because two coefficients are evaluated");
// ReSharper disable once CompareOfFloatsByEqualityOperator
derivative[0].Should().Be(1D, "because the offset is independent of the inmput");
derivative[1].Should().Be(value, "because the coefficient's derivative is the input");
}
