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 MultiOutputHypothesisWorks([Random(5)] double value, [Random(5)] double scale, [Random(5)] double offset) { var h = new DualLinearHypothesis(1); var theta = Vector<double>.Build.Dense(new[] { offset, scale }); var inputs = Vector<double>.Build.Dense(1, value); var outputs = h.Evaluate(theta, inputs); outputs.Count.Should().Be(2, "because two outputs are expected"); outputs.First().Should().BeApproximately(value * scale + offset, 1E-5D, "because the function is linear"); outputs.Last().Should().BeApproximately(value * scale + 2*offset, 1E-5D, "because the function is linear"); }