public void learn_test()
{
#region doc_learn
// We will try to model a plane as an equation in the form
// "ax + by + c = z". We have two input variables (x and y)
// and we will be trying to find two parameters a and b and
// an intercept term c.
// We will use Ordinary Least Squares to create a
// linear regression model with an intercept term
var ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
// Now suppose you have some points
double[][] inputs =
{
new double[] { 1, 1 },
new double[] { 0, 1 },
new double[] { 1, 0 },
new double[] { 0, 0 },
};
// located in the same Z (z = 1)
double[] outputs = { 1, 1, 1, 1 };
// Use Ordinary Least Squares to estimate a regression model
MultipleLinearRegression regression = ols.Learn(inputs, outputs);
// As result, we will be given the following:
double a = regression.Coefficients[0]; // a = 0
double b = regression.Coefficients[1]; // b = 0
double c = regression.Intercept; // c = 1
// This is the plane described by the equation
// ax + by + c = z => 0x + 0y + 1 = z => 1 = z.
// We can compute the predicted points using
double[] predicted = regression.Transform(inputs);
// And the squared error loss using
double error = new SquareLoss(outputs).Loss(predicted);
#endregion
Assert.AreEqual(2, regression.NumberOfInputs);
Assert.AreEqual(1, regression.NumberOfOutputs);
Assert.AreEqual(0.0, a, 1e-6);
Assert.AreEqual(0.0, b, 1e-6);
Assert.AreEqual(1.0, c, 1e-6);
Assert.AreEqual(0.0, error, 1e-6);
double[] expected = regression.Compute(inputs);
double[] actual = regression.Transform(inputs);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
double r = regression.CoefficientOfDetermination(inputs, outputs);
Assert.AreEqual(1.0, r);
}
