public void learn_test1()
{
#region doc_learn
// The multivariate linear regression is a generalization of
// the multiple linear regression. In the multivariate linear
// regression, not only the input variables are multivariate,
// but also are the output dependent variables.
// In the following example, we will perform a regression of
// a 2-dimensional output variable over a 3-dimensional input
// variable.
double[][] inputs =
{
// variables: x1 x2 x3
new double[] { 1, 1, 1 }, // input sample 1
new double[] { 2, 1, 1 }, // input sample 2
new double[] { 3, 1, 1 }, // input sample 3
};
double[][] outputs =
{
// variables: y1 y2
new double[] { 2, 3 }, // corresponding output to sample 1
new double[] { 4, 6 }, // corresponding output to sample 2
new double[] { 6, 9 }, // corresponding output to sample 3
};
// With a quick eye inspection, it is possible to see that
// the first output variable y1 is always the double of the
// first input variable. The second output variable y2 is
// always the triple of the first input variable. The other
// input variables are unused. Nevertheless, we will fit a
// multivariate regression model and confirm the validity
// of our impressions:
// Use Ordinary Least Squares to create the regression
OrdinaryLeastSquares ols = new OrdinaryLeastSquares();
// Now, compute the multivariate linear regression:
MultivariateLinearRegression regression = ols.Learn(inputs, outputs);
// We can obtain predictions using
double[][] predictions = regression.Transform(inputs);
// The prediction error is
double error = new SquareLoss(outputs).Loss(predictions); // 0
// At this point, the regression error will be 0 (the fit was
// perfect). The regression coefficients for the first input
// and first output variables will be 2. The coefficient for
// the first input and second output variables will be 3. All
// others will be 0.
//
// regression.Coefficients should be the matrix given by
//
// double[,] coefficients = {
// { 2, 3 },
// { 0, 0 },
// { 0, 0 },
// };
//
// We can also check the r-squared coefficients of determination:
double[] r2 = regression.CoefficientOfDetermination(inputs, outputs);
#endregion
// The first input variable coefficients will be 2 and 3:
Assert.AreEqual(2, regression.Coefficients[0, 0], 1e-10);
Assert.AreEqual(3, regression.Coefficients[0, 1], 1e-10);
// And all other coefficients will be 0:
Assert.AreEqual(0, regression.Coefficients[1, 0], 1e-10);
Assert.AreEqual(0, regression.Coefficients[1, 1], 1e-10);
Assert.AreEqual(0, regression.Coefficients[2, 0], 1e-10);
Assert.AreEqual(0, regression.Coefficients[2, 1], 1e-10);
Assert.AreEqual(3, regression.NumberOfInputs);
Assert.AreEqual(2, regression.NumberOfOutputs);
// Which should be one for both output variables:
Assert.AreEqual(1, r2[0]);
Assert.AreEqual(1, r2[1]);
foreach (var e in regression.Coefficients)
Assert.IsFalse(double.IsNaN(e));
Assert.AreEqual(0, error, 1e-10);
Assert.IsFalse(double.IsNaN(error));
}