MultivariateLinearRegression Class

[SerializableAttribute]
public class MultivariateLinearRegression : MultipleTransformBase<double[], double>, 
	ILinearRegression

<SerializableAttribute>
Public Class MultivariateLinearRegression
	Inherits MultipleTransformBase(Of Double(), Double)
	Implements ILinearRegression

// 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);