public void learn_test_2()
{
#region doc_learn_2
// Let's say we would like predict a continuous number from a set
// of discrete and continuous input variables. For this, we will
// be using the Servo dataset from UCI's Machine Learning repository
// as an example: http://archive.ics.uci.edu/ml/datasets/Servo
// Create a Servo dataset
Servo servo = new Servo();
object[][] instances = servo.Instances; // 167 x 4
double[] outputs = servo.Output; // 167 x 1
// This dataset contains 4 columns, where the first two are
// symbolic (having possible values A, B, C, D, E), and the
// last two are continuous.
// We will use a codification filter to transform the symbolic
// variables into one-hot vectors, while keeping the other two
// continuous variables intact:
var codebook = new Codification <object>()
{
{ "motor", CodificationVariable.Categorical },
{ "screw", CodificationVariable.Categorical },
{ "pgain", CodificationVariable.Continuous },
{ "vgain", CodificationVariable.Continuous },
};
// Learn the codebook
codebook.Learn(instances);
// We can gather some info about the problem:
int numberOfInputs = codebook.NumberOfInputs; // should be 4 (since there are 4 variables)
int numberOfOutputs = codebook.NumberOfOutputs; // should be 12 (due their one-hot encodings)
// Now we can use it to obtain double[] vectors:
double[][] inputs = codebook.ToDouble().Transform(instances);
// We will use Ordinary Least Squares to create a
// linear regression model with an intercept term
var ols = new OrdinaryLeastSquares()
{
UseIntercept = true
};
// Use Ordinary Least Squares to estimate a regression model:
MultipleLinearRegression regression = ols.Learn(inputs, outputs);
// We can compute the predicted points using:
double[] predicted = regression.Transform(inputs);
// And the squared error using the SquareLoss class:
double error = new SquareLoss(outputs).Loss(predicted);
// We can also compute other measures, such as the coefficient of determination r² using:
double r2 = new RSquaredLoss(numberOfOutputs, outputs).Loss(predicted); // should be 0.55086630162967354
// Or the adjusted or weighted versions of r² using:
var r2loss = new RSquaredLoss(numberOfOutputs, outputs)
{
Adjust = true,
// Weights = weights; // (uncomment if you have a weighted problem)
};
double ar2 = r2loss.Loss(predicted); // should be 0.51586887058782993
// Alternatively, we can also use the less generic, but maybe more user-friendly method directly:
double ur2 = regression.CoefficientOfDetermination(inputs, outputs, adjust: true); // should be 0.51586887058782993
#endregion
Assert.AreEqual(4, numberOfInputs);
Assert.AreEqual(12, numberOfOutputs);
Assert.AreEqual(12, regression.NumberOfInputs);
Assert.AreEqual(1, regression.NumberOfOutputs);
Assert.AreEqual(1.0859586717266123, error, 1e-6);
double[] expected = regression.Compute(inputs);
double[] actual = regression.Transform(inputs);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
Assert.AreEqual(0.55086630162967354, r2);
Assert.AreEqual(0.51586887058782993, ar2);
Assert.AreEqual(0.51586887058782993, ur2);
}
