PolynomialLeastSquares Class

[SerializableAttribute]
public class PolynomialLeastSquares : ISupervisedLearning<PolynomialRegression, double, double>

<SerializableAttribute>
Public Class PolynomialLeastSquares
	Implements ISupervisedLearning(Of PolynomialRegression, Double, Double)

// Let's say we would like to learn 2nd degree polynomial that 
// can map the first column X into its second column Y. We have 
// 5 examples of those (x,y) pairs that we can use to learn this 
// function:

double[,] data =
{
    // X       Y
    { 12,     144 }, // example #1
    { 15,     225 }, // example #2
    { 20,     400 }, // example #3
    { 25,     625 }, // example #4
    { 35,    1225 }, // example #5
};

// Let's retrieve the input and output data:
double[] inputs = data.GetColumn(0);  // X
double[] outputs = data.GetColumn(1); // Y

// We can create a learning algorithm
var ls = new PolynomialLeastSquares()
{
    Degree = 2
};

// Now, we can use the algorithm to learn a polynomial
PolynomialRegression poly = ls.Learn(inputs, outputs);

// The learned polynomial will be given by
string str = poly.ToString("N1"); // "y(x) = 1.0x^2 + 0.0x^1 + 0.0"

// Where its weights can be accessed using
double[] weights = poly.Weights;   // { 1.0000000000000024, -1.2407665029287351E-13 }
double intercept = poly.Intercept; // 1.5652369518855253E-12

// Finally, we can use this polynomial
// to predict values for the input data
double[] pred = poly.Transform(inputs);

// Where the mean-squared-error (MSE) should be
double error = new SquareLoss(outputs).Loss(pred); // 0.0