/// <summary>
// https://www.cs.ubc.ca/~nando/340-2012/lectures/l21.pdf
/// </summary>
/// <param name="inputs"></param>
/// <param name="outputs"></param>
public void Regress(Matrix inputs, Vector outputs)
{
inputs = inputs.AddColumn(1);
var theta = new Vector(inputs.NbColumns);
var previousTheta = new Vector(inputs.NbColumns);
for (int i = 0; i < inputs.NbColumns; i++)
{
previousTheta[i] = double.MaxValue;
}
while (theta.Substract(previousTheta).Abs().Max().Key.GetNumber() >= 1e-6)
{
Vector a = inputs.Multiply(theta.SetHorizontal()).SumAllRows();
var pi = a.Transform(_ => Inverse(_.GetNumber()));
var sx = inputs.Multiply(pi.Substract(pi.Multiply(pi)).SetVertical()).Evaluate();
var xsx = inputs.Transpose().Multiply(sx).Evaluate();
Vector sxTheta = sx.Multiply(theta.SetHorizontal()).SumAllRows();
var result = _multipleLinearRegression.Regress(xsx,
inputs.Transpose().Multiply(sxTheta.Sum(outputs.Substract(pi))).SumAllRows().SetHorizontal(),
false);
previousTheta = theta;
theta = result.LinearRegression.GetCoefficients();
}
_multipleLinearRegression.UpdateInformation(inputs, outputs, useCovariance: false);
}
public SimpleLinearRegression Regress(double[] inputs, double[] outputs)
{
var newInputs = new double[inputs.Length][];
for (int i = 0; i < inputs.Length; i++)
{
newInputs[i] = new double[] { inputs[i] };
}
var result = _multipleLinearRegression.Regress(newInputs, outputs);
_linearRegression = result.LinearRegression;
return(this);
}