public LinearRegressionFactor(IRegressionVariable regressor, double coefficient, double standardError, double nullProbability)
{
Regressor = regressor;
Coefficient = coefficient;
StandardError = standardError;
T = coefficient / standardError;
NullProbability = nullProbability;
}
public static AutomatedLinearRegression Fit(IRegressionVariable regressand, IEnumerable<IRegressionVariable> regressors)
{
if (regressors == null)
{
throw new ArgumentNullException();
}
return Fit(regressand, regressors.ToArray());
}
public static AutomatedLinearRegression Fit(IRegressionVariable regressand, params IRegressionVariable[] regressors)
{
if (regressand == null || regressors == null)
{
throw new ArgumentNullException();
}
int p = regressors.Length;
for (int i = 0; i < p; i++)
{
if (regressors[i] == null)
{
throw new ArgumentNullException();
}
}
// The regressand is required not to be an infinite sequence.
double[] y = regressand.Values.ToArray();
int n = y.Length;
// The regressor sequences may be. But must be at least as long as the regressand.
double[,] x = new double[n, p];
for (int i = 0; i < p; i++)
{
using (IEnumerator<double> iterator = regressors[i].Values.GetEnumerator())
{
for (int j = 0; j < n; j++)
{
if (!iterator.MoveNext())
{
throw new Exception("Regressor sequence ended unexpectedly.");
}
x[j, i] = iterator.Current;
}
}
}
LinearRegression lr = LinearRegression.Fit(new Vector(y), new Matrix(x));
//SimpleLinearRegression lr = new SimpleLinearRegression.Fit(new Vector(y), new Matrix(x));
LinearRegressionFactor[] factors = new LinearRegressionFactor[p];
for (int j = 0; j < p; j++)
{
double t = lr.Beta[j] / lr.Sigma[j];
// Null probability, $Pr(>|t|)$.
// http://sourceforge.net/p/varianttools/mailman/message/29121481/
throw new NotImplementedException(); double pr;//double pr = 2.0 * Gsl.gsl_cdf_tdist_Q(Math.Abs(t), n - p);
factors[j] = new LinearRegressionFactor(regressors[j], lr.Beta[j], lr.Sigma[j], pr);
}
return new AutomatedLinearRegression(factors);
}
public static AutomatedLinearRegression FitBySignificance(double significanceLevel, IRegressionVariable regressand, params IRegressionVariable[] regressors)
{
return FitBySignificance(significanceLevel, regressand, (IEnumerable<IRegressionVariable>)regressors);
}
public static AutomatedLinearRegression FitBySignificance(double significanceLevel, IRegressionVariable regressand, IEnumerable<IRegressionVariable> regressors)
{
if (significanceLevel < 0.0 || significanceLevel > 1.0)
{
throw new ArgumentOutOfRangeException();
}
return FitBySignificanceFactors(significanceLevel, int.MaxValue, regressand, regressors);
}
public static AutomatedLinearRegression FitByFactorsCombinatorial(int factors, IRegressionVariable regressand, params IRegressionVariable[] regressors)
{
return FitByFactorsCombinatorial(factors, regressand, (IEnumerable<IRegressionVariable>)regressors);
}
public static AutomatedLinearRegression FitByFactorsCombinatorial(int factors, IRegressionVariable regressand, IEnumerable<IRegressionVariable> regressors)
{
if (factors < 1)
{
throw new ArgumentOutOfRangeException();
}
int n = regressors.Count(r => !r.Required);
if (n <= factors)
{
// Already below maximum number of factors.
return Fit(regressand, regressors);
}
throw new NotImplementedException();
}
private static AutomatedLinearRegression FitBySignificanceFactors(double significanceLevel, int factors, IRegressionVariable regressand, IEnumerable<IRegressionVariable> regressors)
{
if (regressors.Count(r => r.Required) > factors)
{
throw new ArgumentException("Too many factors are required.");
}
// Threshold p-value.
double p0 = 1.0 - significanceLevel;
// Start by a non-automated regression.
AutomatedLinearRegression lr = AutomatedLinearRegression.Fit(regressand, regressors);
while (true)
{
// Find worst non-significant factor.
LinearRegressionFactor f0 = lr.Factors.Where(f => !f.Regressor.Required).OrderByDescending(f => f.NullProbability).First();
if (lr.Factors.Count <= factors && f0.NullProbability <= p0)
{
// Satisfying maximum number of factors and worst significance level.
return lr;
}
if (lr.Factors.Count == 1)
{
// About to remove last factor.
return new AutomatedLinearRegression(new LinearRegressionFactor[0]);
}
lr = AutomatedLinearRegression.Fit(regressand, lr.Factors.Where(f => f != f0).Select(f => f.Regressor));
}
}
public static AutomatedLinearRegression FitByFactors(int factors, IRegressionVariable regressand, params IRegressionVariable[] regressors)
{
return FitBySignificance(factors, regressand, (IEnumerable<IRegressionVariable>)regressors);
}
public static AutomatedLinearRegression FitByFactors(int factors, IRegressionVariable regressand, IEnumerable<IRegressionVariable> regressors)
{
// The backward mode described here:
// http://faculty.smu.edu/tfomby/eco5385/lecture/Multiple%20Linear%20Regression%20and%20Subset%20Selection.pdf
if (factors < 1)
{
throw new ArgumentOutOfRangeException();
}
return FitBySignificanceFactors(double.NegativeInfinity, factors, regressand, regressors);
}
