/// <summary>
///
/// </summary>
/// <param name="design"></param>
/// <param name="response"></param>
/// <param name="weights"></param>
/// <param name="distribution"></param>
/// <param name="maxIterations"></param>
/// <param name="absoluteTolerance"></param>
/// <param name="relativeTolerance"></param>
/// <returns></returns>
public static (double[] Coefficients, double[] WeightedResponse) RegressIrls([NotNull][ItemNotNull] this double[][] design, [NotNull] double[] response, [NotNull] double[] weights, [NotNull] IDistribution distribution, int maxIterations = 100, double absoluteTolerance = 1e-8, double relativeTolerance = default)
{
if (response is null)
{
throw new ArgumentNullException(nameof(response));
}
if (design is null)
{
throw new ArgumentNullException(nameof(design));
}
if (weights is null)
{
throw new ArgumentNullException(nameof(weights));
}
double[] oldResiduals = new double[design.Length];
double[] wlsCoefficients = new double[design[0].Length];
double[] wlsResponse = new double[weights.Length];
double[] wlsWeights = new double[weights.Length];
Array.Copy(weights, wlsWeights, wlsWeights.Length);
double[] meanResponse = distribution.InitialMean(response);
double[] linearResponse = distribution.Predict(meanResponse);
for (int i = 0; i < maxIterations; i++)
{
wlsWeights =
distribution.Weight(meanResponse)
.Multiply(weights);
wlsResponse =
distribution.LinkFunction
.FirstDerivative(meanResponse)
.Multiply(response.Subtract(meanResponse))
.Add(linearResponse);
wlsCoefficients =
design.RegressWls(wlsResponse, wlsWeights);
linearResponse =
design.MatrixProduct(wlsCoefficients);
meanResponse =
distribution.Fit(linearResponse);
double[] residuals =
response.Subtract(linearResponse);
if (HasConverged(residuals, oldResiduals, absoluteTolerance, relativeTolerance))
{
break;
}
Array.Copy(residuals, oldResiduals, oldResiduals.Length);
}
return(wlsCoefficients, wlsResponse);
}
public void FitTest()
{
IDistribution target = CreateMultivariateContinuousDistribution();
double[][] observations =
{
new double[] { 1, 1 },
new double[] { 1, 1 },
};
double[] weights = { 0.50, 0.50 };
bool thrown;
IFittingOptions options = new NormalOptions()
{
Regularization = 0.1
};
thrown = false;
try
{
target.Fit(observations, weights);
}
catch
{
thrown = true;
}
Assert.AreEqual(true, thrown);
thrown = false;
try
{
target.Fit(observations, weights, options);
}
catch
{
thrown = true;
}
Assert.AreEqual(false, thrown);
}
public void FitTest1()
{
IDistribution target = CreateMultivariateContinuousDistribution(); // TODO: Initialize to an appropriate value
Array observations = new double[][]
{
new double[] { 1, 1 },
new double[] { 1, 1 },
};
bool thrown;
IFittingOptions options = new NormalOptions()
{
Regularization = 0.1
};
thrown = false;
try
{
target.Fit(observations);
}
catch
{
thrown = true;
}
Assert.AreEqual(true, thrown);
thrown = false;
try
{
target.Fit(observations, options);
}
catch
{
thrown = true;
}
Assert.AreEqual(false, thrown);
}
public void FitTest2()
{
IDistribution target = CreateUnivariateDiscreteDistribution();
double[] observations = { 0, 1, 1, 1, 1 };
target.Fit(observations);
double mean = Accord.Statistics.Tools.Mean(observations);
Assert.AreEqual(mean, (target as BernoulliDistribution).Mean);
}
public void FitTest2()
{
IDistribution target = CreateUnivariateContinuousDistribution();
double[] observations = { 0.12, 2, 0.52 };
target.Fit(observations);
double expected = 0.88;
double actual = (target as NormalDistribution).Mean;
Assert.AreEqual(expected, actual);
}
public void FitTest()
{
IDistribution target = CreateUnivariateDiscreteDistribution();
double[] observations = { 0, 1, 1, 1, 1 };
IFittingOptions options = null;
target.Fit(observations, options);
double mean = Measures.Mean(observations);
Assert.AreEqual(mean, (target as BernoulliDistribution).Mean);
}
public void FitTest1()
{
IDistribution target = CreateUnivariateDiscreteDistribution();
double[] observations = { 0, 1, 1, 1, 1 };
double[] weights = { 0.125, 0.125, 0.25, 0.25, 0.25 };
IFittingOptions options = null;
target.Fit(observations, weights, options);
double mean = Accord.Statistics.Tools.WeightedMean(observations, weights);
Assert.AreEqual(mean, (target as BernoulliDistribution).Mean);
}
public void FitTest1()
{
IDistribution target = CreateUnivariateContinuousDistribution();
double[] observations = { 0.12, 2, 0.52 };
double[] weights = { 0.25, 0.25, 0.50 };
IFittingOptions options = null;
target.Fit(observations, weights, options);
double expected = 0.79;
double actual = (target as NormalDistribution).Mean;
Assert.AreEqual(expected, actual);
}
public void ProbabilityFunctionTest()
{
IDistribution target = CreateUnivariateDiscreteDistribution();
double p = 0.42;
double q = 1 - p;
Assert.AreEqual(q, target.ProbabilityFunction(0));
Assert.AreEqual(p, target.ProbabilityFunction(1));
double[] observations = { 0, 1, 0, 0, 1, 0 };
target.Fit(observations);
p = Accord.Statistics.Tools.Mean(observations);
q = 1 - p;
Assert.AreEqual(q, target.ProbabilityFunction(0));
Assert.AreEqual(p, target.ProbabilityFunction(1));
}
public void FitTest2()
{
IDistribution target = CreateMultivariateContinuousDistribution();
double[][] observations =
{
new double[] { 1, 2 },
new double[] { 3, 2 },
new double[] { 2, 3 },
new double[] { 1, 2 },
};
target.Fit(observations);
double[] expectedMean = Measures.Mean(observations, dimension: 0);
double[][] expectedCov = Measures.Covariance(observations, expectedMean);
MultivariateContinuousDistribution actual = target as MultivariateContinuousDistribution;
Assert.IsTrue(expectedMean.IsEqual(actual.Mean));
Assert.IsTrue(expectedCov.IsEqual(actual.Covariance));
}
public void FitTest3()
{
IDistribution target = CreateMultivariateContinuousDistribution();
double[][] observations =
{
new double[] { 1, 2 },
new double[] { 3, 2 },
new double[] { 2, 3 },
new double[] { 1, 2 },
};
target.Fit(observations);
double[] expectedMean = Accord.Statistics.Tools.Mean(observations);
double[,] expectedCov = Accord.Statistics.Tools.Covariance(observations, expectedMean);
MultivariateContinuousDistribution actual = target as MultivariateContinuousDistribution;
Assert.IsTrue(expectedMean.IsEqual(actual.Mean));
Assert.IsTrue(expectedCov.IsEqual(actual.Covariance));
}