public void CoefficientsTest1()
{
double[][] inputs;
int[] outputs;
MultinomialLogisticRegressionTest.CreateInputOutputsExample2(out inputs, out outputs);
var analysis = new MultinomialLogisticRegressionAnalysis(inputs, outputs);
int inputCount = 5;
int coeffCount = inputCount + 1;
var mlr = analysis.regression;
analysis.Iterations = 100;
analysis.Tolerance = 1e-6;
analysis.Compute();
foreach (var coefficient in analysis.Coefficients)
{
Assert.IsNotNull(coefficient.Analysis);
Assert.IsNotNull(coefficient.Confidence);
Assert.IsNotNull(coefficient.ConfidenceLower);
Assert.IsNotNull(coefficient.ConfidenceUpper);
Assert.IsNotNull(coefficient.Name);
Assert.IsNotNull(coefficient.Class);
Assert.IsNotNull(coefficient.StandardError);
Assert.IsNotNull(coefficient.Value);
}
Assert.AreEqual(13, analysis.Coefficients.Count);
Assert.AreEqual(2, analysis.CoefficientValues.Length);
var class1 = analysis.CoefficientValues[0];
Assert.AreEqual(-11.774547061739975, class1[0], 1e-10);
Assert.AreEqual(0.523813075806107, class1[1], 1e-10);
Assert.AreEqual(0.36820307277024716, class1[2], 1e-10);
Assert.AreEqual(0, class1[3], 1e-6);
Assert.AreEqual(0, class1[4], 1e-6);
Assert.AreEqual(0, class1[5], 1e-6);
var class2 = analysis.CoefficientValues[1];
Assert.AreEqual(-22.721272157115514, class2[0], 1e-10);
Assert.AreEqual(0.46593949381162203, class2[1], 1e-10);
Assert.AreEqual(0.68590438098052586, class2[2], 1e-10);
Assert.AreEqual(0, class2[3], 1e-6);
Assert.AreEqual(0, class2[4], 1e-6);
Assert.AreEqual(0, class2[5], 1e-6);
}
public void RegressTest2()
{
Accord.Math.Random.Generator.Seed = 0;
double[][] inputs;
int[] outputs;
MultinomialLogisticRegressionTest.CreateInputOutputsExample1(out inputs, out outputs);
// Create an algorithm to estimate the regression
var msgd = new MultinomialLogisticLearning <ConjugateGradient>();
// Now, we can iteratively estimate our model
MultinomialLogisticRegression mlr = msgd.Learn(inputs, outputs);
int[] predicted = mlr.Decide(inputs);
double acc = new ZeroOneLoss(outputs).Loss(predicted);
Assert.AreEqual(0.61088435374149663, acc, 1e-8);
}
public void GradientTest()
{
double[][] inputs;
int[] outputs;
MultinomialLogisticRegressionTest.CreateInputOutputsExample1(out inputs, out outputs);
// Create an algorithm to estimate the regression
var msgd = new MultinomialLogisticLearning <ConjugateGradient>();
msgd.Method.MaxIterations = 1;
msgd.Learn(inputs, outputs);
int variables = inputs.Columns() * outputs.DistinctCount();
var fd = new FiniteDifferences(variables, msgd.crossEntropy);
double[] probe = { 0.1, 0.2, 0.5, 0.6, 0.2, 0.1 };
double[] expected = fd.Compute(probe);
double[] actual = msgd.crossEntropyGradient(probe);
Assert.IsTrue(expected.IsEqual(actual, 1e-5));
}
public void ComputeTest2()
{
double[][] inputs;
int[] outputs;
MultinomialLogisticRegressionTest.CreateInputOutputsExample2(out inputs, out outputs);
var analysis = new MultinomialLogisticRegressionAnalysis(inputs, outputs);
int inputCount = 5;
int outputCount = 3;
int coeffCount = inputCount + 1;
var mlr = analysis.regression;
Assert.AreEqual(inputCount, mlr.Inputs);
Assert.AreEqual(outputCount, mlr.Categories);
Assert.AreEqual(inputCount, analysis.Inputs.Length);
Assert.AreEqual(outputCount, analysis.OutputNames.Length);
analysis.Iterations = 100;
analysis.Tolerance = 1e-6;
analysis.Compute();
Assert.AreEqual(outputCount - 1, analysis.CoefficientValues.Length);
Assert.AreEqual(outputCount - 1, analysis.StandardErrors.Length);
Assert.AreEqual(outputCount - 1, analysis.WaldTests.Length);
Assert.AreEqual(outputCount - 1, analysis.Confidences.Length);
for (int i = 0; i < analysis.CoefficientValues.Length; i++)
{
Assert.AreEqual(coeffCount, analysis.CoefficientValues[i].Length);
Assert.AreEqual(coeffCount, analysis.StandardErrors[i].Length);
Assert.AreEqual(coeffCount, analysis.WaldTests[i].Length);
Assert.AreEqual(coeffCount, analysis.Confidences[i].Length);
for (int j = 0; j < analysis.CoefficientValues[i].Length; j++)
{
Assert.IsFalse(double.IsNaN(analysis.CoefficientValues[i][j]));
Assert.IsFalse(double.IsNaN(analysis.StandardErrors[i][j]));
}
}
var coefficients = analysis.CoefficientValues;
// brand 2
Assert.AreEqual(-11.774655, coefficients[0][0], 1e-3); // intercept
Assert.AreEqual(0.523814, coefficients[0][1], 1e-3); // female
Assert.AreEqual(0.368206, coefficients[0][2], 1e-3); // age
// brand 3
Assert.AreEqual(-22.721396, coefficients[1][0], 1e-3); // intercept
Assert.AreEqual(0.465941, coefficients[1][1], 1e-3); // female
Assert.AreEqual(0.685908, coefficients[1][2], 1e-3); // age
var standard = analysis.StandardErrors;
Assert.AreEqual(-702.97, analysis.LogLikelihood, 1e-2);
Assert.AreEqual(185.85, analysis.ChiSquare.Statistic, 1e-2);
Assert.AreEqual(1405.9414080469473, analysis.Deviance, 1e-5);
}
public void learn_test_2()
{
double[][] inputs;
int[] outputs;
MultinomialLogisticRegressionTest.CreateInputOutputsExample1(out inputs, out outputs);
var analysis = new MultinomialLogisticRegressionAnalysis();
analysis.Iterations = 100;
analysis.Tolerance = 1e-6;
var regression = analysis.Learn(inputs, outputs);
int inputCount = 2;
int outputCount = 3;
int coeffCount = inputCount + 1;
var mlr = analysis.regression;
Assert.AreEqual(inputCount, mlr.Inputs);
Assert.AreEqual(outputCount, mlr.Categories);
Assert.AreEqual(inputCount, analysis.Inputs.Length);
Assert.AreEqual(outputCount, analysis.OutputNames.Length);
Assert.AreEqual(outputCount - 1, analysis.CoefficientValues.Length);
Assert.AreEqual(outputCount - 1, analysis.StandardErrors.Length);
Assert.AreEqual(outputCount - 1, analysis.WaldTests.Length);
Assert.AreEqual(outputCount - 1, analysis.Confidences.Length);
for (int i = 0; i < analysis.CoefficientValues.Length; i++)
{
Assert.AreEqual(coeffCount, analysis.CoefficientValues[i].Length);
Assert.AreEqual(coeffCount, analysis.StandardErrors[i].Length);
Assert.AreEqual(coeffCount, analysis.WaldTests[i].Length);
Assert.AreEqual(coeffCount, analysis.Confidences[i].Length);
}
var coefficients = analysis.CoefficientValues;
// brand 2
Assert.AreEqual(-11.774655, coefficients[0][0], 1e-3); // intercept
Assert.AreEqual(0.523814, coefficients[0][1], 1e-3); // female
Assert.AreEqual(0.368206, coefficients[0][2], 1e-3); // age
// brand 3
Assert.AreEqual(-22.721396, coefficients[1][0], 1e-3); // intercept
Assert.AreEqual(0.465941, coefficients[1][1], 1e-3); // female
Assert.AreEqual(0.685908, coefficients[1][2], 1e-3); // age
var standard = analysis.StandardErrors;
// Using the lower-bound approximation
Assert.AreEqual(1.047378039787443, standard[0][0], 1e-6);
Assert.AreEqual(0.153150051082552, standard[0][1], 1e-6);
Assert.AreEqual(0.031640507386863, standard[0][2], 1e-6);
Assert.AreEqual(1.047378039787443, standard[1][0], 1e-6);
Assert.AreEqual(0.153150051082552, standard[1][1], 1e-6);
Assert.AreEqual(0.031640507386863, standard[1][2], 1e-6);
Assert.AreEqual(-702.97, analysis.LogLikelihood, 1e-2);
Assert.AreEqual(185.85, analysis.ChiSquare.Statistic, 1e-2);
Assert.AreEqual(1405.9414080469473, analysis.Deviance, 1e-4);
var wald = analysis.WaldTests;
Assert.AreEqual(-11.241995503283842, wald[0][0].Statistic, 1e-3);
Assert.AreEqual(3.4202662152119889, wald[0][1].Statistic, 1e-4);
Assert.AreEqual(11.637150673342207, wald[0][2].Statistic, 1e-3);
Assert.AreEqual(-21.693553825772664, wald[1][0].Statistic, 1e-3);
Assert.AreEqual(3.0423802097069097, wald[1][1].Statistic, 1e-4);
Assert.AreEqual(21.678124991086548, wald[1][2].Statistic, 1e-3);
}