MultinomialLogisticRegressionAnalysis Class

[SerializableAttribute]
public class MultinomialLogisticRegressionAnalysis : TransformBase<double[], int>, 
	IMultivariateRegressionAnalysis, IMultivariateAnalysis, IAnalysis, ISupervisedLearning<MultinomialLogisticRegression, double[], double[]>, 
	ISupervisedLearning<MultinomialLogisticRegression, double[], int>

<SerializableAttribute>
Public Class MultinomialLogisticRegressionAnalysis
	Inherits TransformBase(Of Double(), Integer)
	Implements IMultivariateRegressionAnalysis, IMultivariateAnalysis, IAnalysis, ISupervisedLearning(Of MultinomialLogisticRegression, Double(), Double()), 
	ISupervisedLearning(Of MultinomialLogisticRegression, Double(), Integer)

// This example downloads an example dataset from the web and learns a multinomial logistic 
// regression on it. However, please keep in mind that the Multinomial Logistic Regression 
// can also work without many of the elements that will be shown below, like the codebook, 
// DataTables, and a CsvReader. 

// Let's download an example dataset from the web to learn a multinomial logistic regression:
CsvReader reader = CsvReader.FromUrl("https://raw.githubusercontent.com/rlowrance/re/master/hsbdemo.csv", hasHeaders: true);

// Let's read the CSV into a DataTable. As mentioned above, this step
// can help, but is not necessarily required for learning a the model:
DataTable table = reader.ToTable();

// We will learn a MLR regression between the following input and output fields of this table:
string[] inputNames = new[] { "write", "ses" };
string[] outputNames = new[] { "prog" };

// Now let's create a codification codebook to convert the string fields in the data 
// into integer symbols. This is required because the MLR model can only learn from 
// numeric data, so strings have to be transformed first. We can force a particular
// interpretation for those columns if needed, as shown in the initializer below:
var codification = new Codification()
{
    { "write", CodificationVariable.Continuous },
    { "ses", CodificationVariable.CategoricalWithBaseline, new[] { "low", "middle", "high" } },
    { "prog", CodificationVariable.Categorical, new[] { "academic", "general" } },
};

// Learn the codification
codification.Learn(table);

// Now, transform symbols into a vector representation, growing the number of inputs:
double[][] x = codification.Transform(table, inputNames, out inputNames).ToDouble();
double[][] y = codification.Transform(table, outputNames, out outputNames).ToDouble();

// Create a new Multinomial Logistic Regression Analysis:
var analysis = new MultinomialLogisticRegressionAnalysis()
{
    InputNames = inputNames,
    OutputNames = outputNames,
};

// Learn the regression from the input and output pairs:
MultinomialLogisticRegression regression = analysis.Learn(x, y);

// Let's retrieve some information about what we just learned:
int coefficients = analysis.Coefficients.Count; // should be 9
int numberOfInputs = analysis.NumberOfInputs;   // should be 3
int numberOfOutputs = analysis.NumberOfOutputs; // should be 3

inputNames = analysis.InputNames; // should be "write", "ses: middle", "ses: high"
outputNames = analysis.OutputNames; // should be "prog: academic", "prog: general", "prog: vocation"

// The regression is best visualized when it is data-bound to a 
// Windows.Forms DataGridView or WPF DataGrid. You can get the
// values for all different coefficients and discrete values:

// DataGridBox.Show(regression.Coefficients); // uncomment this line

// You can get the matrix of coefficients:
double[][] coef = analysis.CoefficientValues;

// Should be equal to:
double[][] expectedCoef = new double[][]
{
    new double[] { 2.85217775752471, -0.0579282723520426, -0.533293368378012, -1.16283850605289 },
    new double[] { 5.21813357698422, -0.113601186660817, 0.291387041358367, -0.9826369387481 }
};

// And their associated standard errors:
double[][] stdErr = analysis.StandardErrors;

// Should be equal to:
double[][] expectedErr = new double[][]
{
    new double[] { -2.02458003380033, -0.339533576505471, -1.164084923948, -0.520961533343425, 0.0556314901718 },
    new double[] { -3.73971589217449, -1.47672790071382, -1.76795568348094, -0.495032307980058, 0.113563519656386 }
};

// We can also get statistics and hypothesis tests:
WaldTest[][] wald = analysis.WaldTests;        // should all have p < 0.05
ChiSquareTest chiSquare = analysis.ChiSquare;  // should be p=1.06300120956871E-08
double logLikelihood = analysis.LogLikelihood; // should be -179.98173272217591

// You can use the regression to predict the values:
int[] pred = regression.Transform(x);

// And get the accuracy of the prediction if needed:
var cm = GeneralConfusionMatrix.Estimate(regression, x, y.ArgMax(dimension: 1));

double acc = cm.Accuracy; // should be 0.61
double kappa = cm.Kappa;  // should be 0.2993487536492252

// This example shows how to learn a multinomial logistic regression
// analysis in the famous Fisher's Iris dataset. It should serve to
// demonstrate that this class does not really need to be used with
// DataTables, Codification codebooks and other supplementary features.

Iris iris = new Iris();

// Load Fisher's Iris dataset:
double[][] x = iris.Instances;
int[] y = iris.ClassLabels;

// Create a new Multinomial Logistic Regression Analysis:
var analysis = new MultinomialLogisticRegressionAnalysis();

// Note: we could have passed the class names from iris.ClassNames and 
// variable names from iris.VariableNames during MLR instantiation as:
// 
// var analysis = new MultinomialLogisticRegressionAnalysis()
// {
//     InputNames = iris.VariableNames,
//     OutputNames = iris.ClassNames
// };

// However, this example is also intended to demonstrate that 
// those are not required when learning a regression analysis.

// Learn the regression from the input and output pairs:
MultinomialLogisticRegression regression = analysis.Learn(x, y);

// Let's retrieve some information about what we just learned:
int coefficients = analysis.Coefficients.Count; // should be 11
int numberOfInputs = analysis.NumberOfInputs;   // should be 4
int numberOfOutputs = analysis.NumberOfOutputs; // should be 3

string[] inputNames = analysis.InputNames; // should be "Input 1", "Input 2", "Input 3", "Input 4"
string[] outputNames = analysis.OutputNames; // should be "Class 0", "class 1", "class 2"

// The regression is best visualized when it is data-bound to a 
// Windows.Forms DataGridView or WPF DataGrid. You can get the
// values for all different coefficients and discrete values:

// DataGridBox.Show(regression.Coefficients); // uncomment this line

// You can get the matrix of coefficients:
double[][] coef = analysis.CoefficientValues;

// Should be equal to:
double[][] expectedCoef = new double[][]
{
    new double[] { 2.85217775752471, -0.0579282723520426, -0.533293368378012, -1.16283850605289 },
    new double[] { 5.21813357698422, -0.113601186660817, 0.291387041358367, -0.9826369387481 }
};

// And their associated standard errors:
double[][] stdErr = analysis.StandardErrors;

// Should be equal to:
double[][] expectedErr = new double[][]
{
    new double[] { -2.02458003380033, -0.339533576505471, -1.164084923948, -0.520961533343425, 0.0556314901718 },
    new double[] { -3.73971589217449, -1.47672790071382, -1.76795568348094, -0.495032307980058, 0.113563519656386 }
};

// We can also get statistics and hypothesis tests:
WaldTest[][] wald = analysis.WaldTests;        // should all have p < 0.05
ChiSquareTest chiSquare = analysis.ChiSquare;  // should be p=0
double logLikelihood = analysis.LogLikelihood; // should be -29.558338705646587

// You can use the regression to predict the values:
int[] pred = regression.Transform(x);

// And get the accuracy of the prediction if needed:
var cm = GeneralConfusionMatrix.Estimate(regression, x, y);

double acc = cm.Accuracy; // should be 0.94666666666666666
double kappa = cm.Kappa;  // should be 0.91999999999999982