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Showing content from http://accord-framework.net/docs/html/T_Accord_Statistics_Analysis_LogisticRegressionAnalysis.htm below:

Logistic Regression Analysis.

Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0

[SerializableAttribute]
public class LogisticRegressionAnalysis : TransformBase<double[], double>, 
	IRegressionAnalysis, IMultivariateAnalysis, IAnalysis, ISupervisedLearning<LogisticRegression, double[], int>, 
	ISupervisedLearning<LogisticRegression, double[], double>

<SerializableAttribute>
Public Class LogisticRegressionAnalysis
	Inherits TransformBase(Of Double(), Double)
	Implements IRegressionAnalysis, IMultivariateAnalysis, IAnalysis, ISupervisedLearning(Of LogisticRegression, Double(), Integer), 
	ISupervisedLearning(Of LogisticRegression, Double(), Double)

The LogisticRegressionAnalysis type exposes the following members.

Constructs a Logistic Regression Analysis.

Constructs a Logistic Regression Analysis.

Constructs a Logistic Regression Analysis.

Constructs a Logistic Regression Analysis.

Constructs a Logistic Regression Analysis.

Gets the source matrix from which the analysis was run.

Gets the Chi-Square (Likelihood Ratio) Test for the model.

Gets the collection of coefficients of the model.

Gets the value of each coefficient.

Gets or sets whether nested models should be computed in order to calculate the likelihood-ratio test of each of the coefficients. Default is false.

Gets the 95% Confidence Intervals (C.I.) for each coefficient found in the regression.

Gets the Deviance of the model.

Gets the information matrix obtained during learning.

Gets or sets the name of the input variables for the model.

Gets or sets the maximum number of iterations to be performed by the regression algorithm. Default is 50.

Gets the Likelihood-Ratio Tests for each coefficient.

Gets the Log-Likelihood for the model.

Gets the number of inputs accepted by the model.

Gets the number of outputs generated by the model.

Gets the number of samples used to compute the analysis.

Gets the Odds Ratio for each coefficient found during the logistic regression.

Gets or sets the name of the output variable for the model.

Gets the dependent variable value for each of the source input points.

Gets the Logistic Regression model created and evaluated by this analysis.

Gets or sets the regularization value to be added in the objective function. Default is 1e-10.

Gets the resulting probabilities obtained by the logistic regression model.

Gets the source matrix from which the analysis was run.

Gets the Standard Error for each coefficient found during the logistic regression.

Gets or sets a cancellation token that can be used to stop the learning algorithm while it is running.

Gets or sets the difference between two iterations of the regression algorithm when the algorithm should stop. The difference is calculated based on the largest absolute parameter change of the regression. Default is 1e-5.

Gets the Wald Tests for each coefficient.

Gets the sample weight associated with each input vector.

Computes the Logistic Regression Analysis.

Computes the Logistic Regression Analysis for an already computed regression.

Computes the Logistic Regression Analysis.

Determines whether the specified object is equal to the current object.

Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.

Creates a new LogisticRegressionAnalysis from summarized data. In summary data, instead of having a set of inputs and their associated outputs, we have the number of times an input vector had a positive label in the data set and how many times it had a negative label.

Gets the confidence interval for a given input.

Serves as the default hash function.

Gets the Log-Likelihood Ratio between this model and another model.

Gets the prediction interval for a given input.

Gets the Type of the current instance.

Learns a model that can map the given inputs to the given outputs.

Learns a model that can map the given inputs to the given outputs.

Learns a model that can map the given inputs to the given outputs.

Creates a shallow copy of the current Object.

Returns a string that represents the current object.

Applies the transformation to a set of input vectors, producing an associated set of output vectors.

Applies the transformation to an input, producing an associated output.

Applies the transformation to an input, producing an associated output.

Checks whether an object implements a method with the given name.

Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.

Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.

Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.

The Logistic Regression Analysis tries to extract useful information about a logistic regression model.

This class can also be bound to standard controls such as the DataGridView by setting their DataSource property to the analysis' Coefficients property.

References:

• E. F. Connor. Logistic Regression. Available on: http://userwww.sfsu.edu/~efc/classes/biol710/logistic/logisticreg.htm
• C. Shalizi. Logistic Regression and Newton's Method. Lecture notes. Available on: http://www.stat.cmu.edu/~cshalizi/350/lectures/26/lecture-26.pdf
• A. Storkey. Learning from Data: Learning Logistic Regressors. Available on: http://www.inf.ed.ac.uk/teaching/courses/lfd/lectures/logisticlearn-print.pdf

The following example shows to create a Logistic regresion analysis using a full dataset composed of input vectors and a binary output vector. Each input vector has an associated label (1 or 0) in the output vector, where 1 represents a positive label (yes, or true) and 0 represents a negative label (no, or false).

double[] coef = lra.CoefficientValues;




double[] odds = lra.OddsRatios;
double[] stde = lra.StandardErrors;


double y = lra.Regression.Probability(new double[] { 87, 1 }); 




DoubleRange ci = lra.GetConfidenceInterval(new double[] { 87, 1 });

The resulting table is shown below.

double[][] inputs =
{
    
    new double[] { 55,    0   },
    new double[] { 28,    0   },
    new double[] { 65,    1   },
    new double[] { 46,    0   },
    new double[] { 86,    1   },
    new double[] { 56,    1   },
    new double[] { 85,    0   },
    new double[] { 33,    0   },
    new double[] { 21,    1   },
    new double[] { 42,    1   },
};






double[] output =
{
    0, 0, 0, 1, 1, 1, 0, 0, 0, 1
};


var lra = new LogisticRegressionAnalysis()
{
    Regularization = 0
};


LogisticRegression regression = lra.Learn(inputs, output);

The analysis can also be created from data given in a summary form. Instead of having one input vector associated with one positive or negative label, each input vector is associated with the proportion of positive to negative labels in the original dataset.

int[,] data =
{
    
    {       1,             140,           45       },
    {       2,             130,           60       },
    {       3,             150,           31       },
    {       4,              96,           65       }
};


double[][] inputs = data.GetColumn(0).ToDouble().ToJagged();
int[] positive = data.GetColumn(1);
int[] negative = data.GetColumn(2);


var lra = new LogisticRegressionAnalysis();


LogisticRegression regression = lra.Learn(inputs, positive, negative);









double[] coef = lra.CoefficientValues;




double[] odds = lra.OddsRatios;
double[] stde = lra.StandardErrors;



double y = lra.Regression.Probability(new double[] { 4 }); 

The last example shows how to learn a logistic regression analysis using data given in the form of a System.Data.DataTable. This data is also heterogeneous, mixing both discrete (symbol) variables and continuous variables. This example is also available for MultipleLinearRegressionAnalysis.

var data = new DataTable("Customer Revenue Example");

data.Columns.Add("Day", "CustomerId", "Time (hour)", "Weather", "Buy");
data.Rows.Add("D1", 0, 8, "Sunny", true);
data.Rows.Add("D2", 1, 10, "Sunny", true);
data.Rows.Add("D3", 2, 10, "Rain", false);
data.Rows.Add("D4", 3, 16, "Rain", true);
data.Rows.Add("D5", 4, 15, "Rain", true);
data.Rows.Add("D6", 5, 20, "Rain", false);
data.Rows.Add("D7", 6, 12, "Cloudy", true);
data.Rows.Add("D8", 7, 12, "Sunny", false);







var codebook = new Codification()
{
    { "Weather", CodificationVariable.Categorical },
    { "Time (hour)", CodificationVariable.Continuous },
    { "Revenue", CodificationVariable.Continuous },
};


codebook.Learn(data);





string[] inputNames;  
string outputName;    


double[][] inputs = codebook.Apply(data, "Weather", "Time (hour)").ToJagged(out inputNames);
double[] outputs = codebook.Apply(data, "Buy").ToVector(out outputName);
















var lra = new LogisticRegressionAnalysis()
{
    
    
    

    Inputs = inputNames, 
    Output = outputName  
};


LogisticRegression regression = lra.Learn(inputs, outputs);


double predicted = lra.Transform(inputs[0]); 



int inputCount = lra.NumberOfInputs;   
int outputCount = lra.NumberOfOutputs; 
double logl = lra.LogLikelihood;       
ChiSquareTest x2 = lra.ChiSquare;      
double[] stdErr = lra.StandardErrors;  
double[] or = lra.OddsRatios;          
LogisticCoefficientCollection c = lra.Coefficients; 
double[][] h = lra.InformationMatrix;  

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