LogisticRegression Class

[SerializableAttribute]
public class LogisticRegression : GeneralizedLinearRegression

<SerializableAttribute>
Public Class LogisticRegression
	Inherits GeneralizedLinearRegression

// Suppose we have the following data about some patients.
// The first variable is continuous and represent patient
// age. The second variable is dichotomic and give whether
// they smoke or not (This is completely fictional data).

// We also know if they have had lung cancer or not, and 
// we would like to know whether smoking has any connection
// with lung cancer (This is completely fictional data).

double[][] input =
{              // age, smokes?, had cancer?
    new double[] { 55,    0  }, // false - no cancer
    new double[] { 28,    0  }, // false
    new double[] { 65,    1  }, // false
    new double[] { 46,    0  }, // true  - had cancer
    new double[] { 86,    1  }, // true
    new double[] { 56,    1  }, // true
    new double[] { 85,    0  }, // false
    new double[] { 33,    0  }, // false
    new double[] { 21,    1  }, // false
    new double[] { 42,    1  }, // true
};

bool[] output = // Whether each patient had lung cancer or not
{
    false, false, false, true, true, true, false, false, false, true
};


// To verify this hypothesis, we are going to create a logistic
// regression model for those two inputs (age and smoking), learned
// using a method called "Iteratively Reweighted Least Squares":

var learner = new IterativeReweightedLeastSquares<LogisticRegression>()
{
    Tolerance = 1e-4,  // Let's set some convergence parameters
    Iterations = 100,  // maximum number of iterations to perform
    Regularization = 0
};

// Now, we can use the learner to finally estimate our model:
LogisticRegression regression = learner.Learn(input, output);

// At this point, we can compute the odds ratio of our variables.
// In the model, the variable at 0 is always the intercept term, 
// with the other following in the sequence. Index 1 is the age
// and index 2 is whether the patient smokes or not.

// For the age variable, we have that individuals with
//   higher age have 1.021 greater odds of getting lung
//   cancer controlling for cigarette smoking.
double ageOdds = regression.GetOddsRatio(1); // 1.0208597028836701

// For the smoking/non smoking category variable, however, we
//   have that individuals who smoke have 5.858 greater odds
//   of developing lung cancer compared to those who do not 
//   smoke, controlling for age (remember, this is completely
//   fictional and for demonstration purposes only).
double smokeOdds = regression.GetOddsRatio(2); // 5.8584748789881331

// If we would like to use the model to predict a probability for
// each patient regarding whether they are at risk of cancer or not,
// we can use the Probability function:

double[] scores = regression.Probability(input);

// Finally, if we would like to arrive at a conclusion regarding
// each patient, we can use the Decide method, which will transform
// the probabilities (from 0 to 1) into actual true/false values:

bool[] actual = regression.Decide(input);

// Declare some training data. This is exactly the same
// data used in the LogisticRegression documentation page

// Suppose we have the following data about some patients.
// The first variable is continuous and represent patient
// age. The second variable is dichotomic and give whether
// they smoke or not (This is completely fictional data).

// We also know if they have had lung cancer or not, and 
// we would like to know whether smoking has any connection
// with lung cancer (This is completely fictional data).

double[][] input =
{              // age, smokes?, had cancer?
    new double[] { 55,    0  }, // false - no cancer
    new double[] { 28,    0  }, // false
    new double[] { 65,    1  }, // false
    new double[] { 46,    0  }, // true  - had cancer
    new double[] { 86,    1  }, // true
    new double[] { 56,    1  }, // true
    new double[] { 85,    0  }, // false
    new double[] { 33,    0  }, // false
    new double[] { 21,    1  }, // false
    new double[] { 42,    1  }, // true
};

double[] output = // Whether each patient had lung cancer or not
{
    0, 0, 0, 1, 1, 1, 0, 0, 0, 1
};

// Create the L1-regularization learning algorithm
var teacher = new ProbabilisticCoordinateDescent()
{
    Tolerance = 1e-10,
    Complexity = 1e+10, // learn a hard-margin model
};

// Learn the L1-regularized machine
var svm = teacher.Learn(input, output);

// Convert the svm to logistic regression
var regression = (LogisticRegression)svm;

// Compute the predicted outcome for inputs
bool[] predicted = regression.Decide(input);

// Compute log-likelihood scores for the outputs
double[] scores = regression.Score(input);

// Compute odds-ratio as in the LogisticRegression example
double ageOdds = regression.GetOddsRatio(1);   // 1.0208597029158772
double smokeOdds = regression.GetOddsRatio(2); // 5.8584748789881331

// Compute the classification error as in SVM example
double error = new ZeroOneLoss(output).Loss(predicted);