private void computeInformation(double[][] inputData, double[] outputData, double[] weights)
{
// Store model information
#pragma warning disable 612, 618
this.result = regression.Compute(inputData);
#pragma warning restore 612, 618
this.NumberOfSamples = inputData.Length;
if (weights == null)
{
this.deviance = regression.GetDeviance(inputData, outputData);
this.logLikelihood = regression.GetLogLikelihood(inputData, outputData);
this.chiSquare = regression.ChiSquare(inputData, outputData);
}
else
{
this.deviance = regression.GetDeviance(inputData, outputData, weights);
this.logLikelihood = regression.GetLogLikelihood(inputData, outputData, weights);
this.chiSquare = regression.ChiSquare(inputData, outputData, weights);
}
// Store coefficient information
for (int i = 0; i < regression.NumberOfParameters; i++)
{
this.standardErrors[i] = regression.StandardErrors[i];
this.waldTests[i] = regression.GetWaldTest(i);
this.coefficients[i] = regression.GetCoefficient(i);
this.confidences[i] = regression.GetConfidenceInterval(i);
this.oddsRatios[i] = regression.GetOddsRatio(i);
}
}
private void computeInformation()
{
// Store model information
this.result = regression.Compute(inputData);
if (weights == null)
{
this.deviance = regression.GetDeviance(inputData, outputData);
this.logLikelihood = regression.GetLogLikelihood(inputData, outputData);
this.chiSquare = regression.ChiSquare(inputData, outputData);
}
else
{
this.deviance = regression.GetDeviance(inputData, outputData, weights);
this.logLikelihood = regression.GetLogLikelihood(inputData, outputData, weights);
this.chiSquare = regression.ChiSquare(inputData, outputData, weights);
}
// Store coefficient information
for (int i = 0; i < regression.Coefficients.Length; i++)
{
this.standardErrors[i] = regression.StandardErrors[i];
this.waldTests[i] = regression.GetWaldTest(i);
this.coefficients[i] = regression.Coefficients[i];
this.confidences[i] = regression.GetConfidenceInterval(i);
this.oddsRatios[i] = regression.GetOddsRatio(i);
}
}
/// <summary>
/// Computes the Logistic Regression Analysis.
/// </summary>
/// <remarks>The likelihood surface for the
/// logistic regression learning is convex, so there will be only one
/// peak. Any local maxima will be also a global maxima.
/// </remarks>
/// <param name="limit">
/// The difference between two iterations of the regression algorithm
/// when the algorithm should stop. If not specified, the value of
/// 10e-4 will be used. The difference is calculated based on the largest
/// absolute parameter change of the regression.
/// </param>
/// <param name="maxIterations">
/// The maximum number of iterations to be performed by the regression
/// algorithm.
/// </param>
/// <returns>
/// True if the model converged, false otherwise.
/// </returns>
///
public bool Compute(double limit, int maxIterations)
{
double delta;
int iteration = 0;
do // learning iterations until convergence
{
delta = regression.Regress(inputData, outputData);
iteration++;
} while (delta > limit && iteration < maxIterations);
// Check if the full model has converged
bool converged = iteration <= maxIterations;
// Store model information
this.result = regression.Compute(inputData);
this.deviance = regression.GetDeviance(inputData, outputData);
this.logLikelihood = regression.GetLogLikelihood(inputData, outputData);
this.chiSquare = regression.ChiSquare(inputData, outputData);
// Store coefficient information
for (int i = 0; i < regression.Coefficients.Length; i++)
{
this.waldTests[i] = regression.GetWaldTest(i);
this.standardErrors[i] = regression.GetStandardError(i);
this.coefficients[i] = regression.Coefficients[i];
this.confidences[i] = regression.GetConfidenceInterval(i);
this.oddsRatios[i] = regression.GetOddsRatio(i);
}
// Perform likelihood-ratio tests against diminished nested models
for (int i = 0; i < inputCount; i++)
{
// Create a diminished inner model without the current variable
double[][] data = inputData.RemoveColumn(i);
LogisticRegression inner = new LogisticRegression(inputCount - 1);
iteration = 0;
do // learning iterations until convergence
{
delta = inner.Regress(data, outputData);
iteration++;
} while (delta > limit && iteration < maxIterations);
double ratio = 2.0 * (logLikelihood - inner.GetLogLikelihood(data, outputData));
ratioTests[i + 1] = new ChiSquareTest(ratio, 1);
}
// Returns true if the full model has converged, false otherwise.
return(converged);
}
/// <summary>
/// Constructs a new Logistic regression model.
/// </summary>
///
internal StepwiseLogisticRegressionModel(StepwiseLogisticRegressionAnalysis analysis, LogisticRegression regression,
int[] variables, ChiSquareTest chiSquare, ChiSquareTest[] tests)
{
this.Analysis = analysis;
this.Regression = regression;
int coefficientCount = regression.NumberOfInputs + 1;
this.Inputs = analysis.Inputs.Get(variables);
this.ChiSquare = chiSquare;
this.LikelihoodRatioTests = tests;
this.Variables = variables;
this.StandardErrors = new double[coefficientCount];
this.WaldTests = new WaldTest[coefficientCount];
this.CoefficientValues = new double[coefficientCount];
this.Confidences = new DoubleRange[coefficientCount];
this.OddsRatios = new double[coefficientCount];
// Store coefficient information
for (int i = 0; i < regression.NumberOfInputs + 1; i++)
{
this.StandardErrors[i] = regression.StandardErrors[i];
this.WaldTests[i] = regression.GetWaldTest(i);
this.CoefficientValues[i] = regression.GetCoefficient(i);
this.Confidences[i] = regression.GetConfidenceInterval(i);
this.OddsRatios[i] = regression.GetOddsRatio(i);
}
StringBuilder sb = new StringBuilder();
for (int i = 0; i < Inputs.Length; i++)
{
sb.Append(Inputs[i]);
if (i < Inputs.Length - 1)
{
sb.Append(", ");
}
}
this.Names = sb.ToString();
var logCoefs = new List <NestedLogisticCoefficient>(coefficientCount);
for (int i = 0; i < coefficientCount; i++)
{
logCoefs.Add(new NestedLogisticCoefficient(this, i));
}
this.Coefficients = new NestedLogisticCoefficientCollection(logCoefs);
}
public void learn_new_mechanism()
{
Accord.Math.Random.Generator.Seed = 0;
#region doc_log_reg_1
// 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
// We can also obtain confidence intervals for the odd ratios:
DoubleRange ageRange = regression.GetConfidenceInterval(1); // { 0.955442466180864, 1.09075592717851 }
DoubleRange smokeRange = regression.GetConfidenceInterval(2); // { 0.326598216009923, 105.088535240304 }
// 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);
#endregion
double[] expected =
{
0.21044171509541, 0.132425274863516, 0.657478034489772, 0.181224847711481, 0.747556618035989, 0.614500418479497, 0.331167053803838, 0.144741108525755, 0.436271096256738, 0.544193832738005
};
string str = scores.ToCSharp();
for (int i = 0; i < scores.Length; i++)
{
Assert.AreEqual(expected[i], scores[i], 1e-8);
}
double[] transform = regression.Transform(input, scores);
for (int i = 0; i < scores.Length; i++)
{
Assert.AreEqual(expected[i], transform[i], 1e-8);
}
Assert.AreEqual(1.0208597028836701, ageOdds, 1e-10);
Assert.AreEqual(5.8584748789881331, smokeOdds, 1e-6);
Assert.AreEqual(-2.4577464307294092, regression.Intercept, 1e-8);
Assert.AreEqual(-2.4577464307294092, regression.Coefficients[0], 1e-8);
Assert.AreEqual(0.020645118265359252, regression.Coefficients[1], 1e-10);
Assert.AreEqual(1.7678893101571855, regression.Coefficients[2], 1e-8);
Assert.IsTrue(new[] { 0.955442466180864, 1.09075592717851 }.IsEqual(ageRange, atol: 1e-10));
Assert.IsTrue(new[] { 0.326598216009923, 105.088535240304 }.IsEqual(smokeRange, atol: 1e-10));
Assert.IsFalse(actual[0]);
Assert.IsFalse(actual[1]);
Assert.IsTrue(actual[2]);
Assert.IsFalse(actual[3]);
Assert.IsTrue(actual[4]);
Assert.IsTrue(actual[5]);
Assert.IsFalse(actual[6]);
Assert.IsFalse(actual[7]);
Assert.IsFalse(actual[8]);
Assert.IsTrue(actual[9]);
}
