CrossValidationStatistics Class

[SerializableAttribute]
public class CrossValidationStatistics

<SerializableAttribute>
Public Class CrossValidationStatistics

// Ensure results are reproducible
Accord.Math.Random.Generator.Seed = 0;

// This is a sample code on how to use Cross-Validation
// to assess the performance of Support Vector Machines.

// Consider the example binary data. We will be trying
// to learn a XOR problem and see how well does SVMs
// perform on this data.

double[][] data =
{
    new double[] { -1, -1 }, new double[] {  1, -1 },
    new double[] { -1,  1 }, new double[] {  1,  1 },
    new double[] { -1, -1 }, new double[] {  1, -1 },
    new double[] { -1,  1 }, new double[] {  1,  1 },
    new double[] { -1, -1 }, new double[] {  1, -1 },
    new double[] { -1,  1 }, new double[] {  1,  1 },
    new double[] { -1, -1 }, new double[] {  1, -1 },
    new double[] { -1,  1 }, new double[] {  1,  1 },
};

int[] xor = // result of xor for the sample input data
{
    -1,       1,
     1,      -1,
    -1,       1,
     1,      -1,
    -1,       1,
     1,      -1,
    -1,       1,
     1,      -1,
};


// Create a new Cross-validation algorithm passing the data set size and the number of folds
var crossvalidation = new CrossValidation<SupportVectorMachine<Linear, double[]>, double[]>()
{
    K = 3, // Use 3 folds in cross-validation

    // Indicate how learning algorithms for the models should be created
    Learner = (s) => new SequentialMinimalOptimization<Linear, double[]>()
    {
        Complexity = 100
    },

    // Indicate how the performance of those models will be measured
    Loss = (expected, actual, p) => new ZeroOneLoss(expected).Loss(actual),

    Stratify = false, // do not force balancing of classes
};

// If needed, control the parallelization degree
crossvalidation.ParallelOptions.MaxDegreeOfParallelism = 1;

// Compute the cross-validation
var result = crossvalidation.Learn(data, xor);

// Finally, access the measured performance.
double trainingErrors = result.Training.Mean; // should be 0.30606060606060609 (+/- var. 0.083498622589531682)
double validationErrors = result.Validation.Mean; // should be 0.3666666666666667 (+/- var. 0.023333333333333334)

// If desired, compute an aggregate confusion matrix for the validation sets:
GeneralConfusionMatrix gcm = result.ToConfusionMatrix(data, xor);
double accuracy = gcm.Accuracy; // should be 0.625
double error = gcm.Error; // should be 0.375

// Ensure results are reproducible
Accord.Math.Random.Generator.Seed = 0;

// This is a sample code on how to use Cross-Validation
// to assess the performance of Hidden Markov Models.

// Declare some testing data
int[][] inputs = new int[][]
{
    new int[] { 0,1,1,0 },   // Class 0
    new int[] { 0,0,1,0 },   // Class 0
    new int[] { 0,1,1,1,0 }, // Class 0
    new int[] { 0,1,1,1,0 }, // Class 0
    new int[] { 0,1,1,0 },   // Class 0

    new int[] { 0,0,0,0,0 }, // Class 1
    new int[] { 0,0,0,1,0 }, // Class 1
    new int[] { 0,0,0,0,0 }, // Class 1
    new int[] { 0,0,0 },     // Class 1
    new int[] { 0,0,0,0 },   // Class 1

    new int[] { 1,0,0,1 },   // Class 2
    new int[] { 1,1,0,1 },   // Class 2
    new int[] { 1,0,0,0,1 }, // Class 2
    new int[] { 1,0,1 },     // Class 2
    new int[] { 1,1,0,1 },   // Class 2
};

int[] outputs = new int[]
{
    0,0,0,0,0, // First  5 sequences are of class 0
    1,1,1,1,1, // Middle 5 sequences are of class 1
    2,2,2,2,2, // Last   5 sequences are of class 2
};

// Create a new Cross-validation algorithm passing the data set size and the number of folds
var crossvalidation = new CrossValidation<HiddenMarkovClassifier, int[]>()
{
    K = 3, // Use 3 folds in cross-validation
    Learner = (s) => new HiddenMarkovClassifierLearning()
    {
        Learner = (p) => new BaumWelchLearning()
        {
            NumberOfStates = 3
        }
    },

    Loss = (expected, actual, p) => 
    {
        var cm = new GeneralConfusionMatrix(classes: p.Model.NumberOfClasses, expected: expected, predicted: actual);
        p.Variance = cm.Variance;
        return p.Value = cm.Kappa;
    },

    Stratify = false,
};

// If needed, control the parallelization degree
crossvalidation.ParallelOptions.MaxDegreeOfParallelism = 1;

// Compute the cross-validation
var result = crossvalidation.Learn(inputs, outputs);

// If desired, compute an aggregate confusion matrix for the validation sets:
GeneralConfusionMatrix gcm = result.ToConfusionMatrix(inputs, outputs);

// Finally, access the measured performance.
double trainingErrors = result.Training.Mean;
double validationErrors = result.Validation.Mean;

double trainingErrorVar = result.Training.Variance;
double validationErrorVar = result.Validation.Variance;

double trainingErrorPooledVar = result.Training.PooledVariance;
double validationErrorPooledVar = result.Validation.PooledVariance;

// Ensure we have reproducible results
Accord.Math.Random.Generator.Seed = 0;

// Get some data to be learned. We will be using the Wiconsin's
// (Diagnostic) Breast Cancer dataset, where the goal is to determine
// whether the characteristics extracted from a breast cancer exam
// correspond to a malignant or benign type of cancer:
var data = new WisconsinDiagnosticBreastCancer();
double[][] input = data.Features; // 569 samples, 30-dimensional features
int[] output = data.ClassLabels;  // 569 samples, 2 different class labels

// Let's say we want to measure the cross-validation performance of
// a decision tree with a maximum tree height of 5 and where variables
// are able to join the decision path at most 2 times during evaluation:
var cv = CrossValidation.Create(

    k: 10, // We will be using 10-fold cross validation

    learner: (p) => new C45Learning() // here we create the learning algorithm
    {
        Join = 2,
        MaxHeight = 5
    },

    // Now we have to specify how the tree performance should be measured:
    loss: (actual, expected, p) => new ZeroOneLoss(expected).Loss(actual),

    // This function can be used to perform any special
    // operations before the actual learning is done, but
    // here we will just leave it as simple as it can be:
    fit: (teacher, x, y, w) => teacher.Learn(x, y, w),

    // Finally, we have to pass the input and output data
    // that will be used in cross-validation. 
    x: input, y: output
);

// After the cross-validation object has been created,
// we can call its .Learn method with the input and 
// output data that will be partitioned into the folds:
var result = cv.Learn(input, output);

// We can grab some information about the problem:
int numberOfSamples = result.NumberOfSamples; // should be 569
int numberOfInputs = result.NumberOfInputs;   // should be 30
int numberOfOutputs = result.NumberOfOutputs; // should be 2

double trainingError = result.Training.Mean; // should be 0.017771153143274855
double validationError = result.Validation.Mean; // should be 0.0755952380952381

// If desired, compute an aggregate confusion matrix for the validation sets:
GeneralConfusionMatrix gcm = result.ToConfusionMatrix(input, output);
double accuracy = gcm.Accuracy; // result should be 0.92442882249560632