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CrossValidation Class

k-Fold cross-validation. Please only use the static methods contained in this class, the rest are marked as obsolete.
Inheritance Hierarchy
SystemObject
  Accord.MachineLearningCrossValidationObject
    Accord.MachineLearningCrossValidation

Namespace:  Accord.MachineLearning
Assembly:  Accord.MachineLearning (in Accord.MachineLearning.dll) Version: 3.7.0
Syntax
[SerializableAttribute]
public class CrossValidation : CrossValidation<Object>
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The CrossValidation type exposes the following members.

Constructors
Properties
  NameDescription
Public propertyFitting
Gets or sets the model fitting function.
(Inherited from CrossValidationTModel.)
Public propertyFolds
Gets the array of data set indexes contained in each fold.
(Inherited from CrossValidationTModel.)
Public propertyIndices
Gets the array of fold indices for each point in the data set.
(Inherited from CrossValidationTModel.)
Public propertyK
Gets the number of folds in the k-fold cross validation.
(Inherited from CrossValidationTModel.)
Public propertyRunInParallel
Gets or sets a value indicating whether to use parallel processing through the use of multiple threads or not. Default is true.
(Inherited from CrossValidationTModel.)
Public propertySamples
Gets the total number of data samples in the data set.
(Inherited from CrossValidationTModel.)
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Methods
  NameDescription
Public methodCompute
Computes the cross validation algorithm.
(Inherited from CrossValidationTModel.)
Public methodStatic memberCode exampleCreateTModel, TLearner, TInput, TOutput
Public methodCreatePartitions
Gets the indices for the training and validation sets for the specified validation fold index.
(Inherited from CrossValidationTModel.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetPartitionSize
Gets the number of instances in training and validation sets for the specified validation fold index.
(Inherited from CrossValidationTModel.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodStatic memberSplittings(Int32, Int32) Obsolete.
Obsolete. Please use Random(Int32, Int32) instead.
Public methodStatic memberSplittings(Int32, Int32, Int32) Obsolete.
Obsolete. Please use Classes.Random(labels, classes, folds) instead.
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodToT
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.
(Defined by ExtensionMethods.)
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Remarks

Cross-validation is a technique for estimating the performance of a predictive model. It can be used to measure how the results of a statistical analysis will generalize to an independent data set. It is mainly used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice.

One round of cross-validation involves partitioning a sample of data into complementary subsets, performing the analysis on one subset (called the training set), and validating the analysis on the other subset (called the validation set or testing set). To reduce variability, multiple rounds of cross-validation are performed using different partitions, and the validation results are averaged over the rounds.

References:

Examples
// 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;
double validationErrors = result.Validation.Mean;
// 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);

// 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
double validationError = result.Validation.Mean; // should be 0.089661654135338359
See Also