public void BootstrapConstructorTest2()
{
// Example from Masters, 1995
// Assume a small dataset
double[] data = { 3, 5, 2, 1, 7 };
// indices { 0, 1, 2, 3, 4 }
int[][] resamplings =
{
new [] { 4, 0, 2, 0, 3 }, // indices of { 7, 3, 2, 3, 1 }
new [] { 1, 3, 3, 0, 4 }, // indices of { 5, 1, 1, 3, 7 }
new [] { 2, 2, 4, 3, 0 }, // indices of { 2, 2, 7, 1, 3 }
};
Bootstrap target = new Bootstrap(data.Length, resamplings);
target.Fitting = (int[] trainingSamples, int[] validationSamples) =>
{
double[] subsample = data.Submatrix(trainingSamples);
double mean = subsample.Mean();
return new BootstrapValues(mean, 0);
};
var result = target.Compute();
double actualMean = result.Training.Mean;
double actualVar = result.Training.Variance;
Assert.AreEqual(3.2, actualMean, 1e-10);
Assert.AreEqual(0.04, actualVar, 1e-10);
}
public void BootstrapConstructorTest3()
{
Accord.Math.Tools.SetupGenerator(0);
// This is a sample code on how to use 0.632 Bootstrap
// 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 Bootstrap algorithm passing the set size and the number of resamplings
var bootstrap = new Bootstrap(size: data.Length, subsamples: 50);
// Define a fitting function using Support Vector Machines. The objective of this
// function is to learn a SVM in the subset of the data indicated by the bootstrap.
bootstrap.Fitting = delegate(int[] indicesTrain, int[] indicesValidation)
{
// The fitting function is passing the indices of the original set which
// should be considered training data and the indices of the original set
// which should be considered validation data.
// Lets now grab the training data:
var trainingInputs = data.Submatrix(indicesTrain);
var trainingOutputs = xor.Submatrix(indicesTrain);
// And now the validation data:
var validationInputs = data.Submatrix(indicesValidation);
var validationOutputs = xor.Submatrix(indicesValidation);
// Create a Kernel Support Vector Machine to operate on the set
var svm = new KernelSupportVectorMachine(new Polynomial(2), 2);
// Create a training algorithm and learn the training data
var smo = new SequentialMinimalOptimization(svm, trainingInputs, trainingOutputs);
double trainingError = smo.Run();
// Now we can compute the validation error on the validation data:
double validationError = smo.ComputeError(validationInputs, validationOutputs);
// Return a new information structure containing the model and the errors achieved.
return new BootstrapValues(trainingError, validationError);
};
// Compute the bootstrap estimate
var result = bootstrap.Compute();
// Finally, access the measured performance.
double trainingErrors = result.Training.Mean;
double validationErrors = result.Validation.Mean;
// And compute the 0.632 estimate
double estimate = result.Estimate;
Assert.AreEqual(50, bootstrap.B);
Assert.AreEqual(0, trainingErrors);
Assert.AreEqual(0.021428571428571429, validationErrors);
Assert.AreEqual(50, bootstrap.Subsamples.Length);
Assert.AreEqual(0.013542857142857143, estimate);
}