/// <summary>
/// <para>Using VC-dimension, we can bound the probability of making an error when estimating empirical probability
/// distributions. We are using Theorem 2.41 in "All Of Nonparametric Statistics".
/// http://books.google.com/books?id=MRFlzQfRg7UC&lpg=PP1&dq=all%20of%20nonparametric%20statistics&pg=PA22#v=onepage&q=%22shatter%20coe%EF%AC%83cients%20do%20not%22&f=false .</para>
/// <para>Note that for intervals on the real line the VC-dimension is 2.</para>
/// </summary>
/// <param name="epsilon">The error we are willing to tolerate.</param>
/// <param name="delta">The error probability we are willing to tolerate.</param>
/// <param name="s">The samples to use for testing.</param>
/// <param name="dist">The distribution we are testing.</param>
public static void VapnikChervonenkisTest(double epsilon, double delta, IEnumerable <double> s, IDistribution dist)
{
double N = (double)s.Count();
Assert.GreaterThan(N, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
var histogram = new Histogram(s, NumberOfBuckets);
for (int i = 0; i < NumberOfBuckets; i++)
{
double p = dist.CumulativeDistribution(histogram[i].UpperBound) - dist.CumulativeDistribution(histogram[i].LowerBound);
double pe = histogram[i].Count / N;
Assert.LessThan(Math.Abs(p - pe), epsilon, dist.ToString());
}
}
/// <summary>
/// Vapnik Chervonenkis test.
/// </summary>
/// <param name="epsilon">The error we are willing to tolerate.</param>
/// <param name="delta">The error probability we are willing to tolerate.</param>
/// <param name="s">The samples to use for testing.</param>
/// <param name="dist">The distribution we are testing.</param>
public static void VapnikChervonenkisTest(double epsilon, double delta, IEnumerable <double> s, IDistribution dist)
{
// Using VC-dimension, we can bound the probability of making an error when estimating empirical probability
// distributions. We are using Theorem 2.41 in "All Of Nonparametric Statistics".
// http://books.google.com/books?id=MRFlzQfRg7UC&lpg=PP1&dq=all%20of%20nonparametric%20statistics&pg=PA22#v=onepage&q=%22shatter%20coe%EF%AC%83cients%20do%20not%22&f=false .</para>
// For intervals on the real line the VC-dimension is 2.
double n = s.Count();
Assert.Greater(n, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
var histogram = new Histogram(s, NumberOfBuckets);
for (var i = 0; i < NumberOfBuckets; i++)
{
var p = dist.CumulativeDistribution(histogram[i].UpperBound) - dist.CumulativeDistribution(histogram[i].LowerBound);
var pe = histogram[i].Count / n;
Assert.Less(Math.Abs(p - pe), epsilon, dist.ToString());
}
}
public static void TestIntegrateDistribution(
double x,
ISampler <double> sampler,
IDistribution referenceDistribution,
double error)
{
const int trials = 1000000;
var actual = IntegrateCdf(sampler, x, trials);
var expected = referenceDistribution.CumulativeDistribution(x);
Assert.AreEqual(expected, actual, error);
}
/// <summary>
/// Vapnik Chervonenkis test.
/// </summary>
/// <param name="epsilon">The error we are willing to tolerate.</param>
/// <param name="delta">The error probability we are willing to tolerate.</param>
/// <param name="s">The samples to use for testing.</param>
/// <param name="dist">The distribution we are testing.</param>
public static void VapnikChervonenkisTest(double epsilon, double delta, IEnumerable<double> s, IDistribution dist)
{
// Using VC-dimension, we can bound the probability of making an error when estimating empirical probability
// distributions. We are using Theorem 2.41 in "All Of Nonparametric Statistics".
// http://books.google.com/books?id=MRFlzQfRg7UC&lpg=PP1&dq=all%20of%20nonparametric%20statistics&pg=PA22#v=onepage&q=%22shatter%20coe%EF%AC%83cients%20do%20not%22&f=false .</para>
// For intervals on the real line the VC-dimension is 2.
double n = s.Count();
Assert.Greater(n, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
var histogram = new Histogram(s, NumberOfBuckets);
for (var i = 0; i < NumberOfBuckets; i++)
{
var p = dist.CumulativeDistribution(histogram[i].UpperBound) - dist.CumulativeDistribution(histogram[i].LowerBound);
var pe = histogram[i].Count / n;
Assert.Less(Math.Abs(p - pe), epsilon, dist.ToString());
}
}
/// <summary>
/// <para>Using VC-dimension, we can bound the probability of making an error when estimating empirical probability
/// distributions. We are using Theorem 2.41 in "All Of Nonparametric Statistics".
/// http://books.google.com/books?id=MRFlzQfRg7UC&lpg=PP1&dq=all%20of%20nonparametric%20statistics&pg=PA22#v=onepage&q=%22shatter%20coe%EF%AC%83cients%20do%20not%22&f=false .</para>
/// <para>Note that for intervals on the real line the VC-dimension is 2.</para>
/// </summary>
/// <param name="epsilon">The error we are willing to tolerate.</param>
/// <param name="delta">The error probability we are willing to tolerate.</param>
/// <param name="s">The samples to use for testing.</param>
/// <param name="dist">The distribution we are testing.</param>
public static void VapnikChervonenkisTest(double epsilon, double delta, IEnumerable<double> s, IDistribution dist)
{
double N = (double) s.Count();
Assert.GreaterThan(N, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
var histogram = new Histogram(s, NumberOfBuckets);
for (int i = 0; i < NumberOfBuckets; i++)
{
double p = dist.CumulativeDistribution(histogram[i].UpperBound) - dist.CumulativeDistribution(histogram[i].LowerBound);
double pe = histogram[i].Count / N;
Assert.LessThan(Math.Abs(p - pe), epsilon, dist.ToString());
}
}