/// <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 ContinuousVapnikChervonenkisTest(double epsilon, double delta, double[] s, IContinuousDistribution 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.
Assert.Greater(s.Length, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
var histogram = new Histogram(s, NumberOfHistogramBuckets);
for (var i = 0; i < NumberOfHistogramBuckets; i++)
{
var p = dist.CumulativeDistribution(histogram[i].UpperBound) - dist.CumulativeDistribution(histogram[i].LowerBound);
var pe = histogram[i].Count / (double)s.Length;
Assert.Less(Math.Abs(p - pe), epsilon, dist.ToString());
}
}
void setDistributionText()
{
myText.text = "" + currentDistribution.ToString();
}
public ReferenceDistribution(string key, IContinuousDistribution distribution)
{
Key = key;
Description = distribution.ToString();
Distribution = distribution;
}
/// <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 ContinuousVapnikChervonenkisTest(double epsilon, double delta, double[] s, IContinuousDistribution 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.
Assert.Greater(s.Length, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
var histogram = new Histogram(s, NumberOfHistogramBuckets);
for (var i = 0; i < NumberOfHistogramBuckets; i++)
{
var p = dist.CumulativeDistribution(histogram[i].UpperBound) - dist.CumulativeDistribution(histogram[i].LowerBound);
var pe = histogram[i].Count/(double)s.Length;
Assert.Less(Math.Abs(p - pe), epsilon, dist.ToString());
}
}
