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Distributions: extend sample distribution test to all continuous and most discrete distributions

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Christoph Ruegg 13 years ago
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9e064e827a
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44b0b12db3
2 changed files with 73 additions and 119 deletions
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  1. 176
      src/UnitTests/DistributionTests/CommonDistributionTests.cs
  2. 16
      src/UnitTests/DistributionTests/Multivariate/NormalGammaTests.cs

176
src/UnitTests/DistributionTests/CommonDistributionTests.cs
View File

@ -3,7 +3,9 @@
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
// http://mathnetnumerics.codeplex.com
// Copyright (c) 2009-2010 Math.NET
//
// Copyright (c) 2009-2013 Math.NET
//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without
@ -12,8 +14,10 @@
// copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following
// conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
@ -34,102 +38,58 @@ using NUnit.Framework;
namespace MathNet.Numerics.UnitTests.DistributionTests
{
using Random = System.Random;
/// <summary>
/// This class will perform various tests on discrete and continuous univariate distributions. The multivariate distributions
/// will implement these respective tests in their local unit test classes as they do not adhere to the same interfaces.
/// This class will perform various tests on discrete and continuous univariate distributions.
/// The multivariate distributions will implement these respective tests in their local unit
/// test classes as they do not adhere to the same interfaces.
/// </summary>
[TestFixture, Category("Distributions")]
public class CommonDistributionTests
{
/// <summary>
/// Gets or sets the number of samples we want.
/// </summary>
public static int NumberOfTestSamples
{
get;
set;
}
/// <summary>
/// Gets or sets the number of buckets in the histogram for the sampling function tests.
/// </summary>
public static int NumberOfBuckets
{
get;
set;
}
/// <summary>
/// Gets or sets the error we want to tolerate for sampling functions.
/// </summary>
public static double Error
{
get;
set;
}
/// <summary>
/// Gets or sets the error probability we want to tolerate for sampling functions.
/// </summary>
public static double ErrorProbability
{
get;
set;
}
/// <summary>
/// The list of discrete distributions which we test.
/// </summary>
private List<IDiscreteDistribution> _discreteDistributions;
/// <summary>
/// The list of continuous distributions which we test.
/// </summary>
private List<IContinuousDistribution> _continuousDistributions;
/// <summary>
/// Initializes static members of the CommonDistributionTests class.
/// </summary>
static CommonDistributionTests()
{
NumberOfTestSamples = 3500000;
NumberOfBuckets = 100;
Error = 0.01;
ErrorProbability = 0.001;
}
/// <summary>
/// Set-up test parameters.
/// </summary>
[SetUp]
public void SetupDistributions()
{
_discreteDistributions = new List<IDiscreteDistribution>
{
new Bernoulli(0.6),
new Binomial(0.7, 10),
new Categorical(new[] { 0.7, 0.3 }),
new DiscreteUniform(1, 10)
};
public const int NumberOfTestSamples = 3500000;
public const int NumberOfHistogramBuckets = 100;
public const double ErrorTolerance = 0.01;
public const double ErrorProbability = 0.001;
_continuousDistributions = new List<IContinuousDistribution>
{
new Beta(1.0, 1.0),
new ContinuousUniform(0.0, 1.0),
new Gamma(1.0, 1.0),
new Normal(0.0, 1.0),
new Weibull(1.0, 1.0),
new LogNormal(1.0, 1.0),
new Triangular(0, 1, 0.7),
new StudentT(0.0, 1.0, 5.0)
};
}
readonly List<IDiscreteDistribution> _discreteDistributions =
new List<IDiscreteDistribution>
{
new Bernoulli(0.6),
new Binomial(0.7, 10),
new Categorical(new[] { 0.7, 0.3 }),
//new ConwayMaxwellPoisson(0.2, 0.4),
new DiscreteUniform(1, 10),
//new Geometric(0.1),
new Hypergeometric(20, 3, 5),
//new NegativeBinomial(4, 0.6),
//new Poisson(0.4),
new Zipf(0.6, 10),
};
readonly List<IContinuousDistribution> _continuousDistributions =
new List<IContinuousDistribution>
{
new Beta(1.0, 1.0),
new Cauchy(1.0, 1.0),
new Chi(3.0),
new ChiSquared(3.0),
new ContinuousUniform(0.0, 1.0),
new Erlang(3, 0.4),
new Exponential(0.4),
new FisherSnedecor(0.3, 0.4),
new Gamma(1.0, 1.0),
new InverseGamma(1.0, 1.0),
new Laplace(1.0, 0.5),
new LogNormal(1.0, 1.0),
new Normal(0.0, 1.0),
new Pareto(1.0, 0.5),
new Rayleigh(0.8),
new Stable(0.5, 1.0, 0.5, 1.0),
new StudentT(0.0, 1.0, 5.0),
new Triangular(0, 1, 0.7),
new Weibull(1.0, 1.0),
};
/// <summary>
/// Validate that univariate distributions have random source.
/// </summary>
[Test]
public void ValidateThatUnivariateDistributionsHaveRandomSource()
{
@ -144,9 +104,6 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
}
}
/// <summary>
/// Can set random source.
/// </summary>
[Test]
public void CanSetRandomSource()
{
@ -183,30 +140,28 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
[Test]
public void SampleFollowsCorrectDistribution()
{
Random rnd = new SystemRandomSource(1);
foreach (var dd in _discreteDistributions)
{
dd.RandomSource = rnd;
dd.RandomSource = new SystemRandomSource(1, false);
var samples = new double[NumberOfTestSamples];
for (var i = 0; i < NumberOfTestSamples; i++)
{
samples[i] = dd.Sample();
}
VapnikChervonenkisTest(Error, ErrorProbability, samples, dd);
VapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, dd);
}
foreach (var cd in _continuousDistributions)
{
cd.RandomSource = rnd;
cd.RandomSource = new SystemRandomSource(1, false);
var samples = new double[NumberOfTestSamples];
for (var i = 0; i < NumberOfTestSamples; i++)
{
samples[i] = cd.Sample();
}
VapnikChervonenkisTest(Error, ErrorProbability, samples, cd);
VapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, cd);
}
}
@ -216,18 +171,18 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
[Test]
public void SamplesFollowsCorrectDistribution()
{
Random rnd = new SystemRandomSource(1);
foreach (var dd in _discreteDistributions)
{
dd.RandomSource = rnd;
VapnikChervonenkisTest(Error, ErrorProbability, dd.Samples().Select(x => (double)x).Take(NumberOfTestSamples), dd);
dd.RandomSource = new SystemRandomSource(1, false);
var samples = dd.Samples().Select(x => (double)x).Take(NumberOfTestSamples).ToArray();
VapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, dd);
}
foreach (var cd in _continuousDistributions)
{
cd.RandomSource = rnd;
VapnikChervonenkisTest(Error, ErrorProbability, cd.Samples().Take(NumberOfTestSamples), cd);
cd.RandomSource = new SystemRandomSource(1, false);
var samples = cd.Samples().Take(NumberOfTestSamples).ToArray();
VapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, cd);
}
}
@ -238,20 +193,19 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
/// <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, IUnivariateDistribution dist)
public static void VapnikChervonenkisTest(double epsilon, double delta, double[] s, IUnivariateDistribution 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));
Assert.Greater(s.Length, 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 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 / n;
var pe = histogram[i].Count / s.Length;
Assert.Less(Math.Abs(p - pe), epsilon, dist.ToString());
}
}

16
src/UnitTests/DistributionTests/Multivariate/NormalGammaTests.cs
View File

@ -343,21 +343,21 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
}
// Extract the mean and precisions.
var means = samples.Select(mp => mp.Mean);
var precs = samples.Select(mp => mp.Precision);
var means = samples.Select(mp => mp.Mean).ToArray();
var precs = samples.Select(mp => mp.Precision).ToArray();
var meanMarginal = cd.MeanMarginal();
var precMarginal = cd.PrecisionMarginal();
// Check the precision distribution.
CommonDistributionTests.VapnikChervonenkisTest(
CommonDistributionTests.Error,
CommonDistributionTests.ErrorTolerance,
CommonDistributionTests.ErrorProbability,
precs,
precMarginal);
// Check the mean distribution.
CommonDistributionTests.VapnikChervonenkisTest(
CommonDistributionTests.Error,
CommonDistributionTests.ErrorTolerance,
CommonDistributionTests.ErrorProbability,
means,
meanMarginal);
@ -375,21 +375,21 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
var samples = cd.Samples().Take(CommonDistributionTests.NumberOfTestSamples).ToArray();
// Extract the mean and precisions.
var means = samples.Select(mp => mp.Mean);
var precs = samples.Select(mp => mp.Precision);
var means = samples.Select(mp => mp.Mean).ToArray();
var precs = samples.Select(mp => mp.Precision).ToArray();
var meanMarginal = cd.MeanMarginal();
var precMarginal = cd.PrecisionMarginal();
// Check the precision distribution.
CommonDistributionTests.VapnikChervonenkisTest(
CommonDistributionTests.Error,
CommonDistributionTests.ErrorTolerance,
CommonDistributionTests.ErrorProbability,
precs,
precMarginal);
// Check the mean distribution.
CommonDistributionTests.VapnikChervonenkisTest(
CommonDistributionTests.Error,
CommonDistributionTests.ErrorTolerance,
CommonDistributionTests.ErrorProbability,
means,
meanMarginal);

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