public void TestKernel()
{
var methodName = MethodBase.GetCurrentMethod().Name;
TestUtils.ShowStarting(methodName);
var x = new [] { .2, .3 };
var y = new [] { .1, .4 };
var z = new [] { .3, .4 };
var kernelEstimator = new KernelDensityEstimator();
//kernelEstimator.AddObservation(x);
//kernelEstimator.AddObservation(y);
Console.WriteLine(kernelEstimator.HasObservation());
var estimation = kernelEstimator.GetDensityEstimation(z, .1, 0);
if (estimation == null)
{
return;
}
foreach (var e in estimation)
{
Console.WriteLine(e);
}
}
public void SampleCompare()
{
var kde = new KernelDensityEstimator(0.02f);
//DensityEstimationTests.RunSampleTest(kde, x => x);
DensityEstimationTests.RunSampleTest(kde, x => ColumnVector1D.Create(x.Value));
}
public void ProbabilityOf_LinearSample()
{
var kde = new KernelDensityEstimator();
var data = Enumerable.Range(1, 100).Select(n => (n).OutOf(100)).AsQueryable();
var sample = new ContinuousSample<Fraction>(data, kde);
foreach(var x in Enumerable.Range(1, 100))
{
Console.WriteLine("{0}\t{1}", x, sample.DensityOf(x.OutOf(100)).Value);
}
}
public void KDETestGaussianKernelBandwidth2()
{
var kde = new KernelDensityEstimator(_testData);
kde.Bandwidth = 2.0d;
var estimate = kde.EstimateDensity(-3.5);
AssertHelpers.AlmostEqualRelative(0.046875864115900, estimate, 10);
estimate = kde.EstimateDensity(0);
AssertHelpers.AlmostEqualRelative(0.186580447512078, estimate, 10);
estimate = kde.EstimateDensity(2);
AssertHelpers.AlmostEqualRelative(0.123339405007761, estimate, 10);
}
public void KDETestGaussianKernelBandwidth0p5()
{
var kde = new KernelDensityEstimator(_testData);
kde.Bandwidth = 0.5d;
var estimate = kde.EstimateDensity(-3.5);
AssertHelpers.AlmostEqualRelative(5.311490430807364e-007, estimate, 10);
estimate = kde.EstimateDensity(0);
AssertHelpers.AlmostEqualRelative(0.369994803886827, estimate, 10);
estimate = kde.EstimateDensity(2);
AssertHelpers.AlmostEqualRelative(0.032447347007482, estimate, 10);
}
public void ProbabilityOf_RandomSample()
{
var kde = new KernelDensityEstimator();
var data = Enumerable.Range(1, 50).Select(n => Fraction.Random(100, 1)).AsQueryable();
var sample = new ContinuousSample<Fraction>(data, kde);
foreach (var x in Enumerable.Range(1, 100))
{
try
{
Console.WriteLine("{0}\t{1}", x, sample.DensityOf(x.OutOf(100)).Value);
}
catch (DivideByZeroException)
{
Console.WriteLine("Divide by zero error: {0}", x);
}
}
}
public void KDETestGaussianKernelBandwidth1()
{
var kde = new KernelDensityEstimator(_testData);
Assert.AreEqual(KDEKernelType.Gaussian, kde.KernelType);
Assert.AreEqual(1.0d, kde.Bandwidth);
AssertHelpers.AlmostEqualRelative(0.398942280401433, kde.Kernel(0), 10); //Density of standard normal distribution at 0
var estimate = kde.EstimateDensity(-3.5);
AssertHelpers.AlmostEqualRelative(0.004115405028907, estimate, 10);
estimate = kde.EstimateDensity(0);
AssertHelpers.AlmostEqualRelative(0.310485907659139, estimate, 10);
estimate = kde.EstimateDensity(2);
AssertHelpers.AlmostEqualRelative(0.099698581377801, estimate, 10);
}
public void KDETestTriangularKernelBandwidth1()
{
var kde = new KernelDensityEstimator(_testData);
kde.KernelType = KDEKernelType.Triangular;
Assert.AreEqual(KDEKernelType.Triangular, kde.KernelType);
Assert.AreEqual(1.0d, kde.Bandwidth);
Assert.AreEqual(1.0d, kde.Kernel(0)); //Density of standard normal distribution at 0
var estimate = kde.EstimateDensity(-3.5);
AssertHelpers.AlmostEqualRelative(0, estimate, 10);
estimate = kde.EstimateDensity(0);
AssertHelpers.AlmostEqualRelative(0.347688490533868, estimate, 10);
estimate = kde.EstimateDensity(2);
AssertHelpers.AlmostEqualRelative(0.004216757636608, estimate, 10);
}
public void KDETestEpanechnikovKernelBandwidth1()
{
var kde = new KernelDensityEstimator(_testData);
kde.KernelType = KDEKernelType.Epanechnikov;
Assert.AreEqual(KDEKernelType.Epanechnikov, kde.KernelType);
Assert.AreEqual(1.0d, kde.Bandwidth);
Assert.AreEqual(0.75d, kde.Kernel(0));
var estimate = kde.EstimateDensity(-3.5);
AssertHelpers.AlmostEqualRelative(0, estimate, 10);
estimate = kde.EstimateDensity(0);
AssertHelpers.AlmostEqualRelative(0.353803214812608, estimate, 10);
estimate = kde.EstimateDensity(2);
AssertHelpers.AlmostEqualRelative(0.006248168996717, estimate, 10);
}
public void KDETestUniformKernelBandwidth1()
{
var kde = new KernelDensityEstimator(_testData);
kde.KernelType = KDEKernelType.Uniform;
Assert.AreEqual(KDEKernelType.Uniform, kde.KernelType);
Assert.AreEqual(1.0d, kde.Bandwidth);
Assert.AreEqual(0.5d, kde.Kernel(0));
var estimate = kde.EstimateDensity(-3.5);
AssertHelpers.AlmostEqualRelative(0, estimate, 10);
estimate = kde.EstimateDensity(0);
AssertHelpers.AlmostEqualRelative(0.35, estimate, 10);
estimate = kde.EstimateDensity(2);
AssertHelpers.AlmostEqualRelative(0.1, estimate, 10);
}
public void KDETestCustomKernelBandwidth1()
{
var kde = new KernelDensityEstimator(_testData);
kde.Bandwidth = 1.0d;
kde.Kernel = x => 0.5d * Math.Exp(-Math.Abs(x)); //Picard-Kernel
Assert.AreEqual(KDEKernelType.Custom, kde.KernelType);
Assert.AreEqual(1.0d, kde.Bandwidth);
Assert.AreEqual(0.5d, kde.Kernel(0));
var estimate = kde.EstimateDensity(-3.5);
AssertHelpers.AlmostEqualRelative(0.018396636706009, estimate, 10);
estimate = kde.EstimateDensity(0);
AssertHelpers.AlmostEqualRelative(0.272675897096678, estimate, 10);
estimate = kde.EstimateDensity(2);
AssertHelpers.AlmostEqualRelative(0.092580285110347, estimate, 10);
}
protected void CalculateDensity(Series series, List <double> row, double bandwidth = double.NaN)
{
string densitySeriesName = "Density " + series.Name;
double stepWidth = series.Points[1].XValue - series.Points[0].XValue;
var rowArray = row.ToArray();
if (chart.Series.Any(x => x.Name == densitySeriesName))
{
var ds = chart.Series.Single(x => x.Name == densitySeriesName);
chart.Series.Remove(ds);
}
if (double.IsNaN(bandwidth))
{
bandwidth = KernelDensityEstimator.EstimateBandwidth(rowArray);
decimal bwDecimal = (decimal)bandwidth;
if (bwDecimal < bandwidthMin)
{
bwDecimal = bandwidthMin;
bandwidth = decimal.ToDouble(bwDecimal);
}
suppressUpdate = true;
bandwidthNumericUpDown.Value = bwDecimal;
}
var density = KernelDensityEstimator.Density(rowArray, rowArray.Length, stepWidth, bandwidth);
Series newSeries = new Series(densitySeriesName);
newSeries.Color = series.Color;
newSeries.ChartType = SeriesChartType.FastLine;
newSeries.BorderWidth = 2;
foreach (var d in density)
{
newSeries.Points.Add(new DataPoint(d.Item1, d.Item2));
}
// densities should be plotted on the second axis (different scale)
newSeries.YAxisType = AxisType.Secondary;
chart.Series.Add(newSeries);
}
public void Evaluate_NormalSample()
{
var sample = Enumerable
.Range(1, 10)
.Select(n => new { p = Functions.NormalDistribution(n, 2.87f, 5), n = n })
.SelectMany(x => Enumerable.Range(1, (int)(x.p * 100)).Select(n => (x.n).OutOf(10)))
.ToList()
.AsQueryable();
var hist = new Histogram(0.02f);
var kde = new KernelDensityEstimator(0.02f);
var histF = hist.Evaluate(sample);
var kdeF = kde.Evaluate(sample);
var stdDevMu = Functions.MeanStdDev(sample);
Console.WriteLine("Mean\t{0}", stdDevMu.Item1);
Console.WriteLine("StdDev\t{0}", stdDevMu.Item2);
var hRes = Enumerable.Range(1, 10).Select(n => new { n = n, p = histF(n.OutOf(10)) });
var kRes = Enumerable.Range(1, 10).Select(n => kdeF(n.OutOf(10))).Normalise().ToList();
int i = 0;
foreach (var x in hRes)
{
var kr = kRes[i++];
Console.WriteLine("{0}\t{1}\t{2}", x.n, x.p.Value, kr.Value);
Assert.That(Math.Round(x.p.Value, 4), Is.EqualTo(Math.Round(kr.Value, 4)));
}
}
