public void Bug6162()
{
// When UncertianMeasurementSample.FitToPolynomial used Cholesky inversion of (A^T A), this inversion
// would fail when roundoff errors would made the matrix non-positive-definite. We have now changed
// to QR decomposition, which is more robust.
//real data
double[] X_axis = new double[] { 40270.65625, 40270.6569444444, 40270.6576388888, 40270.6583333332, 40270.6590277776,
40270.659722222, 40270.6604166669, 40270.6611111113, 40270.6618055557, 40270.6625000001 };
double[] Y_axis = new double[] { 246.824996948242, 246.850006103516, 245.875, 246.225006103516, 246.975006103516,
247.024993896484, 246.949996948242, 246.875, 247.5, 247.100006103516 };
UncertainMeasurementSample DataSet = new UncertainMeasurementSample();
for (int i = 0; i < 10; i++)
{
DataSet.Add(X_axis[i], Y_axis[i], 1);
}
UncertainMeasurementFitResult DataFit = DataSet.FitToPolynomial(3);
BivariateSample bs = new BivariateSample();
for (int i = 0; i < 10; i++)
{
bs.Add(X_axis[i], Y_axis[i]);
}
PolynomialRegressionResult bsFit = bs.PolynomialRegression(3);
foreach (Parameter p in bsFit.Parameters)
{
Console.WriteLine(p);
}
}
public void BivariatePolynomialRegressionSimple()
{
// Pick a simple polynomial
Polynomial p = Polynomial.FromCoefficients(3.0, -2.0, 1.0);
// Use it to generate a data set
Random rng = new Random(1);
ContinuousDistribution xDistribution = new CauchyDistribution(1.0, 2.0);
ContinuousDistribution errorDistribution = new NormalDistribution(0.0, 3.0);
List <double> xs = new List <double>(TestUtilities.CreateDataSample(rng, xDistribution, 10));
List <double> ys = new List <double>(xs.Select(x => p.Evaluate(x) + errorDistribution.GetRandomValue(rng)));
PolynomialRegressionResult fit = Bivariate.PolynomialRegression(ys, xs, p.Degree);
// Parameters should agree
Assert.IsTrue(fit.Parameters.Count == p.Degree + 1);
for (int k = 0; k <= p.Degree; k++)
{
Assert.IsTrue(fit.Coefficient(k).ConfidenceInterval(0.99).ClosedContains(p.Coefficient(k)));
}
// Residuals should agree
Assert.IsTrue(fit.Residuals.Count == xs.Count);
for (int i = 0; i < xs.Count; i++)
{
double z = ys[i] - fit.Predict(xs[i]).Value;
Assert.IsTrue(TestUtilities.IsNearlyEqual(z, fit.Residuals[i]));
}
// Intercept is same as coefficient of x^0
Assert.IsTrue(fit.Intercept == fit.Coefficient(0));
}
public void InternetSampleDownload()
{
FrameTable table = DownloadFrameTable(new Uri("https://raw.githubusercontent.com/Dataweekends/zero_to_deep_learning_udemy/master/data/weight-height.csv"));
FrameView view = table.WhereNotNull();
view.AddComputedColumn("Bmi", (FrameRow r) => {
double h = (double)r["Height"];
double w = (double)r["Weight"];
return(w / (h * h));
});
FrameView males = view.Where("Gender", (string s) => (s == "Male"));
FrameView females = view.Where("Gender", (string s) => (s == "Female"));
SummaryStatistics maleSummary = new SummaryStatistics(males["Height"].As <double>());
SummaryStatistics femaleSummary = new SummaryStatistics(females["Height"].As <double>());
TestResult allNormal = view["Height"].As <double>().ShapiroFranciaTest();
TestResult maleNormal = males["Height"].As <double>().ShapiroFranciaTest();
TestResult femaleNormal = females["Height"].As <double>().ShapiroFranciaTest();
TestResult tTest = Univariate.StudentTTest(males["Height"].As <double>(), females["Height"].As <double>());
TestResult mwTest = Univariate.MannWhitneyTest(males["Height"].As <double>(), females["Height"].As <double>());
LinearRegressionResult result0 = males["Weight"].As <double>().LinearRegression(males["Height"].As <double>());
PolynomialRegressionResult result1 = males["Height"].As <double>().PolynomialRegression(males["Weight"].As <double>(), 1);
PolynomialRegressionResult result2 = males["Height"].As <double>().PolynomialRegression(males["Weight"].As <double>(), 2);
PolynomialRegressionResult result3 = males["Height"].As <double>().PolynomialRegression(males["Weight"].As <double>(), 3);
//MultiLinearRegressionResult multi = view["Weight"].As<double>().MultiLinearRegression(view["Height"].As<double>(), view["Gender"].As<string>().Select(s => (s == "Male") ? 1.0 : 0.0).ToList());
}
public void BivariatePolynomialRegressionCovariance()
{
// do a set of polynomial regression fits
// make sure not only that the fit parameters are what they should be, but that their variances/covariances are as claimed
Random rng = new Random(271828);
// define logistic parameters
double[] a = new double[] { 0.0, -1.0, 2.0, -3.0 };
// keep track of sample of returned a and b fit parameters
MultivariateSample A = new MultivariateSample(a.Length);
// also keep track of returned covariance estimates
// since these vary slightly from fit to fit, we will average them
SymmetricMatrix C = new SymmetricMatrix(a.Length);
// also keep track of test statistics
Sample F = new Sample();
// do 100 fits
for (int k = 0; k < 100; k++)
{
// we should be able to draw x's from any distribution; noise should be drawn from a normal distribution
ContinuousDistribution xd = new CauchyDistribution();
ContinuousDistribution nd = new NormalDistribution(0.0, 4.0);
// generate a synthetic data set
BivariateSample s = new BivariateSample();
for (int j = 0; j < 20; j++)
{
double x = xd.GetRandomValue(rng);
double y = nd.GetRandomValue(rng);
for (int i = 0; i < a.Length; i++)
{
y += a[i] * MoreMath.Pow(x, i);
}
s.Add(x, y);
}
// do the regression
PolynomialRegressionResult r = s.PolynomialRegression(a.Length - 1);
ColumnVector ps = r.Parameters.ValuesVector;
// record best fit parameters
A.Add(ps);
// record estimated covariances
C += r.Parameters.CovarianceMatrix;
// record the fit statistic
F.Add(r.F.Statistic.Value);
}
C = (1.0 / A.Count) * C; // allow matrix division by real numbers
// check that mean parameter estimates are what they should be: the underlying population parameters
for (int i = 0; i < A.Dimension; i++)
{
Assert.IsTrue(A.Column(i).PopulationMean.ConfidenceInterval(0.95).ClosedContains(a[i]));
}
// check that parameter covarainces are what they should be: the reported covariance estimates
for (int i = 0; i < A.Dimension; i++)
{
for (int j = i; j < A.Dimension; j++)
{
Assert.IsTrue(A.TwoColumns(i, j).PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(C[i, j]));
}
}
// check that F is distributed as it should be
//Console.WriteLine(fs.KolmogorovSmirnovTest(new FisherDistribution(2, 48)).LeftProbability);
}