public void LinearLogisticRegressionSimple()
{
Polynomial m = Polynomial.FromCoefficients(-1.0, 2.0);
FrameTable table = new FrameTable();
table.AddColumn <double>("x");
table.AddColumn <string>("z");
Random rng = new Random(2);
ContinuousDistribution xDistribution = new CauchyDistribution(4.0, 2.0);
for (int i = 0; i < 24; i++)
{
double x = xDistribution.GetRandomValue(rng);
double y = m.Evaluate(x);
double p = 1.0 / (1.0 + Math.Exp(-y));
bool z = (rng.NextDouble() < p);
table.AddRow(x, z.ToString());
}
LinearLogisticRegressionResult fit = table["z"].As((string s) => Boolean.Parse(s)).LinearLogisticRegression(table["x"].As <double>());
Assert.IsTrue(fit.Intercept.ConfidenceInterval(0.99).ClosedContains(m.Coefficient(0)));
Assert.IsTrue(fit.Slope.ConfidenceInterval(0.99).ClosedContains(m.Coefficient(1)));
}
public void LinearLogisticRegressionVariances()
{
// define model y = a + b0 * x0 + b1 * x1 + noise
double a = -2.0;
double b = 1.0;
ContinuousDistribution xDistribution = new StudentDistribution(2.0);
FrameTable data = new FrameTable();
data.AddColumns <double>("a", "da", "b", "db", "abcov", "p", "dp");
// draw a sample from the model
Random rng = new Random(3);
for (int j = 0; j < 32; j++)
{
List <double> xs = new List <double>();
List <bool> ys = new List <bool>();
for (int i = 0; i < 32; i++)
{
double x = xDistribution.GetRandomValue(rng);
double t = a + b * x;
double p = 1.0 / (1.0 + Math.Exp(-t));
bool y = (rng.NextDouble() < p);
xs.Add(x);
ys.Add(y);
}
// do a linear regression fit on the model
LinearLogisticRegressionResult result = ys.LinearLogisticRegression(xs);
UncertainValue pp = result.Predict(1.0);
data.AddRow(
result.Intercept.Value, result.Intercept.Uncertainty,
result.Slope.Value, result.Slope.Uncertainty,
result.Parameters.CovarianceMatrix[0, 1],
pp.Value, pp.Uncertainty
);
}
// The estimated parameters should agree with the model that generated the data.
// The variances of the estimates should agree with the claimed variances
Assert.IsTrue(data["a"].As <double>().PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["da"].As <double>().Mean()));
Assert.IsTrue(data["b"].As <double>().PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["db"].As <double>().Mean()));
Assert.IsTrue(data["a"].As <double>().PopulationCovariance(data["b"].As <double>()).ConfidenceInterval(0.99).ClosedContains(data["abcov"].As <double>().Mean()));
Assert.IsTrue(data["p"].As <double>().PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["dp"].As <double>().Mean()));
}
public void LinearLogisticRegression()
{
// do a set of logistic regression fits
// make sure not only that the fit parameters are what they should be, but that their variances/covariances are as returned
Random rng = new Random(314159);
// define logistic parameters
double a0 = 1.0; double b0 = -1.0 / 2.0;
//double a0 = -0.5; double b0 = 2.0;
// keep track of sample of returned a and b fit parameters
BivariateSample ps = new BivariateSample();
// also keep track of returned covariance estimates
// since these vary slightly from fit to fit, we will average them
double caa = 0.0;
double cbb = 0.0;
double cab = 0.0;
// do 50 fits
for (int k = 0; k < 50; k++)
{
Console.WriteLine("k={0}", k);
// generate a synthetic data set
BivariateSample s = new BivariateSample();
for (int i = 0; i < 50; i++)
{
double x = 2.0 * rng.NextDouble() - 1.0;
double ez = Math.Exp(a0 + b0 * x);
double P = ez / (1.0 + ez);
if (rng.NextDouble() < P)
{
s.Add(x, 1.0);
}
else
{
s.Add(x, 0.0);
}
}
// do the regression
LinearLogisticRegressionResult r = s.LinearLogisticRegression();
// record best fit parameters
double a = r.Intercept.Value;
double b = r.Slope.Value;
ps.Add(a, b);
Console.WriteLine("{0}, {1}", a, b);
// record estimated covariances
caa += r.Parameters.CovarianceMatrix[0, 0];
cbb += r.Parameters.CovarianceMatrix[1, 1];
cab += r.Parameters.CovarianceMatrix[0, 1];
}
caa /= ps.Count;
cbb /= ps.Count;
cab /= ps.Count;
// check that mean parameter estimates are what they should be: the underlying population parameters
Assert.IsTrue(ps.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(a0));
Assert.IsTrue(ps.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(b0));
// check that parameter covarainces are what they should be: the reported covariance estimates
Assert.IsTrue(ps.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(caa));
Assert.IsTrue(ps.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(cbb));
Assert.IsTrue(ps.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(cab));
}
