public void MultivariateLinearLogisticRegressionSimple()
{
// define model y = a + b0 * x0 + b1 * x1 + noise
double a = 1.0;
double b0 = -1.0 / 2.0;
double b1 = 1.0 / 3.0;
ContinuousDistribution x0distribution = new LaplaceDistribution();
ContinuousDistribution x1distribution = new NormalDistribution();
// draw a sample from the model
Random rng = new Random(1);
MultivariateSample old = new MultivariateSample("y", "x0", "x1");
FrameTable table = new FrameTable();
table.AddColumn <double>("x0");
table.AddColumn <double>("x1");
table.AddColumn <bool>("y");
for (int i = 0; i < 100; i++)
{
double x0 = x0distribution.GetRandomValue(rng);
double x1 = x1distribution.GetRandomValue(rng);
double t = a + b0 * x0 + b1 * x1;
double p = 1.0 / (1.0 + Math.Exp(-t));
bool y = (rng.NextDouble() < p);
old.Add(y ? 1.0 : 0.0, x0, x1);
table.AddRow(x0, x1, y);
}
// do a linear regression fit on the model
MultiLinearLogisticRegressionResult oldResult = old.LogisticLinearRegression(0);
MultiLinearLogisticRegressionResult newResult = table["y"].As <bool>().MultiLinearLogisticRegression(
table["x0"].As <double>(), table["x1"].As <double>()
);
// the result should have the appropriate dimension
Assert.IsTrue(newResult.Parameters.Count == 3);
// The parameters should match the model
Assert.IsTrue(newResult.CoefficientOf(0).ConfidenceInterval(0.99).ClosedContains(b0));
Assert.IsTrue(newResult.CoefficientOf("x1").ConfidenceInterval(0.99).ClosedContains(b1));
Assert.IsTrue(newResult.Intercept.ConfidenceInterval(0.99).ClosedContains(a));
// Our predictions should be better than chance.
int correct = 0;
for (int i = 0; i < table.Rows.Count; i++)
{
FrameRow row = table.Rows[i];
double x0 = (double)row["x0"];
double x1 = (double)row["x1"];
double p = newResult.Predict(x0, x1).Value;
bool y = (bool)row["y"];
if ((y && p > 0.5) || (!y & p < 0.5))
{
correct++;
}
}
Assert.IsTrue(correct > 0.5 * table.Rows.Count);
}
public void MultivariateLinearLogisticRegressionVariances()
{
// define model y = a + b0 * x0 + b1 * x1 + noise
double a = -3.0;
double b0 = 2.0;
double b1 = 1.0;
ContinuousDistribution x0distribution = new ExponentialDistribution();
ContinuousDistribution x1distribution = new LognormalDistribution();
FrameTable data = new FrameTable();
data.AddColumns <double>("a", "da", "b0", "db0", "b1", "db1", "p", "dp");
// draw a sample from the model
Random rng = new Random(2);
for (int j = 0; j < 32; j++)
{
List <double> x0s = new List <double>();
List <double> x1s = new List <double>();
List <bool> ys = new List <bool>();
FrameTable table = new FrameTable();
table.AddColumn <double>("x0");
table.AddColumn <double>("x1");
table.AddColumn <bool>("y");
for (int i = 0; i < 32; i++)
{
double x0 = x0distribution.GetRandomValue(rng);
double x1 = x1distribution.GetRandomValue(rng);
double t = a + b0 * x0 + b1 * x1;
double p = 1.0 / (1.0 + Math.Exp(-t));
bool y = (rng.NextDouble() < p);
x0s.Add(x0);
x1s.Add(x1);
ys.Add(y);
}
// do a linear regression fit on the model
MultiLinearLogisticRegressionResult result = ys.MultiLinearLogisticRegression(
new Dictionary <string, IReadOnlyList <double> > {
{ "x0", x0s }, { "x1", x1s }
}
);
UncertainValue pp = result.Predict(0.0, 1.0);
data.AddRow(
result.Intercept.Value, result.Intercept.Uncertainty,
result.CoefficientOf("x0").Value, result.CoefficientOf("x0").Uncertainty,
result.CoefficientOf("x1").Value, result.CoefficientOf("x1").Uncertainty,
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["b0"].As <double>().PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["db0"].As <double>().Mean()));
Assert.IsTrue(data["b1"].As <double>().PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["db1"].As <double>().Mean()));
Assert.IsTrue(data["p"].As <double>().PopulationStandardDeviation().ConfidenceInterval(0.99).ClosedContains(data["dp"].As <double>().Mean()));
}
public static void AnalyzingData()
{
FrameTable table;
Uri url = new Uri("https://raw.githubusercontent.com/dcwuser/metanumerics/master/Examples/Data/example.csv");
WebRequest request = WebRequest.Create(url);
using (WebResponse response = request.GetResponse()) {
using (StreamReader reader = new StreamReader(response.GetResponseStream())) {
table = FrameTable.FromCsv(reader);
}
}
FrameView view = table.WhereNotNull();
// Get the column with (zero-based) index 4.
FrameColumn column4 = view.Columns[4];
// Get the column named "Height".
FrameColumn heightsColumn = view.Columns["Height"];
// Even easier way to get the column named "Height".
FrameColumn alsoHeightsColumn = view["Height"];
IReadOnlyList <double> heights = view["Height"].As <double>();
SummaryStatistics summary = new SummaryStatistics(view["Height"].As <double>());
Console.WriteLine($"Count = {summary.Count}");
Console.WriteLine($"Mean = {summary.Mean}");
Console.WriteLine($"Standard Deviation = {summary.StandardDeviation}");
Console.WriteLine($"Skewness = {summary.Skewness}");
Console.WriteLine($"Estimated population mean = {summary.PopulationMean}");
Console.WriteLine($"Estimated population standard deviation = {summary.PopulationStandardDeviation}");
IReadOnlyList <double> maleHeights =
view.Where <string>("Sex", s => s == "M").Columns["Height"].As <double>();
IReadOnlyList <double> femaleHeights =
view.Where <string>("Sex", s => s == "F").Columns["Height"].As <double>();
TestResult test = Univariate.StudentTTest(maleHeights, femaleHeights);
Console.WriteLine($"{test.Statistic.Name} = {test.Statistic.Value}");
Console.WriteLine($"P = {test.Probability}");
TestResult maleHeightNormality = maleHeights.ShapiroFranciaTest();
TestResult totalHeightNormality = view["Height"].As <double>().ShapiroFranciaTest();
TestResult heightCompatibility = Univariate.KolmogorovSmirnovTest(maleHeights, femaleHeights);
LinearRegressionResult fit =
view["Weight"].As <double>().LinearRegression(view["Height"].As <double>());
Console.WriteLine($"Model weight = ({fit.Slope}) * height + ({fit.Intercept}).");
Console.WriteLine($"Model explains {fit.RSquared * 100.0}% of variation.");
ContingencyTable <string, bool> contingency =
Bivariate.Crosstabs(view["Sex"].As <string>(), view["Result"].As <bool>());
Console.WriteLine($"Male incidence: {contingency.ProbabilityOfColumnConditionalOnRow(true, "M")}");
Console.WriteLine($"Female incidence: {contingency.ProbabilityOfColumnConditionalOnRow(true, "F")}");
Console.WriteLine($"Log odds ratio = {contingency.Binary.LogOddsRatio}");
view.AddComputedColumn("Bmi", r => ((double)r["Weight"]) / MoreMath.Sqr((double)r["Height"] / 100.0));
view.AddComputedColumn("Age", r => (DateTime.Now - (DateTime)r["Birthdate"]).TotalDays / 365.24);
MultiLinearLogisticRegressionResult result =
view["Result"].As <bool>().MultiLinearLogisticRegression(
view["Bmi"].As <double>(),
view["Sex"].As <string, double>(s => s == "M" ? 1.0 : 0.0)
);
foreach (Parameter parameter in result.Parameters)
{
Console.WriteLine($"{parameter.Name} = {parameter.Estimate}");
}
TestResult spearman = Bivariate.SpearmanRhoTest(view["Age"].As <double>(), view["Result"].As <double>());
Console.WriteLine($"{spearman.Statistic.Name} = {spearman.Statistic.Value} P = {spearman.Probability}");
}
