public void gh_937()
{
#region doc_learn_database
// Note: this example uses a System.Data.DataTable to represent input data,
// but note that this is not required. The data could have been represented
// as jagged double matrices (double[][]) directly.
// If you have to handle heterogeneus data in your application, such as user records
// in a database, this data is best represented within the framework using a .NET's
// DataTable object. In order to try to learn a classification or regression model
// using this datatable, first we will need to convert the table into a representation
// that the machine learning model can understand. Such representation is quite often,
// a matrix of doubles (double[][]).
var data = new DataTable("Customer Revenue Example");
data.Columns.Add("Day", "CustomerId", "Time (hour)", "Weather", "Revenue");
data.Rows.Add("D1", 0, 8, "Sunny", 101.2);
data.Rows.Add("D2", 1, 10, "Sunny", 24.1);
data.Rows.Add("D3", 2, 10, "Rain", 107);
data.Rows.Add("D4", 3, 16, "Rain", 223);
data.Rows.Add("D5", 4, 15, "Rain", 1);
data.Rows.Add("D6", 5, 20, "Rain", 42);
data.Rows.Add("D7", 6, 12, "Cloudy", 123);
data.Rows.Add("D8", 7, 12, "Sunny", 64);
// One way to perform this conversion is by using a Codification filter. The Codification
// filter can take care of converting variables that actually denote symbols (i.e. the
// weather in the example above) into representations that make more sense given the assumption
// of a real vector-based classifier.
// Create a codification codebook
var codebook = new Codification()
{
{ "Weather", CodificationVariable.Categorical },
{ "Time (hour)", CodificationVariable.Continuous },
{ "Revenue", CodificationVariable.Continuous },
};
// Learn from the data
codebook.Learn(data);
// Now, we will use the codebook to transform the DataTable into double[][] vectors. Due
// the way the conversion works, we can end up with more columns in your output vectors
// than the ones started with. If you would like more details about what those columns
// represent, you can pass then as 'out' parameters in the methods that follow below.
string[] inputNames; // (note: if you do not want to run this example yourself, you
string outputName; // can see below the new variable names that will be generated)
// Now, we can translate our training data into integer symbols using our codebook:
double[][] inputs = codebook.Apply(data, "Weather", "Time (hour)").ToJagged(out inputNames);
double[] outputs = codebook.Apply(data, "Revenue").ToVector(out outputName);
// (note: the Apply method transform a DataTable into another DataTable containing the codified
// variables. The ToJagged and ToVector methods are then used to transform those tables into
// double[][] matrices and double[] vectors, respectively.
// If we would like to learn a linear regression model for this data, there are two possible
// ways depending on which aspect of the linear regression we are interested the most. If we
// are interested in interpreting the linear regression, performing hypothesis tests with the
// coefficients and performing an actual _linear regression analysis_, then we can use the
// MultipleLinearRegressionAnalysis class for this. If however we are only interested in using
// the learned model directly to predict new values for the dataset, then we could be using the
// MultipleLinearRegression and OrdinaryLeastSquares classes directly instead.
// This example deals with the former case. For the later, please see the documentation page
// for the MultipleLinearRegression class.
// We can create a new multiple linear analysis for the variables
var mlra = new MultipleLinearRegressionAnalysis(intercept: true)
{
// We can also inform the names of the new variables that have been created by the
// codification filter. Those can help in the visualizing the analysis once it is
// data-bound to a visual control such a Windows.Forms.DataGridView or WPF DataGrid:
Inputs = inputNames, // will be { "Weather: Sunny", "Weather: Rain, "Weather: Cloudy", "Time (hours)" }
Output = outputName // will be "Revenue"
};
// To overcome linear dependency errors
mlra.OrdinaryLeastSquares.IsRobust = true;
// Compute the analysis and obtain the estimated regression
MultipleLinearRegression regression = mlra.Learn(inputs, outputs);
// And then predict the label using
double predicted = mlra.Transform(inputs[0]); // result will be ~72.3
// Because we opted for doing a MultipleLinearRegressionAnalysis instead of a simple
// linear regression, we will have further information about the regression available:
int inputCount = mlra.NumberOfInputs; // should be 4
int outputCount = mlra.NumberOfOutputs; // should be 1
double r2 = mlra.RSquared; // should be 0.12801838425195311
AnovaSourceCollection a = mlra.Table; // ANOVA table (bind to a visual control for quick inspection)
double[][] h = mlra.InformationMatrix; // should contain Fisher's information matrix for the problem
ZTest z = mlra.ZTest; // should be 0 (p=0.999, non-significant)
#endregion
Assert.AreEqual(72.279574468085144d, predicted, 1e-8);
Assert.AreEqual(4, inputCount, 1e-8);
Assert.AreEqual(1, outputCount, 1e-8);
Assert.AreEqual(0.12801838425195311, r2, 1e-8);
Assert.AreEqual(0.11010987669344097, a[0].Statistic, 1e-8);
string str = h.ToCSharp();
double[][] expectedH = new double[][]
{
new double[] { 0.442293243337911, -0.069833718526197, -0.228692384542512, -0.0141758263063635, 0.143767140269202 },
new double[] { -0.0698337185261971, 0.717811616891116, -0.112258662892007, -0.0655549422852099, 0.535719235472913 },
new double[] { -0.228692384542512, -0.112258662892007, 0.717434922237013, -0.0232803210243207, 0.376483874802496 },
new double[] { -0.0141758263063635, -0.0655549422852099, -0.0232803210243207, 0.0370082984668314, -0.103011089615894 },
new double[] { 0.143767140269202, 0.535719235472913, 0.376483874802496, -0.103011089615894, 1.05597025054461 }
};
Assert.IsTrue(expectedH.IsEqual(h, 1e-8));
Assert.AreEqual(0, z.Statistic, 1e-8);
Assert.AreEqual(1, z.PValue, 1e-8);
}
public void RegressTest7()
{
double[][] example2 =
{
new double[] { -0.47, 1.16, -1.25 },
new double[] { 0.55, 1.15, -0.78 },
new double[] { 1.38, 0.63, -0.84 },
new double[] { 0.99, 0.63, -0.81 },
new double[] { 1.72, 0.62, -1.59 },
new double[] { 1.05, 0.62, -1.05 },
new double[] { -0.51, 0.62, -0.98 },
new double[] { 1.83, 0.61, 0.86 },
new double[] { 1.16, 0.61, 0.15 },
new double[] { 0.59, 0.61, -0.28 },
new double[] { 0.40, 0.60, -0.30 },
new double[] { 0.48, 0.60, -0.41 },
new double[] { 1.28, 0.53, -0.31 },
new double[] { 0.36, 0.53, -0.41 },
new double[] { 0.93, 0.16, -0.19 },
new double[] { -0.61, 0.16, -0.32 },
new double[] { -0.58, 0.16, -0.01 },
new double[] { 0.53, 0.16, -0.13 },
new double[] { 1.48, 0.16, 1.12 },
new double[] { -0.34, 0.15, -0.10 },
new double[] { 0.81, 0.15, 0.14 },
new double[] { 0.85, 0.15, -0.02 },
new double[] { 0.69, 0.15, -0.16 },
new double[] { 0.39, 0.15, -0.33 },
new double[] { 0.70, 0.00, 2.00 },
new double[] { 0.25, 0.00, -0.01 },
new double[] { -0.96, 0.85, -0.19 },
new double[] { 1.04, 0.84, 0.35 },
new double[] { 0.30, 0.83, 0.05 },
new double[] { 0.28, 0.83, 0.84 },
new double[] { 0.18, 0.82, 0.06 },
new double[] { 0.49, 0.81, 0.41 },
new double[] { 0.40, 0.81, 0.50 },
new double[] { 0.41, 0.80, 0.00 },
new double[] { 0.06, 0.79, 0.39 },
new double[] { 0.55, 0.79, 0,55 },
};
double[][] inputs = example2.GetColumns(new[] { 1, 2 });
double[] outputs = example2.GetColumn(0);
bool thrown = false;
MultipleLinearRegressionAnalysis target;
try
{
target = new MultipleLinearRegressionAnalysis(inputs, outputs, new string[0], "Test", false);
}
catch (ArgumentException) { thrown = true; }
Assert.IsTrue(thrown);
target = new MultipleLinearRegressionAnalysis(inputs, outputs, new string[2], "Test", false);
target.Compute();
Assert.AreEqual(2, target.NumberOfInputs);
Assert.AreEqual(1, target.NumberOfOutputs);
Assert.AreEqual(target.Array, inputs);
Assert.AreEqual(target.Outputs, outputs);
Assert.AreEqual(-0.19371930561139417, target.RSquared, 1e-5);
Assert.AreEqual(-0.26606593019390279, target.RSquareAdjusted, 1e-5);
Assert.AreEqual(2, target.Table[0].DegreesOfFreedom);
Assert.AreEqual(33, target.Table[1].DegreesOfFreedom);
Assert.AreEqual(35, target.Table[2].DegreesOfFreedom);
Assert.AreEqual(-2.9165797494934651, target.Table[0].SumOfSquares, 1e-10);
Assert.AreEqual(17.972279749493463, target.Table[1].SumOfSquares, 1e-10);
Assert.AreEqual(15.055699999999998, target.Table[2].SumOfSquares, 1e-10);
Assert.IsFalse(Double.IsNaN(target.Table[0].SumOfSquares));
Assert.IsFalse(Double.IsNaN(target.Table[1].SumOfSquares));
Assert.IsFalse(Double.IsNaN(target.Table[2].SumOfSquares));
Assert.AreEqual(-1.4582898747467326, target.Table[0].MeanSquares, 1e-10);
Assert.AreEqual(0.54461453786343827, target.Table[1].MeanSquares, 1e-10);
Assert.IsFalse(Double.IsNaN(target.Table[0].MeanSquares));
Assert.IsFalse(Double.IsNaN(target.Table[1].MeanSquares));
Assert.AreEqual(-2.6776550630978524, target.Table[0].Statistic.Value, 1e-10);
Assert.AreEqual(1, target.Table[0].Significance.PValue, 1e-16);
Assert.IsFalse(Double.IsNaN(target.Table[0].Significance.PValue));
Assert.AreEqual(0.72195200211671728, target.Coefficients[0].Value, 1e-10);
Assert.AreEqual(0.15872233321508125, target.Coefficients[1].Value, 1e-10);
Assert.IsFalse(Double.IsNaN(target.Coefficients[0].Value));
Assert.IsFalse(Double.IsNaN(target.Coefficients[1].Value));
Assert.IsFalse(target.Coefficients[0].IsIntercept);
Assert.IsFalse(target.Coefficients[1].IsIntercept);
Assert.AreEqual(0.20506051379737225, target.Coefficients[0].StandardError, 1e-10);
Assert.AreEqual(0.18842330299464302, target.Coefficients[1].StandardError, 1e-10);
Assert.IsFalse(Double.IsNaN(target.Coefficients[0].StandardError));
Assert.IsFalse(Double.IsNaN(target.Coefficients[1].StandardError));
Assert.AreEqual(3.5206778172325479, target.Coefficients[0].TTest.Statistic, 1e-10);
Assert.AreEqual(0.84237103740609942, target.Coefficients[1].TTest.Statistic, 1e-10);
Assert.IsFalse(Double.IsNaN(target.Coefficients[0].TTest.Statistic));
Assert.IsFalse(Double.IsNaN(target.Coefficients[1].TTest.Statistic));
DoubleRange range;
range = target.Coefficients[0].TTest.GetConfidenceInterval(0.9);
Assert.AreEqual(0.37491572761667513, range.Min, 1e-10);
Assert.AreEqual(1.0689882766167593, range.Max, 1e-10);
range = target.Coefficients[1].TTest.GetConfidenceInterval(0.9);
Assert.AreEqual(-0.16015778606945111, range.Min, 1e-10);
Assert.AreEqual(0.47760245249961364, range.Max, 1e-10);
MultipleLinearRegression mlr = new MultipleLinearRegression(2, false);
mlr.Regress(inputs, outputs);
Assert.AreEqual(2, target.NumberOfInputs);
Assert.AreEqual(1, target.NumberOfOutputs);
double[] actual = target.Transform(inputs);
double[] expected = mlr.Transform(inputs);
Assert.IsTrue(Matrix.IsEqual(actual, expected, 1e-8));
double r2 = mlr.CoefficientOfDetermination(inputs, outputs, false);
double r2a = mlr.CoefficientOfDetermination(inputs, outputs, true);
Assert.AreEqual(r2, target.RSquared, 1e-6);
Assert.AreEqual(r2a, target.RSquareAdjusted, 1e-6);
}
public void RegressTest7()
{
double[][] example2 =
{
new double[] { -0.47, 1.16, -1.25 },
new double[] { 0.55, 1.15, -0.78 },
new double[] { 1.38, 0.63, -0.84 },
new double[] { 0.99, 0.63, -0.81 },
new double[] { 1.72, 0.62, -1.59 },
new double[] { 1.05, 0.62, -1.05 },
new double[] { -0.51, 0.62, -0.98 },
new double[] { 1.83, 0.61, 0.86 },
new double[] { 1.16, 0.61, 0.15 },
new double[] { 0.59, 0.61, -0.28 },
new double[] { 0.40, 0.60, -0.30 },
new double[] { 0.48, 0.60, -0.41 },
new double[] { 1.28, 0.53, -0.31 },
new double[] { 0.36, 0.53, -0.41 },
new double[] { 0.93, 0.16, -0.19 },
new double[] { -0.61, 0.16, -0.32 },
new double[] { -0.58, 0.16, -0.01 },
new double[] { 0.53, 0.16, -0.13 },
new double[] { 1.48, 0.16, 1.12 },
new double[] { -0.34, 0.15, -0.10 },
new double[] { 0.81, 0.15, 0.14 },
new double[] { 0.85, 0.15, -0.02 },
new double[] { 0.69, 0.15, -0.16 },
new double[] { 0.39, 0.15, -0.33 },
new double[] { 0.70, 0.00, 2.00 },
new double[] { 0.25, 0.00, -0.01 },
new double[] { -0.96, 0.85, -0.19 },
new double[] { 1.04, 0.84, 0.35 },
new double[] { 0.30, 0.83, 0.05 },
new double[] { 0.28, 0.83, 0.84 },
new double[] { 0.18, 0.82, 0.06 },
new double[] { 0.49, 0.81, 0.41 },
new double[] { 0.40, 0.81, 0.50 },
new double[] { 0.41, 0.80, 0.00 },
new double[] { 0.06, 0.79, 0.39 },
new double[] { 0.55, 0.79, 0, 55 },
};
double[][] inputs = example2.GetColumns(new[] { 1, 2 });
double[] outputs = example2.GetColumn(0);
bool thrown = false;
MultipleLinearRegressionAnalysis target;
try
{
target = new MultipleLinearRegressionAnalysis(inputs, outputs, new string[0], "Test", false);
}
catch (ArgumentException) { thrown = true; }
Assert.IsTrue(thrown);
target = new MultipleLinearRegressionAnalysis(inputs, outputs, new string[2], "Test", false);
target.Compute();
Assert.AreEqual(2, target.NumberOfInputs);
Assert.AreEqual(1, target.NumberOfOutputs);
Assert.AreEqual(target.Array, inputs);
Assert.AreEqual(target.Outputs, outputs);
Assert.AreEqual(-0.19371930561139417, target.RSquared, 1e-5);
Assert.AreEqual(-0.26606593019390279, target.RSquareAdjusted, 1e-5);
Assert.AreEqual(2, target.Table[0].DegreesOfFreedom);
Assert.AreEqual(33, target.Table[1].DegreesOfFreedom);
Assert.AreEqual(35, target.Table[2].DegreesOfFreedom);
Assert.AreEqual(-2.9165797494934651, target.Table[0].SumOfSquares, 1e-10);
Assert.AreEqual(17.972279749493463, target.Table[1].SumOfSquares, 1e-10);
Assert.AreEqual(15.055699999999998, target.Table[2].SumOfSquares, 1e-10);
Assert.IsFalse(Double.IsNaN(target.Table[0].SumOfSquares));
Assert.IsFalse(Double.IsNaN(target.Table[1].SumOfSquares));
Assert.IsFalse(Double.IsNaN(target.Table[2].SumOfSquares));
Assert.AreEqual(-1.4582898747467326, target.Table[0].MeanSquares, 1e-10);
Assert.AreEqual(0.54461453786343827, target.Table[1].MeanSquares, 1e-10);
Assert.IsFalse(Double.IsNaN(target.Table[0].MeanSquares));
Assert.IsFalse(Double.IsNaN(target.Table[1].MeanSquares));
Assert.AreEqual(-2.6776550630978524, target.Table[0].Statistic.Value, 1e-10);
Assert.AreEqual(1, target.Table[0].Significance.PValue, 1e-16);
Assert.IsFalse(Double.IsNaN(target.Table[0].Significance.PValue));
Assert.AreEqual(0.72195200211671728, target.Coefficients[0].Value, 1e-10);
Assert.AreEqual(0.15872233321508125, target.Coefficients[1].Value, 1e-10);
Assert.IsFalse(Double.IsNaN(target.Coefficients[0].Value));
Assert.IsFalse(Double.IsNaN(target.Coefficients[1].Value));
Assert.IsFalse(target.Coefficients[0].IsIntercept);
Assert.IsFalse(target.Coefficients[1].IsIntercept);
Assert.AreEqual(0.20506051379737225, target.Coefficients[0].StandardError, 1e-10);
Assert.AreEqual(0.18842330299464302, target.Coefficients[1].StandardError, 1e-10);
Assert.IsFalse(Double.IsNaN(target.Coefficients[0].StandardError));
Assert.IsFalse(Double.IsNaN(target.Coefficients[1].StandardError));
Assert.AreEqual(3.5206778172325479, target.Coefficients[0].TTest.Statistic, 1e-10);
Assert.AreEqual(0.84237103740609942, target.Coefficients[1].TTest.Statistic, 1e-10);
Assert.IsFalse(Double.IsNaN(target.Coefficients[0].TTest.Statistic));
Assert.IsFalse(Double.IsNaN(target.Coefficients[1].TTest.Statistic));
DoubleRange range;
range = target.Coefficients[0].TTest.GetConfidenceInterval(0.9);
Assert.AreEqual(0.37491572761667513, range.Min, 1e-10);
Assert.AreEqual(1.0689882766167593, range.Max, 1e-10);
range = target.Coefficients[1].TTest.GetConfidenceInterval(0.9);
Assert.AreEqual(-0.16015778606945111, range.Min, 1e-10);
Assert.AreEqual(0.47760245249961364, range.Max, 1e-10);
MultipleLinearRegression mlr = new MultipleLinearRegression(2, false);
mlr.Regress(inputs, outputs);
Assert.AreEqual(2, target.NumberOfInputs);
Assert.AreEqual(1, target.NumberOfOutputs);
double[] actual = target.Transform(inputs);
double[] expected = mlr.Transform(inputs);
Assert.IsTrue(Matrix.IsEqual(actual, expected, 1e-8));
double r2 = mlr.CoefficientOfDetermination(inputs, outputs, false);
double r2a = mlr.CoefficientOfDetermination(inputs, outputs, true);
Assert.AreEqual(r2, target.RSquared, 1e-6);
Assert.AreEqual(r2a, target.RSquareAdjusted, 1e-6);
}