/// <summary>
/// Performs a linear logistic regression analysis.
/// </summary>
/// <param name="outputIndex">The index of the column to predict.</param>
/// <returns></returns>
/// <remarks>Logistic linear regression is suited to situations where multiple input variables, either continuous or binary indicators, are used to predict
/// the value of a binary output variable. Like a linear regression, a logistic linear regression tries to find a model that predicts the output variable using
/// a linear combination of input variables. Unlike a simple linear regression, the model does not assume that this linear
/// function predicts the output directly; instead it assumes that this function value is then fed into a logit link function, which
/// maps the real numbers into the interval (0, 1), and interprets the value of this link function as the probability of obtaining success value
/// for the output variable.</remarks>
/// <exception cref="InvalidOperationException">The column to be predicted contains values other than 0 and 1.</exception>
/// <exception cref="InsufficientDataException">There are not more rows in the sample than columns.</exception>
public FitResult LogisticLinearRegression(int outputIndex)
{
if ((outputIndex < 0) || (outputIndex >= this.Dimension))
{
throw new ArgumentOutOfRangeException("outputIndex");
}
if (this.Count <= this.Dimension)
{
throw new InsufficientDataException();
}
// Define the log likelihood as a function of the parameter set
Func <IList <double>, double> logLikelihood = (IList <double> a) => {
double L = 0.0;
for (int k = 0; k < this.Count; k++)
{
double z = 0.0;
for (int i = 0; i < this.storage.Length; i++)
{
if (i == outputIndex)
{
z += a[i];
}
else
{
z += a[i] * this.storage[i][k];
}
}
double ez = Math.Exp(z);
double y = this.storage[outputIndex][k];
if (y == 0.0)
{
L -= Math.Log(1.0 + ez);
}
else if (y == 1.0)
{
L -= Math.Log(1.0 + 1.0 / ez);
}
else
{
throw new InvalidOperationException();
}
}
return(L);
};
double[] start = new double[this.Dimension];
//for (int i = 0; i < start.Length; i++) {
// if (i != outputIndex) start[i] = this.TwoColumns(i, outputIndex).Covariance / this.Column(i).Variance / this.Column(outputIndex).Variance;
//}
MultiExtremum maximum = MultiFunctionMath.FindLocalMaximum(logLikelihood, start);
FitResult result = new FitResult(maximum.Location, maximum.HessianMatrix.CholeskyDecomposition().Inverse(), null);
return(result);
}
public void EasomLocal()
{
Func <IList <double>, double> function = (IList <double> x) => Math.Cos(x[0]) * Math.Cos(x[1]) * Math.Exp(-(MoreMath.Sqr(x[0] - Math.PI) + MoreMath.Sqr(x[1] - Math.PI)));
// We can't start too far from minimum, since cosines introduce many local minima.
ColumnVector start = new ColumnVector(1.5, 2.0);
MultiExtremum maximum = MultiFunctionMath.FindLocalMaximum(function, start);
Console.WriteLine(maximum.Value);
Assert.IsTrue(TestUtilities.IsNearlyEqual(maximum.Value, 1.0, new EvaluationSettings()
{
AbsolutePrecision = 2.0 * maximum.Precision
}));
Assert.IsTrue(TestUtilities.IsNearlyEqual(maximum.Location, new ColumnVector(Math.PI, Math.PI), new EvaluationSettings {
AbsolutePrecision = 2.0 * Math.Sqrt(maximum.Precision)
}));
}
internal static DistributionFitResult <ContinuousDistribution> MaximumLikelihoodFit(IReadOnlyList <double> sample, Func <IReadOnlyList <double>, ContinuousDistribution> factory, IReadOnlyList <double> start, IReadOnlyList <string> names)
{
Debug.Assert(sample != null);
Debug.Assert(factory != null);
Debug.Assert(start != null);
Debug.Assert(names != null);
Debug.Assert(start.Count == names.Count);
// Define a log likelihood function
Func <IReadOnlyList <double>, double> logL = (IReadOnlyList <double> a) => {
ContinuousDistribution d = factory(a);
double lnP = 0.0;
foreach (double value in sample)
{
double P = d.ProbabilityDensity(value);
if (P == 0.0)
{
throw new InvalidOperationException();
}
lnP += Math.Log(P);
}
return(lnP);
};
// Maximize it
MultiExtremum maximum = MultiFunctionMath.FindLocalMaximum(logL, start);
ColumnVector b = maximum.Location;
SymmetricMatrix C = maximum.HessianMatrix;
CholeskyDecomposition CD = C.CholeskyDecomposition();
if (CD == null)
{
throw new DivideByZeroException();
}
C = CD.Inverse();
ContinuousDistribution distribution = factory(maximum.Location);
TestResult test = sample.KolmogorovSmirnovTest(distribution);
return(new ContinuousDistributionFitResult(names, b, C, distribution, test));
}
internal MultiLinearLogisticRegressionResult(IReadOnlyList <bool> yColumn, IReadOnlyList <IReadOnlyList <double> > xColumns, IReadOnlyList <string> xNames)
{
Debug.Assert(yColumn != null);
Debug.Assert(xColumns != null);
Debug.Assert(xNames != null);
Debug.Assert(xColumns.Count == xNames.Count);
int n = yColumn.Count;
int m = xColumns.Count;
if (n <= m)
{
throw new InsufficientDataException();
}
interceptIndex = -1;
for (int c = 0; c < m; c++)
{
IReadOnlyList <double> xColumn = xColumns[c];
if (xColumn == null)
{
Debug.Assert(interceptIndex < 0);
Debug.Assert(xNames[c] == "Intercept");
interceptIndex = c;
}
else
{
if (xColumn.Count != n)
{
throw new DimensionMismatchException();
}
}
}
Debug.Assert(interceptIndex >= 0);
// Define the log likelihood as a function of the parameter set
Func <IReadOnlyList <double>, double> logLikelihood = (IReadOnlyList <double> a) => {
Debug.Assert(a != null);
Debug.Assert(a.Count == m);
double L = 0.0;
for (int k = 0; k < n; k++)
{
double t = 0.0;
for (int i = 0; i < m; i++)
{
if (i == interceptIndex)
{
t += a[i];
}
else
{
t += a[i] * xColumns[i][k];
}
}
double ez = Math.Exp(t);
if (yColumn[k])
{
L -= MoreMath.LogOnePlus(1.0 / ez);
}
else
{
L -= MoreMath.LogOnePlus(ez);
}
}
return(L);
};
// We need a better starting value.
double[] start = new double[m];
//double[] start = new double[] { -1.5, +2.5, +0.5 };
// Search out the likelihood-maximizing parameter set.
MultiExtremum maximum = MultiFunctionMath.FindLocalMaximum(logLikelihood, start);
b = maximum.Location;
CholeskyDecomposition CD = maximum.HessianMatrix.CholeskyDecomposition();
if (CD == null)
{
throw new DivideByZeroException();
}
C = CD.Inverse();
names = xNames;
}