/// <summary>
/// Predictive covariance at a given pair of points
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <returns></returns>
public double Covariance(Vector x, Vector y)
{
double kxy = FixedParameters.Prior.Covariance(x, y);
Vector kxB = FixedParameters.KernelOf_X_B(x);
Vector kyB = FixedParameters.KernelOf_X_B(y);
return(kxy - kxB.Inner(Beta * kyB));
}
/// <summary>
/// Mean at a given point
/// </summary>
/// <param name="X"></param>
/// <returns></returns>
public double Mean(Vector X)
{
if (IsUniform())
{
return(Gaussian.Uniform().GetMean());
}
else
{
Vector kxB = FixedParameters.KernelOf_X_B(X);
return(kxB.Inner(Alpha) + FixedParameters.Prior.Mean(X));
}
}
/// <summary>
/// Predictive Variance at a given point
/// </summary>
/// <param name="X">Input</param>
/// <returns>Predictive variance</returns>
public double Variance(Vector X)
{
if (IsUniform())
{
Gaussian temp = new Gaussian();
temp.SetToUniform();
return(temp.GetVariance());
}
else
{
Vector kxB = FixedParameters.KernelOf_X_B(X);
return(FixedParameters.Prior.Variance(X) - Beta.QuadraticForm(kxB));
}
}
/// <summary>
/// Predictive distribution at a given list of points
/// </summary>
/// <param name="XList">List of inputs</param>
/// <returns>Predictive distribution</returns>
public VectorGaussian Joint(IList <Vector> XList)
{
if (IsUniform())
{
return(VectorGaussian.Uniform(XList.Count));
}
else
{
PositiveDefiniteMatrix kXX = FixedParameters.Prior.Covariance(XList);
Matrix kXB = FixedParameters.KernelOf_X_B(XList);
kXX.SetToDifference(kXX, kXB * Beta * kXB.Transpose());
VectorGaussian result = new VectorGaussian(kXB * Alpha + FixedParameters.Prior.Mean(XList), kXX);
return(result);
}
}
/// <summary>
/// Predictive distribution at a given point
/// </summary>
/// <param name="X">Input</param>
/// <returns>Predictive distribution</returns>
public Gaussian Marginal(Vector X)
{
if (IsUniform())
{
return(Gaussian.Uniform());
}
else
{
double kxx = FixedParameters.Prior.Variance(X);
Vector kxb = FixedParameters.KernelOf_X_B(X);
Gaussian result = new Gaussian(
kxb.Inner(Alpha) + FixedParameters.Prior.Mean(X), kxx - Beta.QuadraticForm(kxb));
return(result);
}
}
/// <summary>
/// Predictive coariance at a given list of points
/// </summary>
/// <param name="XList">List of inputs</param>
/// <returns>Predictive covariance</returns>
public PositiveDefiniteMatrix Covariance(IList <Vector> XList)
{
if (IsUniform())
{
VectorGaussian temp = new VectorGaussian(XList.Count);
temp.SetToUniform();
return(temp.GetVariance());
}
else
{
PositiveDefiniteMatrix kXX = FixedParameters.Prior.Covariance(XList);
Matrix kXB = FixedParameters.KernelOf_X_B(XList);
kXX.SetToDifference(kXX, kXB * Beta * kXB.Transpose());
return(kXX);
}
}
