GaussProcApproximation Class Reference

Derived approximation class for Gaussian Process implementation. More...

Inheritance diagram for GaussProcApproximation:

List of all members.

Public Member Functions
	GaussProcApproximation ()
	default constructor
	GaussProcApproximation (const ProblemDescDB &problem_db, const size_t &num_acv)
	standard constructor
	~GaussProcApproximation ()
	destructor
Protected Member Functions
int	min_coefficients () const
	build the derived class approximation type in numVars dimensions
int	num_constraints () const
	return the number of constraints to be enforced via anchorPoint
void	find_coefficients ()
	find the covariance parameters governing the Gaussian process response
const Real &	get_value (const RealVector &x)
	retrieve the function value for a given parameter set x
const Real &	get_variance (const RealVector &x)
	retrieve the variance of the predicted value for a given parameter set x
const RealBaseVector &	get_gradient (const RealVector &x)
	for a given parameter set x
Private Member Functions
void	GPmodel_build ()
	Function to compute hyperparameters governing the GP.
void	GPmodel_apply (const RealVector &new_x, bool variance_flag, bool gradients_flag)
	Function returns a response value using the GP surface.
void	normalize_training_data ()
	Normalizes the initial inputs upon which the GP surface is based.
void	get_trend ()
	linear, if order = 2, trend is quadratic.
void	get_beta_coefficients ()
	Gets the beta coefficients for the calculation of the mean of the GP.
int	get_cholesky_factor ()
	error checking
void	get_process_variance ()
	the correlation lengthscales
void	get_cov_matrix ()
	calculates the covariance matrix for a given set of input points
void	get_cov_vector ()
	set of inputs upon which the GP is based
void	optimize_theta_global ()
	parameters using NCSUDirect
void	optimize_theta_multipoint ()
	parameters using a gradient-based solver and multiple staring points
void	predict (bool variance_flag, bool gradients_flag)
	Calculates the predicted new response value for x in normalized space.
Real	calc_nll ()
	matrix)
void	calc_grad_nll ()
	to the correlation lengthscales, theta
void	get_grad_cov_vector ()
	to each componeent of x.
void	run_point_selection ()
	estimate the necessary parameters
void	initialize_point_selection ()
	initial subset of the training points
void	pointsel_get_errors (RealVector &)
	training points and find the errors
int	addpoint (int, IntVector &)
	Adds a point to the effective training set. Returns 1 on success.
int	pointsel_add_sel (RealVector &)
	them
Real	maxval (RealVector &)
	Return the maximum value of the elements in a vector.
void	pointsel_write_points ()
	Writes out the training set before and after point selection.
void	lhood_2d_grid_eval ()
	likelihood on a grid
void	writex (char[])
	specified file
void	writeCovMat (char[])
	Writes out the covariance matrix to a specified file.
Static Private Member Functions
static void	negloglik (int mode, int n, const NEWMAT::ColumnVector &X, NEWMAT::Real &fx, NEWMAT::ColumnVector &grad_x, int &result_mode)
	by minimizing the negative log likelihood
static void	constraint_eval (int mode, int n, const NEWMAT::ColumnVector &X, NEWMAT::ColumnVector &g, NEWMAT::Matrix &gradC, int &result_mode)
	this function is empty: it is an unconstrained optimization.
static double	negloglikNCSU (const RealVector &x)
	function used by NCSUOptimizer to optimize negloglik objective
Private Attributes
RealDenseMatrix	trainPoints
	used to create the Gaussian process
RealDenseMatrix	trainValues
	An array of response values; one response value per sample site.
RealDenseVector	trainMeans
	The mean of the input columns of trainPoints.
RealDenseVector	trainStdvs
	The standard deviation of the input columns of trainPoints.
RealDenseMatrix	normTrainPoints
	Current working set of normalized points upon which the GP is based.
RealDenseMatrix	trendFunction
	matrix to hold the trend function
RealDenseMatrix	betaCoeffs
	matrix to hold the beta coefficients for the trend function
RealSymDenseMatrix	covMatrix
	between points Xi and Xj in the initial set of samples
RealDenseMatrix	covVector
	between a new point X and point Xj from the initial set of samples
RealDenseMatrix	approxPoint
	single point, but it could be generalized to be a vector of points.
RealDenseMatrix	gradNegLogLikTheta
	with respect to the theta correlation terms
RealSpdDenseSolver	covSlvr
	the covariance matrix
RealDenseMatrix	gradCovVector
	with respect to a particular componenet of X
RealDenseMatrix	normTrainPointsAll
	Set of all original samples available.
RealDenseMatrix	trainValuesAll
	All original samples available.
RealDenseMatrix	trendFunctionAll
	Trend function values corresponding to all original samples.
size_t	numObs
	The number of observations on which the GP surface is built.
size_t	numObsAll
	The original number of observations.
short	trendOrder
	linear, if order = 2, trend is quadratic.
RealVector	thetaParams
	same point. sige is the underlying process error.
Real	procVar
	The process variance, the multiplier of the correlation matrix.
RealVector	pointsAddedIndex
	all points which have been added
int	cholFlag
	A global indicator for success of the Cholesky factorization.
bool	usePointSelection
	a flag to indicate the use of point selection
Static Private Attributes
static GaussProcApproximation *	GPinstance
	pointer to the active object instance used within the static evaluator

---

Detailed Description

Derived approximation class for Gaussian Process implementation.

The GaussProcApproximation class provides a global approximation (surrogate) based on a Gaussian process. The Gaussian process is built after normalizing the function values, with zero mean. Opt++ is used to determine the optimal values of the covariance parameters, those which minimize the negative log likelihood function.

---

Member Function Documentation

void GPmodel_apply	(	const RealVector &	new_x,
		bool	variance_flag,
		bool	gradients_flag
	)			[private]

Function returns a response value using the GP surface.

The response value is computed at the design point specified by the RealVector function argument.

---

The documentation for this class was generated from the following files:

• GaussProcApproximation.H
• GaussProcApproximation.C

---