The GaussianProcess constructs a Gaussian Process regressor surrogate given a matrix of data. More...

Inheritance diagram for GaussianProcess:

Public Member Functions
	GaussianProcess ()
	Constructor that uses defaultConfigOptions and does not build.

	GaussianProcess (const ParameterList &param_list)
	Constructor that sets configOptions but does not build. More...

	GaussianProcess (const std::string &param_list_yaml_filename)
	Constructor for the GaussianProcess that sets configOptions but does not build the GP. More...

	GaussianProcess (const MatrixXd &samples, const MatrixXd &response, const ParameterList &param_list)
	Constructor for the GaussianProcess that sets configOptions and builds the GP. More...

	GaussianProcess (const MatrixXd &samples, const MatrixXd &response, const std::string &param_list_yaml_filename)
	Constructor for the GaussianProcess that sets configOptions and builds the GP. More...

	~GaussianProcess ()
	Default destructor.

void	build (const MatrixXd &eval_points, const MatrixXd &response) override
	Build the GP using specified build data. More...

VectorXd	value (const MatrixXd &eval_points, const int qoi) override
	Evaluate the Gaussian Process at a set of prediction points for a single qoi. More...

VectorXd	value (const MatrixXd &eval_points)
	Evaluate the Gaussian Process at a set of prediction points for QoI index 0. More...

MatrixXd	gradient (const MatrixXd &eval_points, const int qoi) override
	Evaluate the gradient of the Gaussian process at a set of prediction points for a single QoI. More...

MatrixXd	gradient (const MatrixXd &eval_points)
	Evaluate the gradient of the Gaussian process at a set of prediction points for QoI index 0. More...

MatrixXd	hessian (const MatrixXd &eval_point, const int qoi) override
	Evaluate the Hessian of the Gaussian process at a single point for a single QoI. More...

MatrixXd	hessian (const MatrixXd &eval_point)
	Evaluate the Hessian of the Gaussian process at a single point for QoI index 0. More...

MatrixXd	covariance (const MatrixXd &eval_points, const int qoi)
	Evaluate the covariance matrix for the Gaussian Process at a set of prediction points for a single QoI index. More...

MatrixXd	covariance (const MatrixXd &eval_points)
	Evaluate the covariance matrix for the Gaussian Process at a set of prediction points for QoI index 0. More...

VectorXd	variance (const MatrixXd &eval_points, const int qoi)
	Evaluate the variance of the Gaussian Process at a set of prediction points for a given QoI index. More...

VectorXd	variance (const MatrixXd &eval_points)
	Evaluate the variance of the Gaussian Process at a set of prediction points for QoI index 0. More...

void	negative_marginal_log_likelihood (bool compute_grad, bool compute_gram, double &obj_value, VectorXd &obj_gradient)
	Evaluate the negative marginal loglikelihood and its gradient. More...

void	setup_hyperparameter_bounds (VectorXd &sigma_bounds, MatrixXd &length_scale_bounds, VectorXd &nugget_bounds)
	Initialize the hyperparameter bounds for MLE from values in configOptions. More...

int	get_num_opt_variables ()
	Get the number of optimization variables. More...

int	get_num_variables () const
	Get the dimension of the feature space. More...

VectorXd	get_objective_function_history ()
	Get the history of objective function values from MLE with restarts. More...

MatrixXd	get_objective_gradient_history ()
	Get the history of objective function gradients from MLE with restarts. More...

MatrixXd	get_theta_history ()
	Get the history of hyperparameter values from MLE with restarts. More...

void	set_opt_params (const std::vector< double > &opt_params)
	Update the vector of optimization parameters. More...

std::shared_ptr< Surrogate >	clone () const override
	clone derived Surrogate class for use in cross-validation

Public Member Functions inherited from Surrogate
	Surrogate ()
	Constructor that uses defaultConfigOptions and does not build.

	Surrogate (const ParameterList &param_list)
	Constructor that sets configOptions but does not build. More...

	Surrogate (const MatrixXd &samples, const MatrixXd &response, const ParameterList &param_list)
	Constructor for the Surrogate that sets configOptions and builds the surrogate (does nothing in the base class). More...

virtual	~Surrogate ()
	Default destructor.

VectorXd	value (const MatrixXd &eval_points)
	Evaluate the Surrogate at a set of prediction points for QoI index 0. More...

MatrixXd	gradient (const MatrixXd &eval_points)
	Evaluate the gradient of the Surrogate at a set of prediction points for QoI index 0. More...

MatrixXd	hessian (const MatrixXd &eval_point)
	Evaluate the Hessian of the Surrogate at a single point for QoI index 0. More...

void	variable_labels (const std::vector< std::string > &var_labels)
	Set the variable/feature names. More...

const std::vector< std::string > &	variable_labels () const
	Get the (possibly empty) variable/feature names. More...

void	response_labels (const std::vector< std::string > &resp_labels)
	Set the response/QoI names. More...

const std::vector< std::string > &	response_labels () const
	Get the (possibly empty) response/QoI names. More...

void	set_options (const ParameterList &options)
	Set the Surrogate's configOptions. More...

void	get_options (ParameterList &options)
	Get the Surrogate's configOptions. More...

void	print_options ()
	Print the Surrogate's configOptions.

VectorXd	evaluate_metrics (const StringArray &mnames, const MatrixXd &points, const MatrixXd &ref_values)
	Evalute metrics at specified points (within surrogates)

VectorXd	cross_validate (const MatrixXd &samples, const MatrixXd &response, const StringArray &mnames, const int num_folds=5, const int seed=20)
	Perform K-folds cross-validation (within surrogates)

template<typename DerivedSurr >
void	save (const DerivedSurr &surr_out, const std::string &outfile, const bool binary)
	Serialize a derived (i.e. non-base) surrogate model. More...

template<typename DerivedSurr >
void	load (const std::string &infile, const bool binary, DerivedSurr &surr_in)
	Load a derived (i.e. non-base) surrogate model. More...

Private Member Functions
void	default_options () override
	Construct and populate the defaultConfigOptions.

void	compute_build_dists ()
	Compute squared distances between the scaled build points.

void	compute_pred_dists (const MatrixXd &scaled_pred_pts)
	Compute distances between build and prediction points. This includes build-prediction and prediction-prediction distance matrices. More...

void	compute_gram (const std::vector< MatrixXd > &dists2, bool add_nugget, bool compute_derivs, MatrixXd &gram)
	Compute a Gram matrix given a vector of squared distances and optionally compute its derivatives and/or adds nugget terms. More...

void	generate_initial_guesses (const VectorXd &sigma_bounds, const MatrixXd &length_scale_bounds, const VectorXd &nugget_bounds, const int num_restarts, const int seed, MatrixXd &initial_guesses)
	Randomly generate initial guesses for the optimization routine. More...

void	setup_default_optimization_params (Teuchos::RCP< ParameterList > rol_params)
	Set the default optimization parameters for ROL for GP hyperparameter estimation. More...

template<class Archive >
void	serialize (Archive &archive, const unsigned int version)
	Serializer for save/load.

Private Attributes
double	fixedNuggetValue
	Small constant added to the diagonal of the Gram matrix to avoid ill-conditioning.

MatrixXd	eyeMatrix
	Identity matrix for the build points space.

MatrixXd	basisMatrix
	Basis matrix for the sample points in polynomial regression.

MatrixXd	targetValues
	Target values for the surrogate dataset.

MatrixXd	scaledBuildPoints
	The scaled build points for the surrogate dataset.

VectorXd	thetaValues
	Vector of log-space hyperparameters.

VectorXd	betaValues
	Vector of polynomial coefficients.

double	estimatedNuggetValue
	Estimated nugget term.

VectorXd	bestThetaValues
	Vector of best hyperparameters from MLE with restarts.

VectorXd	bestBetaValues
	Vector of best polynomial coefficients from MLE with restarts.

double	bestEstimatedNuggetValue
	Best estimated nugget value from MLE with restarts.

VectorXd	objectiveFunctionHistory
	Final objective function values for each optimization run.

MatrixXd	objectiveGradientHistory
	Final objective function gradients for each optimization run.

MatrixXd	thetaHistory
	Final hyperparameter values for each optimization run.

MatrixXd	GramMatrix
	Gram matrix for the build points.

VectorXd	trendTargetResidual
	Difference between target values and trend predictions.

VectorXd	GramResidualSolution
	Cholesky solve for Gram matrix with trendTargetResidual rhs.

std::vector< MatrixXd >	GramMatrixDerivs
	Derivatives of the Gram matrix w.r.t. the hyperparameters.

std::vector< MatrixXd >	cwiseDists2
	Squared component-wise distances between points in the surrogate dataset.

std::vector< MatrixXd >	cwiseMixedDists
	Component-wise distances between prediction and build points.

std::vector< MatrixXd >	cwiseMixedDists2
	Squared component-wise distances between prediction and build points.

std::vector< MatrixXd >	cwisePredDists2
	Component-wise distances between prediction points.

Eigen::LDLT< MatrixXd >	CholFact
	Pivoted Cholesky factorization.

bool	hasBestCholFact
	Flag for recomputation of the best Cholesky factorization.

MatrixXd	predGramMatrix
	Gram matrix for the prediction points.

MatrixXd	predMixedGramMatrix
	Gram matrix for the mixed prediction/build points.

MatrixXd	predCovariance
	Covariance matrix for the prediction points.

MatrixXd	predBasisMatrix
	Polynomial basis matrix for the prediction points.

std::shared_ptr< PolynomialRegression >	polyRegression
	PolynomialRegression for trend function.

std::string	kernel_type
	Kernel type.

std::shared_ptr< Kernel >	kernel
	Kernel.

const double	betaBound = 1.0e20
	Large constant for polynomial coefficients upper/lower bounds.

bool	estimateTrend
	Bool for polynomial trend (i.e. semi-parametric GP) estimation.

int	numPolyTerms = 0
	Number of terms in polynomial trend.

int	numNuggetTerms = 0
	Number of terms for the (estimated) nugget parameter.

bool	estimateNugget
	Bool for nugget estimation.

int	verbosity
	Verbosity level.

double	bestObjFunValue = std::numeric_limits<double>::max()
	Final objective function value.

const double	PI = 3.14159265358979323846
	Numerical constant – needed for negative marginal log-likelihood.

Friends
class	boost::serialization::access
	Allow serializers access to private class data.

Additional Inherited Members
Static Public Member Functions inherited from Surrogate
template<typename SurrHandle >
static void	save (const SurrHandle &surr_out, const std::string &outfile, const bool binary)
	serialize Surrogate to file (typically through shared_ptr<Surrogate>, but Derived& or Derived* okay too)

template<typename SurrHandle >
static void	load (const std::string &infile, const bool binary, SurrHandle &surr_in)
	serialize Surrogate from file (typically through shared_ptr<Surrogate>, but Derived& or Derived* okay too)

static std::shared_ptr< Surrogate >	load (const std::string &infile, const bool binary)
	serialize Surrogate from file through pointer to base class (must have been saved via same data type)

Public Attributes inherited from Surrogate
util::DataScaler	dataScaler
	DataScaler class for a Surrogate's build samples.

double	responseOffset = 0.
	Response offset.

double	responseScaleFactor = 1.
	Response scale factor.

Protected Attributes inherited from Surrogate
int	numSamples
	Number of samples in the Surrogate's build samples.

int	numVariables
	Number of features/variables in the Surrogate's build samples.

std::vector< std::string >	variableLabels
	Names of the variables/features; need not be populated.

int	numQOI
	Number of quantities of interest predicted by the surrogate. For scalar-valued surrogates numQOI = 1.

std::vector< std::string >	responseLabels
	Names of the responses/QoIs; need not be populated.

ParameterList	defaultConfigOptions
	Default Key/value options to configure the surrogate.

ParameterList	configOptions
	Key/value options to configure the surrogate - will override defaultConfigOptions.

Detailed Description

The GaussianProcess constructs a Gaussian Process regressor surrogate given a matrix of data.

The Gaussian Process (GP) uses an anisotropic squared exponential kernel with a constant multiplicative scaling factor. This yields a total of num_features + 1 kernel hyperparameters. These parameters are internally transformed to a log-space vector (theta) for optimization and evaluation of the GP. Polynomial trend and nugget estimation are optional.

The GP's parameters are determined through maximum likelihood estimation (MLE) via minimization of the negative marginal log-likelihood function. ROL's implementation of L-BFGS-B is used to solve the optimization problem, and the algorithm may be run from multiple random initial guesses to increase the chance of finding the global minimum.

Once the GP is constructed its mean, variance, and covariance matrix can be computed for a set of prediction points. Gradients and Hessians are available.

Constructor & Destructor Documentation

◆ GaussianProcess() [1/4]

GaussianProcess ( const ParameterList & param_list )

Constructor that sets configOptions but does not build.

Parameters

[in] param_list List that overrides entries in defaultConfigOptions.

References Surrogate::configOptions, GaussianProcess::default_options(), and Surrogate::defaultConfigOptions.

◆ GaussianProcess() [2/4]

GaussianProcess ( const std::string & param_list_yaml_filename )

Constructor for the GaussianProcess that sets configOptions but does not build the GP.

Parameters

[in] param_list_yaml_filename A ParameterList file (relative to the location of the Dakota input file) that overrides entries in defaultConfigOptions.

References Surrogate::configOptions, GaussianProcess::default_options(), and Surrogate::defaultConfigOptions.

◆ GaussianProcess() [3/4]

GaussianProcess	(	const MatrixXd &	samples,
		const MatrixXd &	response,
		const ParameterList &	param_list
	)

Constructor for the GaussianProcess that sets configOptions and builds the GP.

Parameters

[in]	samples	Matrix of data for surrogate construction - (num_samples by num_features)
[in]	response	Vector of targets for surrogate construction - (num_samples by num_qoi = 1; only 1 response is supported currently).
[in]	param_list	List that overrides entries in defaultConfigOptions

References GaussianProcess::build(), Surrogate::configOptions, and GaussianProcess::default_options().

◆ GaussianProcess() [4/4]

GaussianProcess	(	const MatrixXd &	samples,
		const MatrixXd &	response,
		const std::string &	param_list_yaml_filename
	)

Constructor for the GaussianProcess that sets configOptions and builds the GP.

Parameters

[in]	samples	Matrix of data for surrogate construction - (num_samples by num_features)
[in]	response	Vector of targets for surrogate construction - (num_samples by num_qoi = 1; only 1 response is supported currently).
[in]	param_list_yaml_filename	A ParameterList file (relative to the location of the Dakota input file) that overrides entries in defaultConfigOptions.

References GaussianProcess::build(), Surrogate::configOptions, and GaussianProcess::default_options().

Member Function Documentation

◆ build()

void build	(	const MatrixXd &	eval_points,
		const MatrixXd &	response
	)

overridevirtual

Build the GP using specified build data.

Parameters

[in]	eval_points	Matrix of data for surrogate construction - (num_samples by num_features)
[in]	response	Vector of targets for surrogate construction - (num_samples by num_qoi = 1; only 1 response is supported currently).

Implements Surrogate.

References GaussianProcess::basisMatrix, GaussianProcess::bestBetaValues, GaussianProcess::bestEstimatedNuggetValue, GaussianProcess::bestObjFunValue, GaussianProcess::bestThetaValues, GaussianProcess::betaBound, GaussianProcess::betaValues, GaussianProcess::CholFact, GaussianProcess::compute_build_dists(), GaussianProcess::compute_gram(), Surrogate::configOptions, GaussianProcess::cwiseDists2, Surrogate::dataScaler, Surrogate::defaultConfigOptions, GaussianProcess::estimatedNuggetValue, GaussianProcess::estimateNugget, GaussianProcess::estimateTrend, GaussianProcess::eyeMatrix, GaussianProcess::fixedNuggetValue, GaussianProcess::generate_initial_guesses(), GaussianProcess::GramMatrix, GaussianProcess::GramMatrixDerivs, GaussianProcess::hasBestCholFact, GaussianProcess::kernel, dakota::surrogates::kernel_factory(), GaussianProcess::kernel_type, GaussianProcess::negative_marginal_log_likelihood(), GaussianProcess::numNuggetTerms, GaussianProcess::numPolyTerms, Surrogate::numQOI, Surrogate::numSamples, Surrogate::numVariables, GaussianProcess::objectiveFunctionHistory, GaussianProcess::objectiveGradientHistory, GaussianProcess::polyRegression, Surrogate::responseOffset, Surrogate::responseScaleFactor, DataScaler::scale_samples(), GaussianProcess::scaledBuildPoints, dakota::util::scaler_factory(), DataScaler::scaler_type(), GaussianProcess::setup_default_optimization_params(), GaussianProcess::setup_hyperparameter_bounds(), GaussianProcess::targetValues, GaussianProcess::thetaHistory, GaussianProcess::thetaValues, and GaussianProcess::verbosity.

Referenced by GaussianProcess::GaussianProcess().

◆ value() [1/2]

VectorXd value	(	const MatrixXd &	eval_points,
		const int	qoi
	)

overridevirtual

Evaluate the Gaussian Process at a set of prediction points for a single qoi.

Parameters

[in]	eval_points	Matrix for prediction points - (num_points by num_features).
[in]	qoi	Index for surrogate QoI.

Returns: Mean of the Gaussian process at the prediction points.

Implements Surrogate.

References GaussianProcess::basisMatrix, GaussianProcess::betaValues, GaussianProcess::CholFact, GaussianProcess::compute_gram(), GaussianProcess::compute_pred_dists(), GaussianProcess::cwiseDists2, GaussianProcess::cwiseMixedDists2, Surrogate::dataScaler, GaussianProcess::estimateTrend, GaussianProcess::GramMatrix, GaussianProcess::hasBestCholFact, Surrogate::numVariables, GaussianProcess::polyRegression, GaussianProcess::predBasisMatrix, GaussianProcess::predMixedGramMatrix, Surrogate::responseOffset, Surrogate::responseScaleFactor, DataScaler::scale_samples(), dakota::silence_unused_args(), and GaussianProcess::targetValues.

◆ value() [2/2]

VectorXd value ( const MatrixXd & eval_points )

inline

Evaluate the Gaussian Process at a set of prediction points for QoI index 0.

Parameters

[in] eval_points Matrix for prediction points - (num_points by num_features).

Returns: Mean of the Gaussian process at the prediction points.

References Surrogate::value().

◆ gradient() [1/2]

MatrixXd gradient	(	const MatrixXd &	eval_points,
		const int	qoi
	)

overridevirtual

Evaluate the gradient of the Gaussian process at a set of prediction points for a single QoI.

Parameters

[in]	eval_points	Coordinates of the prediction points - (num_pts by num_features).
[in]	qoi	Index of response/QoI for which to compute derivatives.

Returns: Matrix of gradient vectors at the prediction points - (num_pts by num_features).

Reimplemented from Surrogate.

References GaussianProcess::basisMatrix, GaussianProcess::betaValues, GaussianProcess::CholFact, GaussianProcess::compute_gram(), GaussianProcess::compute_pred_dists(), GaussianProcess::cwiseDists2, GaussianProcess::cwiseMixedDists, GaussianProcess::cwiseMixedDists2, Surrogate::dataScaler, GaussianProcess::estimateTrend, GaussianProcess::GramMatrix, GaussianProcess::hasBestCholFact, GaussianProcess::kernel, Surrogate::numVariables, GaussianProcess::polyRegression, GaussianProcess::predMixedGramMatrix, Surrogate::responseScaleFactor, DataScaler::scale_samples(), dakota::silence_unused_args(), GaussianProcess::targetValues, and GaussianProcess::thetaValues.

◆ gradient() [2/2]

MatrixXd gradient ( const MatrixXd & eval_points )

inline

Evaluate the gradient of the Gaussian process at a set of prediction points for QoI index 0.

Parameters

[in] eval_points Coordinates of the prediction points - (num_pts by num_features).

Returns: Matrix of gradient vectors at the prediction points - (num_pts by num_features).

References Surrogate::gradient().

◆ hessian() [1/2]

MatrixXd hessian	(	const MatrixXd &	eval_point,
		const int	qoi
	)

overridevirtual

Evaluate the Hessian of the Gaussian process at a single point for a single QoI.

Parameters

[in]	eval_point	Coordinates of the prediction point - (1 by num_features).
[in]	qoi	Index of response/QoI for which to compute derivatives

Returns: Hessian matrix at the prediction point - (num_features by num_features).

Reimplemented from Surrogate.

References GaussianProcess::basisMatrix, GaussianProcess::betaValues, GaussianProcess::CholFact, GaussianProcess::compute_gram(), GaussianProcess::compute_pred_dists(), GaussianProcess::cwiseDists2, GaussianProcess::cwiseMixedDists, GaussianProcess::cwiseMixedDists2, Surrogate::dataScaler, GaussianProcess::estimateTrend, GaussianProcess::GramMatrix, GaussianProcess::hasBestCholFact, GaussianProcess::kernel, Surrogate::numVariables, GaussianProcess::polyRegression, GaussianProcess::predMixedGramMatrix, Surrogate::responseScaleFactor, DataScaler::scale_samples(), dakota::silence_unused_args(), GaussianProcess::targetValues, and GaussianProcess::thetaValues.

◆ hessian() [2/2]

MatrixXd hessian ( const MatrixXd & eval_point )

inline

Evaluate the Hessian of the Gaussian process at a single point for QoI index 0.

Parameters

[in] eval_point Coordinates of the prediction point - (1 by num_features).

Returns: Hessian matrix at the prediction point - (num_features by num_features).

References Surrogate::hessian().

◆ covariance() [1/2]

MatrixXd covariance	(	const MatrixXd &	eval_points,
		const int	qoi
	)

Evaluate the covariance matrix for the Gaussian Process at a set of prediction points for a single QoI index.

Parameters

[in]	eval_points	Matrix for the prediction points - (num_points by num_features).
[in]	qoi	Index of response/QoI for which to compute derivatives

Returns: [out] Covariance matrix for the Gaussian process at the prediction points.

References GaussianProcess::basisMatrix, GaussianProcess::betaValues, GaussianProcess::CholFact, GaussianProcess::compute_gram(), GaussianProcess::compute_pred_dists(), GaussianProcess::cwiseDists2, GaussianProcess::cwiseMixedDists2, GaussianProcess::cwisePredDists2, Surrogate::dataScaler, GaussianProcess::estimateTrend, GaussianProcess::GramMatrix, GaussianProcess::hasBestCholFact, Surrogate::numVariables, GaussianProcess::polyRegression, GaussianProcess::predBasisMatrix, GaussianProcess::predCovariance, GaussianProcess::predGramMatrix, GaussianProcess::predMixedGramMatrix, Surrogate::responseScaleFactor, DataScaler::scale_samples(), dakota::silence_unused_args(), and GaussianProcess::targetValues.

Referenced by GaussianProcess::covariance(), and GaussianProcess::variance().

◆ covariance() [2/2]

MatrixXd covariance ( const MatrixXd & eval_points )

inline

Evaluate the covariance matrix for the Gaussian Process at a set of prediction points for QoI index 0.

Parameters

[in] eval_points Matrix for the prediction points - (num_points by num_features).

Returns: [out] Covariance of the Gaussian process at the prediction points.

References GaussianProcess::covariance().

◆ variance() [1/2]

VectorXd variance	(	const MatrixXd &	eval_points,
		const int	qoi
	)

Evaluate the variance of the Gaussian Process at a set of prediction points for a given QoI index.

Parameters

[in]	eval_points	Matrix for the prediction points - (num_points by num_features).
[in]	qoi	Index of response/QoI for which to compute derivatives

Returns: [out] Variance of the Gaussian process at the prediction points.

References GaussianProcess::covariance(), and dakota::silence_unused_args().

Referenced by PYBIND11_MODULE(), and GaussianProcess::variance().

◆ variance() [2/2]

VectorXd variance ( const MatrixXd & eval_points )

inline

Evaluate the variance of the Gaussian Process at a set of prediction points for QoI index 0.

Parameters

[in] eval_points Matrix for the prediction points - (num_points by num_features).

Returns: [out] Variance of the Gaussian process at the prediction points.

References GaussianProcess::variance().

◆ negative_marginal_log_likelihood()

void negative_marginal_log_likelihood	(	bool	compute_grad,
		bool	compute_gram,
		double &	obj_value,
		VectorXd &	obj_gradient
	)

Evaluate the negative marginal loglikelihood and its gradient.

Parameters

[in]	compute_grad	Flag for computation of gradient.
[in]	compute_gram	Flag for various Gram matrix calculations.
[out]	obj_value	Value of the objection function.
[out]	obj_gradient	Gradient of the objective function.

References GaussianProcess::basisMatrix, GaussianProcess::betaValues, GaussianProcess::CholFact, GaussianProcess::compute_gram(), GaussianProcess::cwiseDists2, GaussianProcess::estimatedNuggetValue, GaussianProcess::estimateNugget, GaussianProcess::estimateTrend, GaussianProcess::eyeMatrix, GaussianProcess::GramMatrix, GaussianProcess::GramMatrixDerivs, GaussianProcess::GramResidualSolution, GaussianProcess::numPolyTerms, Surrogate::numSamples, Surrogate::numVariables, GaussianProcess::PI, GaussianProcess::targetValues, and GaussianProcess::trendTargetResidual.

Referenced by GaussianProcess::build(), GP_Objective::gradient(), and GP_Objective::value().

◆ setup_hyperparameter_bounds()

void setup_hyperparameter_bounds	(	VectorXd &	sigma_bounds,
		MatrixXd &	length_scale_bounds,
		VectorXd &	nugget_bounds
	)

Initialize the hyperparameter bounds for MLE from values in configOptions.

Parameters

[out]	sigma_bounds	Bounds for the sigma (i.e. scale) hyperparameter.
[out]	length_scale_bounds	Bounds for the anisotropic length-scale hyperparameters.
[out]	nugget_bounds	Bounds for the estimated nugget hyperparameter.

References Surrogate::configOptions, GaussianProcess::estimateNugget, GaussianProcess::numNuggetTerms, and Surrogate::numVariables.

Referenced by GaussianProcess::build().

◆ get_num_opt_variables()

int get_num_opt_variables ( )

Get the number of optimization variables.

Returns: Number of total optimization variables (hyperparameters + trend coefficients + nugget)

References GaussianProcess::numNuggetTerms, GaussianProcess::numPolyTerms, and Surrogate::numVariables.

Referenced by GP_Objective::GP_Objective().

◆ get_num_variables()

int get_num_variables ( ) const

Get the dimension of the feature space.

Returns: numVariables The dimension of the feature space.

References Surrogate::numVariables.

◆ get_objective_function_history()

VectorXd get_objective_function_history ( )

inline

Get the history of objective function values from MLE with restarts.

Returns: objectiveFunctionHistory Vector of final objective function values.

References GaussianProcess::objectiveFunctionHistory.

◆ get_objective_gradient_history()

MatrixXd get_objective_gradient_history ( )

inline

Get the history of objective function gradients from MLE with restarts.

Returns

objectiveGradientHistory Matrix of final objective funciton values

(num_restarts, num_hyperparameters).

References GaussianProcess::objectiveGradientHistory.

◆ get_theta_history()

MatrixXd get_theta_history ( )

inline

Get the history of hyperparameter values from MLE with restarts.

Returns

thetaHistory Vector of final hyperparameter (theta) values

(num_restarts, num_hyperparameters).

References GaussianProcess::thetaHistory.

Referenced by PYBIND11_MODULE().

◆ set_opt_params()

void set_opt_params ( const std::vector< double > & opt_params )

Update the vector of optimization parameters.

Parameters

[in] opt_params Vector of optimization parameter values.

References GaussianProcess::betaValues, GaussianProcess::estimatedNuggetValue, GaussianProcess::estimateNugget, GaussianProcess::estimateTrend, GaussianProcess::numPolyTerms, Surrogate::numVariables, and GaussianProcess::thetaValues.

Referenced by GP_Objective::gradient(), and GP_Objective::value().

◆ compute_pred_dists()

void compute_pred_dists ( const MatrixXd & scaled_pred_pts )

private

Compute distances between build and prediction points. This includes build-prediction and prediction-prediction distance matrices.

Parameters

[in] scaled_pred_pts Matrix of scaled prediction points.

References GaussianProcess::cwiseMixedDists, GaussianProcess::cwiseMixedDists2, GaussianProcess::cwisePredDists2, Surrogate::numSamples, Surrogate::numVariables, and GaussianProcess::scaledBuildPoints.

Referenced by GaussianProcess::covariance(), GaussianProcess::gradient(), GaussianProcess::hessian(), and GaussianProcess::value().

◆ compute_gram()

void compute_gram	(	const std::vector< MatrixXd > &	dists2,
		bool	add_nugget,
		bool	compute_derivs,
		MatrixXd &	gram
	)

private

Compute a Gram matrix given a vector of squared distances and optionally compute its derivatives and/or adds nugget terms.

Parameters

[in]	dists2	Vector of squared distance matrices.
[in]	add_nugget	Bool for whether or add nugget terms.
[in]	compute_derivs	Bool for whether or not to compute the derivatives of the Gram matrix.
[out]	gram	Gram matrix.

References GaussianProcess::estimatedNuggetValue, GaussianProcess::estimateNugget, GaussianProcess::fixedNuggetValue, GaussianProcess::GramMatrixDerivs, GaussianProcess::kernel, and GaussianProcess::thetaValues.

Referenced by GaussianProcess::build(), GaussianProcess::covariance(), GaussianProcess::gradient(), GaussianProcess::hessian(), GaussianProcess::negative_marginal_log_likelihood(), and GaussianProcess::value().

◆ generate_initial_guesses()

void generate_initial_guesses	(	const VectorXd &	sigma_bounds,
		const MatrixXd &	length_scale_bounds,
		const VectorXd &	nugget_bounds,
		const int	num_restarts,
		const int	seed,
		MatrixXd &	initial_guesses
	)

private

Randomly generate initial guesses for the optimization routine.

Parameters

[in]	sigma_bounds	Bounds for the scaling hyperparameter (sigma).
[in]	length_scale_bounds	Bounds for the length scales for each feature (l).
[in]	nugget_bounds	Bounds for the nugget term.
[in]	num_restarts	Number of restarts for the optimizer.
[in]	seed	Seed for the random number generator.
[out]	initial_guesses	Matrix of initial guesses.

References dakota::util::create_uniform_random_double_matrix(), GaussianProcess::estimateNugget, GaussianProcess::estimateTrend, GaussianProcess::numNuggetTerms, GaussianProcess::numPolyTerms, and Surrogate::numVariables.

Referenced by GaussianProcess::build().

◆ setup_default_optimization_params()

void setup_default_optimization_params ( Teuchos::RCP< ParameterList > rol_params )

private

Set the default optimization parameters for ROL for GP hyperparameter estimation.

Parameters

[in] rol_params RCP to a Teuchos::ParameterList of ROL's options.

Referenced by GaussianProcess::build().

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

SurrogatesGaussianProcess.hpp
SurrogatesGaussianProcess.cpp

Public Member Functions

Private Member Functions

Private Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ GaussianProcess() [1/4]

◆ GaussianProcess() [2/4]

◆ GaussianProcess() [3/4]

◆ GaussianProcess() [4/4]

Member Function Documentation

◆ build()

◆ value() [1/2]

◆ value() [2/2]

◆ gradient() [1/2]

◆ gradient() [2/2]

◆ hessian() [1/2]

◆ hessian() [2/2]

◆ covariance() [1/2]

◆ covariance() [2/2]

◆ variance() [1/2]

◆ variance() [2/2]

◆ negative_marginal_log_likelihood()

◆ setup_hyperparameter_bounds()

◆ get_num_opt_variables()

◆ get_num_variables()

◆ get_objective_function_history()

◆ get_objective_gradient_history()

◆ get_theta_history()

◆ set_opt_params()

◆ compute_pred_dists()

◆ compute_gram()

◆ generate_initial_guesses()

◆ setup_default_optimization_params()