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GaussProcApproximation Class Reference

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

Inheritance diagram for GaussProcApproximation:
Approximation

Public Member Functions

 GaussProcApproximation ()
 default constructor More...
 
 GaussProcApproximation (const SharedApproxData &shared_data)
 alternate constructor
 
 GaussProcApproximation (const ProblemDescDB &problem_db, const SharedApproxData &shared_data, const String &approx_label)
 standard constructor
 
 ~GaussProcApproximation ()
 destructor
 
- Public Member Functions inherited from Approximation
 Approximation ()
 default constructor More...
 
 Approximation (ProblemDescDB &problem_db, const SharedApproxData &shared_data, const String &approx_label)
 standard constructor for envelope More...
 
 Approximation (const SharedApproxData &shared_data)
 alternate constructor More...
 
 Approximation (const Approximation &approx)
 copy constructor More...
 
virtual ~Approximation ()
 destructor
 
Approximation operator= (const Approximation &approx)
 assignment operator
 
virtual void active_model_key (const Pecos::ActiveKey &sd_key)
 activate an approximation state based on its multi-index key
 
virtual void clear_model_keys ()
 reset initial state by removing all model keys for an approximation
 
virtual void export_model (const StringArray &var_labels=StringArray(), const String &fn_label="", const String &export_prefix="", const unsigned short export_format=NO_MODEL_FORMAT)
 exports the approximation; if export_format > NO_MODEL_FORMAT, uses all 3 parameters, otherwise extracts these from the Approximation's sharedDataRep to build a filename
 
virtual void export_model (const Variables &vars, const String &fn_label="", const String &export_prefix="", const unsigned short export_format=NO_MODEL_FORMAT)
 approximation export that generates labels from the passed Variables, since only the derived classes know how the variables are ordered w.r.t. the surrogate build; if export_format > NO_MODEL_FORMAT, uses all 3 parameters, otherwise extracts these from the Approximation's sharedDataRep to build a filename
 
virtual void rebuild ()
 rebuilds the approximation incrementally
 
virtual void replace (const IntResponsePair &response_pr, size_t fn_index)
 replace the response data
 
virtual void pop_coefficients (bool save_data)
 removes entries from end of SurrogateData::{vars,resp}Data (last points appended, or as specified in args)
 
virtual void push_coefficients ()
 restores state prior to previous pop()
 
virtual void finalize_coefficients ()
 finalize approximation by applying all remaining trial sets
 
virtual void clear_current_active_data ()
 clear current build data in preparation for next build More...
 
virtual void combine_coefficients ()
 combine all level approximations into a single aggregate approximation
 
virtual void combined_to_active_coefficients (bool clear_combined=true)
 promote combined approximation into active approximation
 
virtual void clear_inactive_coefficients ()
 prune inactive coefficients following combination and promotion to active
 
virtual const RealSymMatrix & hessian (const Variables &vars)
 retrieve the approximate function Hessian for a given parameter vector
 
virtual Real value (const RealVector &c_vars)
 retrieve the approximate function value for a given parameter vector
 
virtual const RealVector & gradient (const RealVector &c_vars)
 retrieve the approximate function gradient for a given parameter vector
 
virtual const RealSymMatrix & hessian (const RealVector &c_vars)
 retrieve the approximate function Hessian for a given parameter vector
 
virtual Real prediction_variance (const RealVector &c_vars)
 retrieve the variance of the predicted value for a given parameter vector
 
virtual Real mean ()
 return the mean of the expansion, where all active vars are random
 
virtual Real mean (const RealVector &x)
 return the mean of the expansion for a given parameter vector, where a subset of the active variables are random
 
virtual Real combined_mean ()
 return the mean of the combined expansion, where all active vars are random
 
virtual Real combined_mean (const RealVector &x)
 return the mean of the combined expansion for a given parameter vector, where a subset of the active variables are random
 
virtual const RealVector & mean_gradient ()
 return the gradient of the expansion mean
 
virtual const RealVector & mean_gradient (const RealVector &x, const SizetArray &dvv)
 return the gradient of the expansion mean
 
virtual Real variance ()
 return the variance of the expansion, where all active vars are random
 
virtual Real variance (const RealVector &x)
 return the variance of the expansion for a given parameter vector, where a subset of the active variables are random
 
virtual const RealVector & variance_gradient ()
 
virtual const RealVector & variance_gradient (const RealVector &x, const SizetArray &dvv)
 
virtual Real covariance (Approximation &approx_2)
 return the covariance between two response expansions, treating all variables as random
 
virtual Real covariance (const RealVector &x, Approximation &approx_2)
 return the covariance between two response expansions, treating a subset of the variables as random
 
virtual Real combined_covariance (Approximation &approx_2)
 return the covariance between two combined response expansions, where all active variables are random
 
virtual Real combined_covariance (const RealVector &x, Approximation &approx_2)
 return the covariance between two combined response expansions, where a subset of the active variables are random
 
virtual void compute_moments (bool full_stats=true, bool combined_stats=false)
 
virtual void compute_moments (const RealVector &x, bool full_stats=true, bool combined_stats=false)
 
virtual const RealVector & moments () const
 
virtual const RealVector & expansion_moments () const
 
virtual const RealVector & numerical_integration_moments () const
 
virtual const RealVector & combined_moments () const
 
virtual Real moment (size_t i) const
 
virtual void moment (Real mom, size_t i)
 
virtual Real combined_moment (size_t i) const
 
virtual void combined_moment (Real mom, size_t i)
 
virtual void clear_component_effects ()
 
virtual void compute_component_effects ()
 
virtual void compute_total_effects ()
 
virtual const RealVector & sobol_indices () const
 
virtual const RealVector & total_sobol_indices () const
 
virtual ULongULongMap sparse_sobol_index_map () const
 
virtual bool advancement_available ()
 check if resolution advancement (e.g., order, rank) is available for this approximation instance
 
virtual bool diagnostics_available ()
 check if diagnostics are available for this approximation type
 
virtual Real diagnostic (const String &metric_type)
 retrieve a single diagnostic metric for the diagnostic type specified
 
virtual RealArray cv_diagnostic (const StringArray &metric_types, unsigned num_folds)
 retrieve diagnostic metrics for the diagnostic types specified, applying
 
virtual void primary_diagnostics (size_t fn_index)
 compute and print all requested diagnostics and cross-validation
 
virtual RealArray challenge_diagnostic (const StringArray &metric_types, const RealMatrix &challenge_points, const RealVector &challenge_responses)
 compute requested diagnostics for user provided challenge pts
 
virtual void challenge_diagnostics (size_t fn_index, const RealMatrix &challenge_points, const RealVector &challenge_responses)
 compute and print all requested diagnostics for user provided challenge pts
 
virtual RealVector approximation_coefficients (bool normalized) const
 return the coefficient array computed by build()/rebuild()
 
virtual void approximation_coefficients (const RealVector &approx_coeffs, bool normalized)
 set the coefficient array from external sources, rather than computing with build()/rebuild()
 
virtual void coefficient_labels (std::vector< std::string > &coeff_labels) const
 print the coefficient array computed in build()/rebuild()
 
virtual void print_coefficients (std::ostream &s, bool normalized)
 print the coefficient array computed in build()/rebuild()
 
virtual int recommended_coefficients () const
 return the recommended number of samples (unknowns) required to build the derived class approximation type in numVars dimensions
 
virtual int num_constraints () const
 return the number of constraints to be enforced via an anchor point
 
virtual void expansion_coefficient_flag (bool)
 
virtual bool expansion_coefficient_flag () const
 
virtual void expansion_gradient_flag (bool)
 
virtual bool expansion_gradient_flag () const
 
virtual void clear_computed_bits ()
 clear tracking of computed moments, due to (expansion) change that invalidates previous results
 
virtual void map_variable_labels (const Variables &dfsm_vars)
 if needed, map passed all variable labels to approximation's labels
 
int min_points (bool constraint_flag) const
 return the minimum number of points required to build the approximation type in numVars dimensions. Uses *_coefficients() and num_constraints().
 
int recommended_points (bool constraint_flag) const
 return the recommended number of samples to build the approximation type in numVars dimensions (default same as min_points)
 
void pop_data (bool save_data)
 removes entries from end of SurrogateData::{vars,resp}Data (last points appended, or as specified in args)
 
void push_data ()
 restores SurrogateData state prior to previous pop()
 
void finalize_data ()
 finalize SurrogateData by applying all remaining trial sets
 
const Pecos::SurrogateData & surrogate_data () const
 return approxData
 
Pecos::SurrogateData & surrogate_data ()
 return approxData
 
void add (const Variables &vars, bool v_copy, const Response &response, size_t fn_index, bool r_copy, bool anchor_flag, int eval_id, size_t key_index=_NPOS)
 create SurrogateData{Vars,Resp} and append to SurrogateData:: {varsData,respData,dataIdentifiers}
 
void add (const Real *c_vars, bool v_copy, const Response &response, size_t fn_index, bool r_copy, bool anchor_flag, int eval_id, size_t key_index=_NPOS)
 create SurrogateData{Vars,Resp} and append to SurrogateData:: {varsData,respData,dataIdentifiers}
 
void add (const Pecos::SurrogateDataVars &sdv, bool v_copy, const Response &response, size_t fn_index, bool r_copy, bool anchor_flag, int eval_id, size_t key_index=_NPOS)
 create a SurrogateDataResp and append to SurrogateData:: {varsData,respData,dataIdentifiers}
 
void add (const Pecos::SurrogateDataVars &sdv, bool v_copy, const Pecos::SurrogateDataResp &sdr, bool r_copy, bool anchor_flag, int eval_id, size_t key_index=_NPOS)
 append to SurrogateData::{varsData,respData,dataIdentifiers}
 
void add_array (const RealMatrix &sample_vars, bool v_copy, const RealVector &sample_resp, bool r_copy, size_t key_index=_NPOS)
 add surrogate data from the provided sample and response data, assuming continuous variables and function values only More...
 
void pop_count (size_t count, size_t key_index)
 appends to SurrogateData::popCountStack (number of entries to pop from end of SurrogateData::{vars,resp}Data, based on size of last data append)
 
void clear_data ()
 clear SurrogateData::{vars,resp}Data for activeKey + embedded keys More...
 
void clear_active_data ()
 clear active approximation data
 
void clear_inactive_data ()
 clear inactive approximation data
 
void clear_active_popped ()
 clear SurrogateData::popped{Vars,Resp}Trials,popCountStack for activeKey
 
void clear_popped ()
 clear SurrogateData::popped{Vars,Resp}Trials,popCountStack for all keys
 
void set_bounds (const RealVector &c_l_bnds, const RealVector &c_u_bnds, const IntVector &di_l_bnds, const IntVector &di_u_bnds, const RealVector &dr_l_bnds, const RealVector &dr_u_bnds)
 set approximation lower and upper bounds (currently only used by graphics)
 
std::shared_ptr< Approximationapprox_rep () const
 returns approxRep for access to derived class member functions that are not mapped to the top Approximation level
 

Protected Member Functions

int min_coefficients () const
 return the minimum number of samples (unknowns) required to build the derived class approximation type in numVars dimensions
 
void build ()
 find the covariance parameters governing the Gaussian process response
 
Real value (const Variables &vars)
 retrieve the function value for a given parameter set
 
const RealVector & gradient (const Variables &vars)
 retrieve the function gradient at the predicted value for a given parameter set
 
Real prediction_variance (const Variables &vars)
 retrieve the variance of the predicted value for a given parameter set
 
- Protected Member Functions inherited from Approximation
 Approximation (BaseConstructor, const ProblemDescDB &problem_db, const SharedApproxData &shared_data, const String &approx_label)
 constructor initializes the base class part of letter classes (BaseConstructor overloading avoids infinite recursion in the derived class constructors - Coplien, p. 139) More...
 
 Approximation (NoDBBaseConstructor, const SharedApproxData &shared_data)
 constructor initializes the base class part of letter classes (BaseConstructor overloading avoids infinite recursion in the derived class constructors - Coplien, p. 139) More...
 
Pecos::SurrogateDataVars variables_to_sdv (const Real *sample_c_vars)
 create a SurrogateDataVars instance from a Real*
 
Pecos::SurrogateDataVars variables_to_sdv (const Variables &vars)
 create a SurrogateDataVars instance by extracting data from a Variables object
 
Pecos::SurrogateDataResp response_to_sdr (const Response &response, size_t fn_index)
 create a SurrogateDataResp instance by extracting data for a particular QoI from a Response object
 
void add (const Pecos::SurrogateDataVars &sdv, bool v_copy, const Pecos::SurrogateDataResp &sdr, bool r_copy, bool anchor_flag)
 tracks a new data point by appending to SurrogateData::{vars,Resp}Data
 
void add (int eval_id)
 tracks a new data point by appending to SurrogateData::dataIdentifiers
 
void check_points (size_t num_build_pts)
 Check number of build points against minimum required.
 
void assign_key_index (size_t key_index)
 extract and assign i-th embedded active key
 

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. More...
 
void normalize_training_data ()
 Normalizes the initial inputs upon which the GP surface is based.
 
void get_trend ()
 Gets the trend (basis) functions for the calculation of the mean of the GP If the order = 0, the trend is a constant, if the order = 1, trend is 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 ()
 Gets the Cholesky factorization of the covariance matrix, with error checking.
 
void get_process_variance ()
 Gets the estimate of the process variance given the values of beta and the correlation lengthscales.
 
void get_cov_matrix ()
 calculates the covariance matrix for a given set of input points
 
void get_cov_vector ()
 calculates the covariance vector between a new point x and the set of inputs upon which the GP is based
 
void optimize_theta_global ()
 sets up and performs the optimization of the negative log likelihood to determine the optimal values of the covariance parameters using NCSUDirect
 
void optimize_theta_multipoint ()
 sets up and performs the optimization of the negative log likelihood to determine the optimal values of the covariance parameters using a gradient-based solver and multiple starting points
 
void predict (bool variance_flag, bool gradients_flag)
 Calculates the predicted new response value for x in normalized space.
 
Real calc_nll ()
 calculates the negative log likelihood function (based on covariance matrix)
 
void calc_grad_nll ()
 Gets the gradient of the negative log likelihood function with respect to the correlation lengthscales, theta.
 
void get_grad_cov_vector ()
 Calculate the derivatives of the covariance vector, with respect to each componeent of x.
 
void run_point_selection ()
 Runs the point selection algorithm, which will choose a subset of the training set with which to construct the GP model, and estimate the necessary parameters.
 
void initialize_point_selection ()
 Initializes the point selection routine by choosing a small initial subset of the training points.
 
void pointsel_get_errors (RealArray &delta)
 Uses the current GP model to compute predictions at all of the training points and find the errors.
 
int addpoint (int, IntArray &added_index)
 Adds a point to the effective training set. Returns 1 on success.
 
int pointsel_add_sel (const RealArray &delta)
 Accepts a vector of unsorted prediction errors, determines which points should be added to the effective training set, and adds them.
 
Real maxval (const RealArray &) const
 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 ()
 For problems with 2D input, evaluates the negative log likelihood on a grid.
 
void writex (const char[])
 Writes out the current training set (in original units) to a 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 Teuchos::SerialDenseVector< int, double > &X, Real &fx, Teuchos::SerialDenseVector< int, double > &grad_x, int &result_mode)
 static function used by OPT++ as the objective function to optimize the hyperparameters in the covariance of the GP by minimizing the negative log likelihood
 
static void constraint_eval (int mode, int n, const Teuchos::SerialDenseVector< int, double > &X, Teuchos::SerialDenseVector< int, double > &g, Teuchos::SerialDenseMatrix< int, double > &gradC, int &result_mode)
 static function used by OPT++ as the constraint function in the optimization of the negative log likelihood. Currently 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

Real approxValue
 value of the approximation returned by value()
 
Real approxVariance
 value of the approximation returned by prediction_variance()
 
RealMatrix trainPoints
 A 2-D array (num sample sites = rows, num vars = columns) used to create the Gaussian process.
 
RealMatrix trainValues
 An array of response values; one response value per sample site.
 
RealVector trainMeans
 The mean of the input columns of trainPoints.
 
RealVector trainStdvs
 The standard deviation of the input columns of trainPoints.
 
RealMatrix normTrainPoints
 Current working set of normalized points upon which the GP is based.
 
RealMatrix trendFunction
 matrix to hold the trend function
 
RealMatrix betaCoeffs
 matrix to hold the beta coefficients for the trend function
 
RealSymMatrix covMatrix
 The covariance matrix where each element (i,j) is the covariance between points Xi and Xj in the initial set of samples.
 
RealMatrix covVector
 The covariance vector where each element (j,0) is the covariance between a new point X and point Xj from the initial set of samples.
 
RealMatrix approxPoint
 Point at which a prediction is requested. This is currently a single point, but it could be generalized to be a vector of points.
 
RealMatrix gradNegLogLikTheta
 matrix to hold the gradient of the negative log likelihood with respect to the theta correlation terms
 
Teuchos::SerialSpdDenseSolver
< int, Real > 
covSlvr
 The global solver for all computations involving the inverse of the covariance matrix.
 
RealMatrix gradCovVector
 A matrix, where each column is the derivative of the covVector with respect to a particular componenet of X.
 
RealMatrix normTrainPointsAll
 Set of all original samples available.
 
RealMatrix trainValuesAll
 All original samples available.
 
RealMatrix trendFunctionAll
 Trend function values corresponding to all original samples.
 
RealMatrix Rinv_YFb
 Matrix for storing inverse of correlation matrix Rinv*(Y-FB)
 
size_t numObs
 The number of observations on which the GP surface is built.
 
size_t numObsAll
 The original number of observations.
 
short trendOrder
 The number of variables in each X variable (number of dimensions of the problem). More...
 
RealVector thetaParams
 Theta is the vector of covariance parameters for the GP. We determine the values of theta by optimization Currently, the covariance function is theta[0]*exp(-0.5*sume)+delta*pow(sige,2). sume is the sum squared of weighted distances; it involves a sum of theta[1](Xi(1)-Xj(1))^2 + theta[2](Xi(2)-Xj(2))^2 + ... where Xi(1) is the first dimension value of multi-dimensional variable Xi. delta*pow(sige,2) is a jitter term used to improve matrix computations. delta is zero for the covariance between different points and 1 for the covariance between the same point. sige is the underlying process error.
 
Real procVar
 The process variance, the multiplier of the correlation matrix.
 
IntArray pointsAddedIndex
 Used by the point selection algorithm, this vector keeps track 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 GaussProcApproximationGPinstance
 pointer to the active object instance used within the static evaluator
 

Additional Inherited Members

- Protected Attributes inherited from Approximation
Pecos::SurrogateData approxData
 contains the variables/response data for constructing a single approximation model (one response function). There is only one SurrogateData instance per Approximation, although it may contain keys for different model forms/resolutions and aggregations (e.g., discrepancies) among forms/resolutions.
 
RealVector approxGradient
 gradient of the approximation returned by gradient()
 
RealSymMatrix approxHessian
 Hessian of the approximation returned by hessian()
 
String approxLabel
 label for approximation, if applicable
 
std::shared_ptr< SharedApproxDatasharedDataRep
 contains the approximation data that is shared among the response set
 

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.

Constructor & Destructor Documentation

default constructor

alternate constructor used by EffGlobalOptimization and NonDGlobalReliability that does not use a problem database defaults here are no point selectinn and quadratic trend function.

Member Function Documentation

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

Member Data Documentation

short trendOrder
private

The number of variables in each X variable (number of dimensions of the problem).

The order of the basis function for the mean of the GP If the order = 0, the trend is a constant, if the order = 1, trend is linear, if order = 2, trend is quadratic.

Referenced by GaussProcApproximation::GaussProcApproximation(), GaussProcApproximation::get_beta_coefficients(), GaussProcApproximation::get_trend(), GaussProcApproximation::GPmodel_build(), and GaussProcApproximation::predict().


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