sgpp::datadriven::SparseGridDensityEstimator Class Reference

#include <SparseGridDensityEstimator.hpp>

Inheritance diagram for sgpp::datadriven::SparseGridDensityEstimator:

Public Member Functions
void	cov (base::DataMatrix &cov, base::DataMatrix *bounds=nullptr) override
	Computes the covariance of the density function. More...
size_t	getDim () override
	get number of dimensions More...
virtual base::Grid &	getGrid ()
	returns the grid More...
size_t	getNsamples () override
	get number of samples More...
std::shared_ptr< base::DataVector >	getSamples (size_t dim) override
	returns the samples in the given dimension More...
std::shared_ptr< base::DataMatrix >	getSamples () override
	returns the complete sample set More...
virtual base::DataVector &	getSurpluses ()
	returns the surpluses More...
virtual void	initialize (base::DataMatrix &samples)
	Estimate a sparse grid density based on the given data set and the specified configurations. More...
virtual sgpp::datadriven::SparseGridDensityEstimator *	marginalize (size_t idim)
	Marginalize the density in one dimension and return result. More...
virtual sgpp::datadriven::SparseGridDensityEstimator *	margToDimX (size_t idim)
	Compute marginal density. More...
double	mean () override
	This method computes the mean of the density function. More...
double	pdf (base::DataVector &x) override
	This methods evaluates the sparse grid density at a single point. More...
void	pdf (base::DataMatrix &points, base::DataVector &res) override
	Evaluation of the sparse grid density at a set of points. More...
	SparseGridDensityEstimator (sgpp::base::RegularGridConfiguration &gridConfig, sgpp::base::AdaptivityConfiguration &adaptivityConfig, sgpp::solver::SLESolverConfiguration &solverConfig, sgpp::datadriven::RegularizationConfiguration &regularizationConfig, CrossvalidationForRegularizationConfiguration &crossvalidationConfig, SGDEConfiguration &sgdeConfig)
	Constructor. More...
	SparseGridDensityEstimator (SparseGridDensityEstimatorConfiguration &learnerSGDEConfig)
	SparseGridDensityEstimator (base::Grid &grid, base::DataVector &alpha, base::DataMatrix &samples)
	construct learner from given grid and coefficients More...
	SparseGridDensityEstimator (const SparseGridDensityEstimator &learnerSGDE)
virtual void	train (base::Grid &grid, base::DataVector &alpha, base::DataMatrix &train, double lambdaReg)
	Does the learning step on a given grid, training set and regularization parameter lambda. More...
double	variance () override
	Computes the variance of the density function. More...
virtual	~SparseGridDensityEstimator ()
Public Member Functions inherited from sgpp::datadriven::DensityEstimator
virtual void	corrcoef (base::DataMatrix &corr, base::DataMatrix *bounds=nullptr)
double	crossEntropy (sgpp::base::DataMatrix &samples)
	DensityEstimator ()
virtual double	std_deviation ()
virtual	~DensityEstimator ()

Protected Member Functions
std::shared_ptr< datadriven::DensitySystemMatrix >	computeDensitySystemMatrix (base::Grid &grid, base::DataMatrix &train, double lambdaReg)
	generates the density system matrix More...
base::OperationMatrix *	computeLTwoDotProductMatrix (base::Grid &grid)
	generates the L^2 dot product matrix More...
base::OperationMultipleEval *	computeMultipleEvalMatrix (base::Grid &grid, base::DataMatrix &train)
	generates the MultipleEval matrix More...
base::OperationMatrix *	computeRegularizationMatrix (base::Grid &grid)
	generates the regularization matrix More...
double	computeResidual (base::Grid &grid, base::DataVector &alpha, base::DataMatrix &test, double lambdaReg)
	Compute the residual for a given test data set on a learned grid. More...
std::shared_ptr< base::Grid >	createRegularGrid ()
	generates a regular grid More...
double	mean (base::Grid &grid, base::DataVector &alpha)
double	optimizeLambdaCV ()
	Does cross-validation to obtain a suitable regularization parameter. More...
void	splitset (std::vector< std::shared_ptr< base::DataMatrix > > &strain, std::vector< std::shared_ptr< base::DataMatrix > > &stest)
	splits the complete sample set in a set of smaller training and test samples for cross-validation. More...
double	variance (base::Grid &grid, base::DataVector &alpha)

Protected Attributes
sgpp::base::AdaptivityConfiguration	adaptivityConfig
std::shared_ptr< base::DataVector >	alpha
CrossvalidationForRegularizationConfiguration	crossvalidationConfig
std::shared_ptr< base::Grid >	grid
sgpp::base::RegularGridConfiguration	gridConfig
sgpp::datadriven::RegularizationConfiguration	regularizationConfig
std::shared_ptr< base::DataMatrix >	samples
SGDEConfiguration	sgdeConfig
sgpp::solver::SLESolverConfiguration	solverConfig

Constructor & Destructor Documentation

SparseGridDensityEstimator() [1/4]

sgpp::datadriven::SparseGridDensityEstimator::SparseGridDensityEstimator	(	sgpp::base::RegularGridConfiguration &	gridConfig,
		sgpp::base::AdaptivityConfiguration &	adaptivityConfig,
		sgpp::solver::SLESolverConfiguration &	solverConfig,
		sgpp::datadriven::RegularizationConfiguration &	regularizationConfig,
		CrossvalidationForRegularizationConfiguration &	crossvalidationConfig,
		SGDEConfiguration &	sgdeConfig
	)

Constructor.

Parameters

gridConfig	grid configuration
adaptivityConfig	adaptive refinement configuration
solverConfig	solver configuration (CG)
regularizationConfig	config for regularization operator
crossvalidationConfig	configuration for the cross validation
sgdeConfig	configuration for the sparse grid density estimation

Referenced by marginalize(), and margToDimX().

SparseGridDensityEstimator() [2/4]

sgpp::datadriven::SparseGridDensityEstimator::SparseGridDensityEstimator ( SparseGridDensityEstimatorConfiguration &  learnerSGDEConfig )

explicit

SparseGridDensityEstimator() [3/4]

sgpp::datadriven::SparseGridDensityEstimator::SparseGridDensityEstimator	(	base::Grid &	grid,
		base::DataVector &	alpha,
		base::DataMatrix &	samples
	)

construct learner from given grid and coefficients

Parameters

grid
alpha
samples

References alpha, sgpp::base::Grid::clone(), and samples.

SparseGridDensityEstimator() [4/4]

sgpp::datadriven::SparseGridDensityEstimator::SparseGridDensityEstimator

(

const SparseGridDensityEstimator &

learnerSGDE

)

References adaptivityConfig, alpha, crossvalidationConfig, grid, gridConfig, regularizationConfig, samples, sgdeConfig, and solverConfig.

~SparseGridDensityEstimator()

sgpp::datadriven::SparseGridDensityEstimator::~SparseGridDensityEstimator ( )

virtual

Member Function Documentation

computeDensitySystemMatrix()

std::shared_ptr< datadriven::DensitySystemMatrix > sgpp::datadriven::SparseGridDensityEstimator::computeDensitySystemMatrix ( base::Grid &  grid, base::DataMatrix &  train, double  lambdaReg  )

protected

generates the density system matrix

Parameters

grid	grid
train	train
lambdaReg	regularization parameter

References python.utils.pca_normalize_dataset::C, computeLTwoDotProductMatrix(), computeMultipleEvalMatrix(), computeRegularizationMatrix(), and sgpp::base::DataMatrix::getNrows().

Referenced by computeResidual(), and train().

computeLTwoDotProductMatrix()

base::OperationMatrix * sgpp::datadriven::SparseGridDensityEstimator::computeLTwoDotProductMatrix ( base::Grid &  grid )

protected

generates the L^2 dot product matrix

Parameters

grid

grid

References sgpp::op_factory::createOperationLTwoDotProduct().

Referenced by computeDensitySystemMatrix().

computeMultipleEvalMatrix()

base::OperationMultipleEval * sgpp::datadriven::SparseGridDensityEstimator::computeMultipleEvalMatrix ( base::Grid &  grid, base::DataMatrix &  train  )

protected

generates the MultipleEval matrix

Parameters

grid	grid
train	training data

References sgpp::base::Bspline, sgpp::base::BsplineBoundary, sgpp::base::BsplineClenshawCurtis, sgpp::op_factory::createOperationMultipleEval(), sgpp::op_factory::createOperationMultipleEvalNaive(), sgpp::base::Grid::getType(), sgpp::base::ModBspline, sgpp::base::ModBsplineClenshawCurtis, sgpp::base::ModPolyClenshawCurtis, sgpp::base::PolyClenshawCurtis, and sgpp::base::PolyClenshawCurtisBoundary.

Referenced by computeDensitySystemMatrix().

computeRegularizationMatrix()

base::OperationMatrix * sgpp::datadriven::SparseGridDensityEstimator::computeRegularizationMatrix ( base::Grid &  grid )

protected

generates the regularization matrix

Parameters

grid

grid

References python.utils.pca_normalize_dataset::C, sgpp::op_factory::createOperationIdentity(), sgpp::op_factory::createOperationLaplace(), sgpp::datadriven::Identity, sgpp::datadriven::Laplace, regularizationConfig, and sgpp::datadriven::RegularizationConfiguration::type_.

Referenced by computeDensitySystemMatrix().

computeResidual()

double sgpp::datadriven::SparseGridDensityEstimator::computeResidual ( base::Grid &  grid, base::DataVector &  alpha, base::DataMatrix &  test, double  lambdaReg  )

protected

Compute the residual for a given test data set on a learned grid.

$|(A - lambda C) alpha - 1/n B|$

This is used as quality criterion for the estimated density.

Parameters

grid	grid
alpha	coefficient vector
test	test set
lambdaReg	regularization parameter

Returns

References computeDensitySystemMatrix(), sgpp::base::Grid::getSize(), and python.statsfileInfo::i.

Referenced by optimizeLambdaCV().

cov()

void sgpp::datadriven::SparseGridDensityEstimator::cov ( base::DataMatrix &  cov, base::DataMatrix *  bounds = nullptr  )

overridevirtual

Computes the covariance of the density function.

Implements sgpp::datadriven::DensityEstimator.

References alpha, sgpp::op_factory::createOperationCovariance(), and grid.

createRegularGrid()

std::shared_ptr< base::Grid > sgpp::datadriven::SparseGridDensityEstimator::createRegularGrid ( )

protected

generates a regular grid

Returns

grid

References sgpp::base::Grid::createGrid(), gridConfig, and sgpp::base::GeneralGridConfiguration::level_.

Referenced by initialize(), and optimizeLambdaCV().

getDim()

size_t sgpp::datadriven::SparseGridDensityEstimator::getDim ( )

overridevirtual

get number of dimensions

Implements sgpp::datadriven::DensityEstimator.

References sgpp::base::GeneralGridConfiguration::dim_, and gridConfig.

Referenced by python.uq.dists.SGDEdist.SGDEdist::__str__(), and python.uq.dists.KDEDist.KDEDist::getBandwidths().

getGrid()

base::Grid & sgpp::datadriven::SparseGridDensityEstimator::getGrid ( )

virtual

returns the grid

References grid.

getNsamples()

size_t sgpp::datadriven::SparseGridDensityEstimator::getNsamples ( )

overridevirtual

get number of samples

Implements sgpp::datadriven::DensityEstimator.

References samples.

Referenced by getSamples(), and optimizeLambdaCV().

getSamples() [1/2]

std::shared_ptr< base::DataVector > sgpp::datadriven::SparseGridDensityEstimator::getSamples ( size_t  dim )

overridevirtual

returns the samples in the given dimension

Parameters

dim

Implements sgpp::datadriven::DensityEstimator.

References getNsamples(), and samples.

getSamples() [2/2]

std::shared_ptr< base::DataMatrix > sgpp::datadriven::SparseGridDensityEstimator::getSamples ( )

overridevirtual

returns the complete sample set

Implements sgpp::datadriven::DensityEstimator.

References samples.

getSurpluses()

base::DataVector & sgpp::datadriven::SparseGridDensityEstimator::getSurpluses ( )

virtual

returns the surpluses

References alpha.

initialize()

void sgpp::datadriven::SparseGridDensityEstimator::initialize ( base::DataMatrix &  samples )

virtual

Estimate a sparse grid density based on the given data set and the specified configurations.

Parameters

samples

DataMatrix (nrows = number of samples, ncols = dimensionality)

Implements sgpp::datadriven::DensityEstimator.

References alpha, sgpp::op_factory::createOperationMakePositive(), sgpp::op_factory::createOperationQuadrature(), createRegularGrid(), crossvalidationConfig, sgpp::base::GeneralGridConfiguration::dim_, sgpp::base::OperationQuadrature::doQuadrature(), sgpp::datadriven::CrossvalidationForRegularizationConfiguration::enable_, sgpp::base::DataMatrix::getNcols(), grid, gridConfig, sgpp::datadriven::CrossvalidationForRegularizationConfiguration::lambda_, sgpp::datadriven::OperationMakePositive::makePositive(), sgpp::datadriven::SGDEConfiguration::makePositive_, sgpp::datadriven::SGDEConfiguration::makePositive_candidateSearchAlgorithm_, sgpp::datadriven::SGDEConfiguration::makePositive_generateConsistentGrid_, sgpp::datadriven::SGDEConfiguration::makePositive_interpolationAlgorithm_, sgpp::datadriven::SGDEConfiguration::makePositive_verbose_, optimizeLambdaCV(), samples, sgdeConfig, train(), and sgpp::datadriven::SGDEConfiguration::unitIntegrand_.

marginalize()

SparseGridDensityEstimator * sgpp::datadriven::SparseGridDensityEstimator::marginalize ( size_t  idim )

virtual

Marginalize the density in one dimension and return result.

Parameters

idim	dimension which should be marginalized

References alpha, sgpp::op_factory::createOperationDensityMarginalize(), grid, samples, and SparseGridDensityEstimator().

margToDimX()

SparseGridDensityEstimator * sgpp::datadriven::SparseGridDensityEstimator::margToDimX ( size_t  idim )

virtual

Compute marginal density.

Parameters

idim	dimension which should be left after marginalization

References alpha, sgpp::op_factory::createOperationDensityMargTo1D(), grid, samples, and SparseGridDensityEstimator().

mean() [1/2]

double sgpp::datadriven::SparseGridDensityEstimator::mean ( )

overridevirtual

This method computes the mean of the density function.

Implements sgpp::datadriven::DensityEstimator.

References alpha, and grid.

Referenced by python.uq.analysis.mc.MCAnalysis.MCAnalysis::computeMoments(), and python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::computeMoments().

mean() [2/2]

double sgpp::datadriven::SparseGridDensityEstimator::mean ( base::Grid &  grid, base::DataVector &  alpha  )

protected

References sgpp::op_factory::createOperationFirstMoment().

Referenced by python.uq.analysis.mc.MCAnalysis.MCAnalysis::computeMoments(), and python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::computeMoments().

optimizeLambdaCV()

double sgpp::datadriven::SparseGridDensityEstimator::optimizeLambdaCV ( )

protected

Does cross-validation to obtain a suitable regularization parameter.

References alpha, computeResidual(), createRegularGrid(), crossvalidationConfig, getNsamples(), grid, python.statsfileInfo::i, python.utils.statsfile2gnuplot::j, sgpp::datadriven::CrossvalidationForRegularizationConfiguration::kfold_, sgpp::datadriven::CrossvalidationForRegularizationConfiguration::lambdaEnd_, sgpp::datadriven::CrossvalidationForRegularizationConfiguration::lambdaStart_, sgpp::datadriven::CrossvalidationForRegularizationConfiguration::lambdaSteps_, sgpp::datadriven::CrossvalidationForRegularizationConfiguration::logScale_, sgpp::base::DataVector::max(), sgpp::base::DataVector::min(), sgpp::base::DataVector::resizeZero(), sgpp::datadriven::CrossvalidationForRegularizationConfiguration::silent_, splitset(), and train().

Referenced by initialize().

pdf() [1/2]

double sgpp::datadriven::SparseGridDensityEstimator::pdf ( base::DataVector &  x )

overridevirtual

This methods evaluates the sparse grid density at a single point.

Parameters

x	DataVector length equal to dimensionality

Implements sgpp::datadriven::DensityEstimator.

References alpha, sgpp::op_factory::createOperationEval(), and grid.

pdf() [2/2]

void sgpp::datadriven::SparseGridDensityEstimator::pdf ( base::DataMatrix &  points, base::DataVector &  res  )

overridevirtual

Evaluation of the sparse grid density at a set of points.

Parameters

points	DataMatrix (nrows = number of samples, ncols = dimensionality)
res	DataVector (size = number of samples) where the results are stored

Implements sgpp::datadriven::DensityEstimator.

References alpha, sgpp::op_factory::createOperationMultipleEval(), and grid.

splitset()

void sgpp::datadriven::SparseGridDensityEstimator::splitset ( std::vector< std::shared_ptr< base::DataMatrix > > &  strain, std::vector< std::shared_ptr< base::DataMatrix > > &  stest  )

protected

splits the complete sample set in a set of smaller training and test samples for cross-validation.

Parameters

strain	vector containing the training samples for cv
stest	vector containing the test samples for cv

References crossvalidationConfig, python.statsfileInfo::i, python.utils.statsfile2gnuplot::j, sgpp::datadriven::CrossvalidationForRegularizationConfiguration::kfold_, friedman::p, chess::r, create_scripts::s, sgpp::datadriven::CrossvalidationForRegularizationConfiguration::seed_, sgpp::datadriven::CrossvalidationForRegularizationConfiguration::shuffle_, sgpp::datadriven::CrossvalidationForRegularizationConfiguration::silent_, and analyse_erg::tmp.

Referenced by optimizeLambdaCV().

train()

void sgpp::datadriven::SparseGridDensityEstimator::train ( base::Grid &  grid, base::DataVector &  alpha, base::DataMatrix &  train, double  lambdaReg  )

virtual

Does the learning step on a given grid, training set and regularization parameter lambda.

Parameters

grid	grid
alpha	coefficient vector
train	sample set
lambdaReg	regularization parameter

References adaptivityConfig, computeDensitySystemMatrix(), sgpp::op_factory::createOperationEval(), crossvalidationConfig, chess::dim, sgpp::solver::SLESolverConfiguration::eps_, sgpp::base::Grid::getGenerator(), sgpp::base::DataMatrix::getNcols(), sgpp::base::HashGridStorage::getPoint(), sgpp::solver::SGSolver::getResiduum(), sgpp::base::DataVector::getSize(), sgpp::base::Grid::getSize(), sgpp::base::HashGridPoint::getStandardCoordinates(), sgpp::base::Grid::getStorage(), python.utils.sg_projections::gridStorage, python.statsfileInfo::i, sgpp::solver::SLESolverConfiguration::maxIterations_, sgpp::base::AdaptivityConfiguration::noPoints_, sgpp::base::AdaptivityConfiguration::numRefinements_, friedman::p, sgpp::base::GridGenerator::refine(), sgpp::base::DataVector::setAll(), sgpp::datadriven::CrossvalidationForRegularizationConfiguration::silent_, sgpp::solver::ConjugateGradients::solve(), solverConfig, sgpp::solver::SLESolverConfiguration::threshold_, sgpp::base::AdaptivityConfiguration::threshold_, and sgpp::solver::SLESolverConfiguration::verbose_.

Referenced by initialize(), and optimizeLambdaCV().

variance() [1/2]

double sgpp::datadriven::SparseGridDensityEstimator::variance ( )

overridevirtual

Computes the variance of the density function.

Implements sgpp::datadriven::DensityEstimator.

References alpha, and grid.

variance() [2/2]

double sgpp::datadriven::SparseGridDensityEstimator::variance ( base::Grid &  grid, base::DataVector &  alpha  )

protected

References sgpp::op_factory::createOperationFirstMoment(), and sgpp::op_factory::createOperationSecondMoment().

Member Data Documentation

adaptivityConfig

sgpp::base::AdaptivityConfiguration sgpp::datadriven::SparseGridDensityEstimator::adaptivityConfig

protected

Referenced by SparseGridDensityEstimator(), and train().

alpha

std::shared_ptr<base::DataVector> sgpp::datadriven::SparseGridDensityEstimator::alpha

protected

Referenced by cov(), getSurpluses(), initialize(), marginalize(), margToDimX(), mean(), optimizeLambdaCV(), pdf(), python.learner.Classifier.Classifier::refineGrid(), SparseGridDensityEstimator(), and variance().

crossvalidationConfig

CrossvalidationForRegularizationConfiguration sgpp::datadriven::SparseGridDensityEstimator::crossvalidationConfig

protected

Referenced by initialize(), optimizeLambdaCV(), SparseGridDensityEstimator(), splitset(), and train().

grid

std::shared_ptr<base::Grid> sgpp::datadriven::SparseGridDensityEstimator::grid

protected

Referenced by cov(), python.uq.learner.Interpolant.Interpolant::doLearningIteration(), python.learner.Classifier.Classifier::evalError(), python.uq.learner.Interpolant.Interpolant::evalError(), python.uq.learner.SimulationLearner.SimulationLearner::getCollocationNodes(), python.uq.learner.SimulationLearner.SimulationLearner::getGrid(), getGrid(), python.uq.learner.SimulationLearner.SimulationLearner::getLearner(), initialize(), python.uq.learner.Regressor.Regressor::learnData(), python.uq.learner.Regressor.Regressor::learnDataWithFolding(), python.uq.learner.Regressor.Regressor::learnDataWithTest(), marginalize(), margToDimX(), mean(), optimizeLambdaCV(), pdf(), python.learner.Classifier.Classifier::refineGrid(), python.learner.Regressor.Regressor::refineGrid(), python.uq.learner.Regressor.Regressor::refineGrid(), python.uq.learner.SimulationLearner.SimulationLearner::refineGrid(), SparseGridDensityEstimator(), python.learner.Classifier.Classifier::updateResults(), python.learner.Regressor.Regressor::updateResults(), python.uq.learner.Regressor.Regressor::updateResults(), and variance().

gridConfig

sgpp::base::RegularGridConfiguration sgpp::datadriven::SparseGridDensityEstimator::gridConfig

protected

Referenced by createRegularGrid(), getDim(), initialize(), and SparseGridDensityEstimator().

regularizationConfig

sgpp::datadriven::RegularizationConfiguration sgpp::datadriven::SparseGridDensityEstimator::regularizationConfig

protected

Referenced by computeRegularizationMatrix(), and SparseGridDensityEstimator().

samples

std::shared_ptr<base::DataMatrix> sgpp::datadriven::SparseGridDensityEstimator::samples

protected

Referenced by getNsamples(), getSamples(), initialize(), marginalize(), margToDimX(), and SparseGridDensityEstimator().

sgdeConfig

SGDEConfiguration sgpp::datadriven::SparseGridDensityEstimator::sgdeConfig

protected

Referenced by initialize(), and SparseGridDensityEstimator().

solverConfig

sgpp::solver::SLESolverConfiguration sgpp::datadriven::SparseGridDensityEstimator::solverConfig

protected

Referenced by SparseGridDensityEstimator(), and train().

---

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

• datadriven/src/sgpp/datadriven/application/SparseGridDensityEstimator.hpp
• datadriven/src/sgpp/datadriven/application/SparseGridDensityEstimator.cpp