The KDE class is a template class for performing Kernel Density Estimations. More...

#include <kde.hpp>

Public Types
typedef TreeType< MetricType, kde::KDEStat, MatType >	Tree
	Convenience typedef.

Public Member Functions
	KDE (const double relError=KDEDefaultParams::relError, const double absError=KDEDefaultParams::absError, KernelType kernel=KernelType(), const KDEMode mode=KDEDefaultParams::mode, MetricType metric=MetricType(), const bool monteCarlo=KDEDefaultParams::monteCarlo, const double mcProb=KDEDefaultParams::mcProb, const size_t initialSampleSize=KDEDefaultParams::initialSampleSize, const double mcEntryCoef=KDEDefaultParams::mcEntryCoef, const double mcBreakCoef=KDEDefaultParams::mcBreakCoef)
	Initialize KDE object using custom instantiated Metric and Kernel objects. More...

	KDE (const KDE &other)
	Construct KDE object as a copy of the given model. More...

	KDE (KDE &&other)
	Construct KDE object taking ownership of the given model. More...

KDE &	operator= (const KDE &other)
	Copy a KDE model. More...

KDE &	operator= (KDE &&other)
	Move a KDE model. More...

	~KDE ()
	Destroy the KDE object. More...

void	Train (MatType referenceSet)
	Trains the KDE model. More...

void	Train (Tree referenceTree, std::vector< size_t > oldFromNewReferences)
	Trains the KDE model. More...

void	Evaluate (MatType querySet, arma::vec &estimations)
	Estimate density of each point in the query set given the data of the reference set. More...

void	Evaluate (Tree *queryTree, const std::vector< size_t > &oldFromNewQueries, arma::vec &estimations)
	Estimate density of each point in the query set given the data of an already created query tree. More...

void	Evaluate (arma::vec &estimations)
	Estimate density of each point in the reference set given the data of the reference set. More...

const KernelType &	Kernel () const
	Get the kernel.

KernelType &	Kernel ()
	Modify the kernel.

const MetricType &	Metric () const
	Get the metric.

MetricType &	Metric ()
	Modify the metric.

Tree *	ReferenceTree ()
	Get the reference tree.

double	RelativeError () const
	Get relative error tolerance.

void	RelativeError (const double newError)
	Modify relative error tolerance (0 <= newError <= 1).

double	AbsoluteError () const
	Get absolute error tolerance.

void	AbsoluteError (const double newError)
	Modify absolute error tolerance (0 <= newError).

bool	OwnsReferenceTree () const
	Check whether reference tree is owned by the KDE model.

bool	IsTrained () const
	Check whether KDE model is trained or not.

KDEMode	Mode () const
	Get the mode of KDE.

KDEMode &	Mode ()
	Modify the mode of KDE.

bool	MonteCarlo () const
	Get whether Monte Carlo estimations are being used or not.

bool &	MonteCarlo ()
	Modify whether Monte Carlo estimations are being used or not.

double	MCProb () const
	Get Monte Carlo probability of error being bounded by relative error.

void	MCProb (const double newProb)
	Modify Monte Carlo probability of error being bounded by relative error. More...

size_t	MCInitialSampleSize () const
	Get Monte Carlo initial sample size.

size_t &	MCInitialSampleSize ()
	Modify Monte Carlo initial sample size.

double	MCEntryCoef () const
	Get Monte Carlo entry coefficient.

void	MCEntryCoef (const double newCoef)
	Modify Monte Carlo entry coefficient. (newCoef >= 1).

double	MCBreakCoef () const
	Get Monte Carlo break coefficient.

void	MCBreakCoef (const double newCoef)
	Modify Monte Carlo break coefficient. (0 < newCoef <= 1).

template<typename Archive >
void	serialize (Archive &ar, const uint32_t version)
	Serialize the model.

Detailed Description

template<typename KernelType = kernel::GaussianKernel, typename MetricType = mlpack::metric::EuclideanDistance, typename MatType = arma::mat, template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType = tree::KDTree, template< typename RuleType > class DualTreeTraversalType = TreeType<MetricType, kde::KDEStat, MatType>::template DualTreeTraverser, template< typename RuleType > class SingleTreeTraversalType = TreeType<MetricType, kde::KDEStat, MatType>::template SingleTreeTraverser>
class mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >

The KDE class is a template class for performing Kernel Density Estimations.

In statistics, kernel density estimation is a way to estimate the probability density function of a variable in a non parametric way. This implementation performs this estimation using a tree-independent dual-tree algorithm. Details about this algorithm are available in KDERules.

Template Parameters

KernelType	Kernel function to use for KDE calculations.
MetricType	Metric to use for KDE calculations.
MatType	Type of data to use.
TreeType	Type of tree to use; must satisfy the TreeType policy API.
DualTreeTraversalType	Type of dual-tree traversal to use.
SingleTreeTraversalType	Type of single-tree traversal to use.

Constructor & Destructor Documentation

◆ KDE() [1/3]

template<typename KernelType, typename MetricType, typename MatType , template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::KDE	(	const double	relError = `KDEDefaultParams::relError`,
		const double	absError = `KDEDefaultParams::absError`,
		KernelType	kernel = `KernelType()`,
		const KDEMode	mode = `KDEDefaultParams::mode`,
		MetricType	metric = `MetricType()`,
		const bool	monteCarlo = `KDEDefaultParams::monteCarlo`,
		const double	mcProb = `KDEDefaultParams::mcProb`,
		const size_t	initialSampleSize = `KDEDefaultParams::initialSampleSize`,
		const double	mcEntryCoef = `KDEDefaultParams::mcEntryCoef`,
		const double	mcBreakCoef = `KDEDefaultParams::mcBreakCoef`
	)

Initialize KDE object using custom instantiated Metric and Kernel objects.

Parameters

relError	Relative error tolerance of the model.
absError	Absolute error tolerance of the model.
kernel	Instantiated kernel object.
mode	Mode for the algorithm.
metric	Instantiated metric object.
monteCarlo	Whether to use Monte Carlo estimations when possible.
mcProb	Probability of a Monte Carlo estimation to be bounded by relative error tolerance.
initialSampleSize	Initial sample size for Monte Carlo estimations.
mcEntryCoef	Coefficient to control how much larger does the amount of node descendants has to be compared to the initial sample size in order for it to be a candidate for Monte Carlo estimations.
mcBreakCoef	Coefficient to control what fraction of the node's descendants evaluated is the limit before Monte Carlo estimation recurses.

◆ KDE() [2/3]

template<typename KernelType, typename MetricType, typename MatType , template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::KDE ( const KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType > & other )

Construct KDE object as a copy of the given model.

This may be computationally intensive!

Parameters

other KDE object to copy.

◆ KDE() [3/3]

template<typename KernelType, typename MetricType, typename MatType , template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::KDE ( KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType > && other )

Construct KDE object taking ownership of the given model.

Parameters

other KDE object to take ownership of.

◆ ~KDE()

template<typename KernelType , typename MetricType , typename MatType , template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::~KDE ( )

Destroy the KDE object.

If this object created any trees, they will be deleted. If you created the trees then you have to delete them yourself.

Member Function Documentation

◆ Evaluate() [1/3]

template<typename KernelType , typename MetricType , typename MatType, template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

void mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::Evaluate	(	MatType	querySet,
		arma::vec &	estimations
	)

Estimate density of each point in the query set given the data of the reference set.

The result is stored in an estimations vector. Estimations might not be normalized.

Dimension of each point in the query set must match the dimension of each point in the reference set.
Use std::move if the query set is no longer needed.

Precondition: The model has to be previously trained.

Parameters

querySet	Set of query points to get the density of.
estimations	Object which will hold the density of each query point.

◆ Evaluate() [2/3]

template<typename KernelType , typename MetricType , typename MatType, template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

void mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::Evaluate	(	Tree *	queryTree,
		const std::vector< size_t > &	oldFromNewQueries,
		arma::vec &	estimations
	)

Estimate density of each point in the query set given the data of an already created query tree.

The result is stored in an estimations vector. Estimations might not be normalized.

Dimension of each point in the queryTree dataset must match the dimension of each point in the reference set.
Use std::move if the query tree is no longer needed.

Precondition: The model has to be previously trained and mode has to be dual-tree.

Parameters

queryTree	Tree of query points to get the density of.
oldFromNewQueries	Mappings of query points to the tree dataset.
estimations	Object which will hold the density of each query point.

◆ Evaluate() [3/3]

template<typename KernelType , typename MetricType , typename MatType, template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

void mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::Evaluate ( arma::vec & estimations )

Estimate density of each point in the reference set given the data of the reference set.

It does not compute the estimation of a point with itself. The result is stored in an estimations vector. Estimations might not be normalized.

Precondition: The model has to be previously trained.

Parameters

estimations Object which will hold the density of each reference point.

◆ MCProb()

template<typename KernelType , typename MetricType , typename MatType , template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

void mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::MCProb ( const double newProb )

Modify Monte Carlo probability of error being bounded by relative error.

(0 <= newProb < 1).

◆ operator=() [1/2]

template<typename KernelType , typename MetricType , typename MatType , template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType > & mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::operator= ( const KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType > & other )

Copy a KDE model.

Parameters

other KDE model to copy.

◆ operator=() [2/2]

template<typename KernelType , typename MetricType , typename MatType , template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType > & mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::operator= ( KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType > && other )

Move a KDE model.

Parameters

other KDE model to copy.

◆ Train() [1/2]

template<typename KernelType , typename MetricType , typename MatType, template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

void mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::Train ( MatType referenceSet )

Trains the KDE model.

It builds a tree using a reference set.

Use std::move if the reference set is no longer needed.

Parameters

referenceSet Set of reference data.

◆ Train() [2/2]

template<typename KernelType , typename MetricType , typename MatType, template< typename TreeMetricType, typename TreeStatType, typename TreeMatType > class TreeType, template< typename > class DualTreeTraversalType, template< typename > class SingleTreeTraversalType>

void mlpack::kde::KDE< KernelType, MetricType, MatType, TreeType, DualTreeTraversalType, SingleTreeTraversalType >::Train	(	Tree *	referenceTree,
		std::vector< size_t > *	oldFromNewReferences
	)

Trains the KDE model.

Sets the reference tree to an already created tree.

If TreeTraits<TreeType>::RearrangesDataset is false then it is possible to use an empty oldFromNewReferences vector.

Parameters

referenceTree	Built reference tree.
oldFromNewReferences	Permutations of reference points obtained during tree generation.

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

src/mlpack/methods/kde/kde.hpp
src/mlpack/methods/kde/kde_impl.hpp

Public Types

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ KDE() [1/3]

◆ KDE() [2/3]

◆ KDE() [3/3]

◆ ~KDE()

Member Function Documentation

◆ Evaluate() [1/3]

◆ Evaluate() [2/3]

◆ Evaluate() [3/3]

◆ MCProb()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ Train() [1/2]

◆ Train() [2/2]