Gaussian kernel density estimate over a ParticleSet. More...

#include <EmrysFilter/Distributions/KernelDensity.h>

Public Types
using	SpaceType = Space_
	the particles' space
using	ParamsType = ParticleSet<Space_, Scalar_, Allocator_>
	the particles it reads
using	allocator_type = Allocator_
	the particles' allocator
using	KernelType
	The zero-mean kernel, in the linear tangent space of Space_.
using	MomentsType = typename ParamsType::MomentsType
	a mean and covariance together
using	Scalar = typename ParamsType::Scalar
	the scalar type
using	Index = typename ParamsType::Index
	Eigen's index type.
using	VectorType = typename ParamsType::VectorType
	a value, such as a state
using	DifferenceVectorType = typename ParamsType::DifferenceVectorType
	a difference
using	MatrixType = typename ParamsType::MatrixType
	a matrix over differences
using	SampleSetType = typename ParamsType::SampleSetType
	states as columns

Public Member Functions
Index	size () const
Index	valueDimension () const
Index	differenceDimension () const
Space_ const &	space () const
ParamsType const &	particles () const
Scalar	logTotalWeight () const
MatrixType const &	bandwidth () const
KernelType::DensityType	kernel () const
MomentsType	moments () const
template<ExecutionPolicy P>
MomentsType	moments (P &&policy) const
	moments() under policy: the particles' moments are reductions over them (see Execution policies).
template<typename Derived>
Scalar	logDensity (Eigen::MatrixBase< Derived > const &x) const
template<ExecutionPolicy P, typename Derived>
Scalar	logDensity (P &&policy, Eigen::MatrixBase< Derived > const &x) const
	logDensity() under policy: a log-sum-exp over the particles, reduced over chunks of them (see Execution policies).
template<typename Derived>
Scalar	density (Eigen::MatrixBase< Derived > const &x) const

Static Public Attributes
static constexpr int	ValueDimensionAtCompileTime = ParamsType::ValueDimensionAtCompileTime
	the length of a state, or Eigen::Dynamic
static constexpr int	MaxValueDimensionAtCompileTime = ParamsType::MaxValueDimensionAtCompileTime
	a bound on the length of a state, or Eigen::Dynamic
static constexpr int	DifferenceDimensionAtCompileTime = ParamsType::DifferenceDimensionAtCompileTime
	the length of a difference and the rows of the bandwidth, or Eigen::Dynamic
static constexpr int	MaxDifferenceDimensionAtCompileTime = ParamsType::MaxDifferenceDimensionAtCompileTime
	a bound on the length of a difference, or Eigen::Dynamic

Detailed Description

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>
class Emrys::KernelDensity< Space_, Scalar_, Allocator_ >

Gaussian kernel density estimate over a ParticleSet.

Represents the density

\[ \hat p(x) = \sum_i \hat w_i \, \mathcal{N}(x; x_i, H), \]

where \( x_i \) are the particles, \( \hat w_i \) their normalized weights, and \( H \) the bandwidth (kernel covariance), which is factorized once and shared by every kernel: a weighted kernel density estimate with a multivariate Gaussian kernel (Silverman (1986), as given in Multivariate KDE).

Created by ParticleSet::toDensity(). It checks the source set for changes, as its copies do: reading it after the set has changed is a programmer error (decisions.md [view-stamp]). A KernelDensity must not outlive its source.

See also: ParticleSet::toDensity(), silvermanBandwidth()

Member Typedef Documentation

◆ KernelType

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

using Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::KernelType

Initial value:

GaussianParams<Linear<DifferenceDimensionAtCompileTime, MaxDifferenceDimensionAtCompileTime>, Scalar_>

Emrys::GaussianParams

A Gaussian distribution: a mean and covariance in a space.

Definition Gaussian.h:259

The zero-mean kernel, in the linear tangent space of Space_.

Member Function Documentation

◆ bandwidth()

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

MatrixType const & Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::bandwidth ( ) const

inlinenodiscard

Returns: the kernel covariance \( H \)

◆ density()

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

template<typename Derived>

Scalar Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::density ( Eigen::MatrixBase< Derived > const & x ) const

inlinenodiscard

Returns: the density \( \hat p(x) \) at x

Warning: Underflows easily in high dimensions; prefer logDensity().

See also: logDensity()

◆ differenceDimension()

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

Index Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::differenceDimension ( ) const

inlinenodiscard

Returns: the number of rows and columns of the bandwidth

◆ kernel()

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

KernelType::DensityType Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::kernel ( ) const

inlinenodiscard

Returns: a view of the zero-mean kernel \( \mathcal{N}(0, H) \). It must not outlive this estimate.

◆ logDensity()

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

template<typename Derived>

Scalar Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::logDensity ( Eigen::MatrixBase< Derived > const & x ) const

inlinenodiscard

Returns: the log of the density at x

Costs one triangular solve per particle, each into a vector sized by the space, so it allocates nothing for a bounded space. It writes nothing, so it may be evaluated at several points at once.

See also: density()

◆ logTotalWeight()

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

Scalar Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::logTotalWeight ( ) const

inlinenodiscard

Returns: the log of the sum of the (unnormalized) particle weights

◆ moments()

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

MomentsType Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::moments ( ) const

inlinenodiscard

Returns: the mean and covariance of the estimate: the particles' mean, and their weighted covariance plus \( H \).

◆ particles()

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

ParamsType const & Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::particles ( ) const

inlinenodiscard

Returns: the particles; a programmer error if they have changed since toDensity()

◆ size()

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

Index Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::size ( ) const

inlinenodiscard

Returns: the number of particles

◆ space()

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

Space_ const & Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::space ( ) const

inlinenodiscard

Returns: the particles' space

◆ valueDimension()

template<Space Space_, RealScalar Scalar_ = double, typename Allocator_ = DefaultAllocator>

Index Emrys::KernelDensity< Space_, Scalar_, Allocator_ >::valueDimension ( ) const

inlinenodiscard

Returns: the number of coordinates of every particle state

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

EmrysFilter/Distributions/KernelDensity.h

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ KernelType

Member Function Documentation

◆ bandwidth()

◆ density()

◆ differenceDimension()

◆ kernel()

◆ logDensity()

◆ logTotalWeight()

◆ moments()

◆ particles()

◆ size()

◆ space()

◆ valueDimension()