The density of a Mixture whose components have been factorized: a read-only view. More...

#include <EmrysFilter/Distributions/Mixture.h>

Public Types
using	ParamsType = MixtureParams<Component_, Allocator_>
	the parameters it reads
using	ComponentType = Params<Component_>
	a component
using	SpaceType = typename ParamsType::SpaceType
	the components' space
using	allocator_type = Allocator_
	the parameters' allocator
using	Entry = typename ParamsType::Entry
	one weighted component
using	const_iterator = typename ParamsType::const_iterator
	iterates the entries
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 mean
using	DifferenceVectorType = typename ParamsType::DifferenceVectorType
	a difference
using	MatrixType = typename ParamsType::MatrixType
	a matrix over differences

Public Member Functions
Index	size () const
Index	valueDimension () const
Index	differenceDimension () const
SpaceType const &	space () const
allocator_type	get_allocator () const
const_iterator	begin () const
const_iterator	end () const
ParamsType::Entry const &	operator[] (Index i) const
Scalar	logTotalWeight () const
Scalar	ess () const
Index	mostProbable () const
ComponentType	collapsed () const
MomentsType	moments () const
template<typename Derived>
Scalar	logDensity (Eigen::MatrixBase< Derived > const &x) const
template<typename Derived>
Scalar	density (Eigen::MatrixBase< Derived > const &x) const
template<typename Path>
auto	marginal () const
	marginal() of the subspace named by the tag path Path; see MixtureParams::marginal().
template<typename Path>
auto	marginal (Index element) const
	marginal() of one repetition of a repeated block; see GaussianParams::marginal(element).
template<typename GivenPath, typename Derived> requires (isGaussian<ComponentType>)
auto	conditional (Eigen::MatrixBase< Derived > const &values) const

Static Public Attributes
static constexpr int	ValueDimensionAtCompileTime = ParamsType::ValueDimensionAtCompileTime
	the length of a value, or Eigen::Dynamic
static constexpr int	MaxValueDimensionAtCompileTime = ParamsType::MaxValueDimensionAtCompileTime
	a bound on the length of a value, or Eigen::Dynamic
static constexpr int	DifferenceDimensionAtCompileTime = ParamsType::DifferenceDimensionAtCompileTime
	the length of a difference and the rows of a covariance, or Eigen::Dynamic
static constexpr int	MaxDifferenceDimensionAtCompileTime = ParamsType::MaxDifferenceDimensionAtCompileTime
	a bound on the length of a difference, or Eigen::Dynamic
static constexpr bool	IsParams = false
	a view: it checks its parameters

Detailed Description

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>
class Emrys::Mixture< Component_, Allocator_ >

The density of a Mixture whose components have been factorized: a read-only view.

Represents the normalized density

\[ p(x) = \frac{\sum_i w_i \, p_i(x)}{\sum_i w_i}, \]

with \( p_i \) the density of component \( i \), read from its factorization under this view's check (see ComponentTraits).

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

See also: class MixtureParams

Member Function Documentation

◆ begin()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

const_iterator Emrys::Mixture< Component_, Allocator_ >::begin ( ) const

inlinenodiscard

Returns: an iterator to the first entry

◆ collapsed()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

ComponentType Emrys::Mixture< Component_, Allocator_ >::collapsed ( ) const

inlinenodiscard

Returns: the mixture as one component, moment-matched over the components with their normalized weights (see ComponentTraits): for Gaussian components the Gaussian with moments(), and for hybrid components the hybrid whose mode probabilities are the weighted sums and whose conditionals are collapsed per mode

◆ conditional()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

template<typename GivenPath, typename Derived>
requires (isGaussian<ComponentType>)

auto Emrys::Mixture< Component_, Allocator_ >::conditional ( Eigen::MatrixBase< Derived > const & values ) const

inlinenodiscard

Returns: a copy of the conditional distribution; see MixtureParams::conditional().

◆ density()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

template<typename Derived>

Scalar Emrys::Mixture< Component_, Allocator_ >::density ( Eigen::MatrixBase< Derived > const & x ) const

inlinenodiscard

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

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

See also: logDensity()

◆ differenceDimension()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

Index Emrys::Mixture< Component_, Allocator_ >::differenceDimension ( ) const

inlinenodiscard

Returns: the number of rows and columns of every component's covariance

◆ end()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

const_iterator Emrys::Mixture< Component_, Allocator_ >::end ( ) const

inlinenodiscard

Returns: an iterator past the last entry

◆ ess()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

Scalar Emrys::Mixture< Component_, Allocator_ >::ess ( ) const

inlinenodiscard

Returns: the effective sample size \( 1 / \sum_i \hat w_i^2 \) of the normalized weights, between 1 and size()

◆ get_allocator()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

allocator_type Emrys::Mixture< Component_, Allocator_ >::get_allocator ( ) const

inlinenodiscard

Returns: the source's allocator

◆ logDensity()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

template<typename Derived>

Scalar Emrys::Mixture< Component_, Allocator_ >::logDensity ( Eigen::MatrixBase< Derived > const & x ) const

inlinenodiscard

Returns: the log of the density at x: the log-sum-exp of each component's log-weight plus its log-density, less the log of the total weight (LogSumExp). It reads the components' factorizations under this view's check and makes none of its own, so it may be evaluated at several points at once.

See also: density()

◆ logTotalWeight()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

Scalar Emrys::Mixture< Component_, Allocator_ >::logTotalWeight ( ) const

inlinenodiscard

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

◆ moments()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

MomentsType Emrys::Mixture< Component_, Allocator_ >::moments ( ) const

inlinenodiscard

Returns: the mean and covariance of the mixture, \( \mu = \sum_i \hat w_i \mu_i \) and \( \Sigma = \sum_i \hat w_i \left(\Sigma_i + (\mu_i - \mu)(\mu_i - \mu)^T\right) \), where \( \hat w_i \) are the normalized weights. In a non-linear space the mean is a tangent-space mean and the deviations are \( \mu_i \boxminus \mu \).

Only the lower triangle of each component covariance is read; the result is symmetric. It allocates nothing sized by the number of components.

◆ mostProbable()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

Index Emrys::Mixture< Component_, Allocator_ >::mostProbable ( ) const

inlinenodiscard

Returns: the index of the most probable component, the one with the largest weight; ties go to the lowest. The factorization checked the weights, so none is NaN.

See also: MixtureParams::mostProbable()

◆ operator[]()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

ParamsType::Entry const & Emrys::Mixture< Component_, Allocator_ >::operator[] ( Index i ) const

inlinenodiscard

Returns: entry i of the source, which must be less than size()

◆ size()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

Index Emrys::Mixture< Component_, Allocator_ >::size ( ) const

inlinenodiscard

Returns: the number of components

◆ space()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

SpaceType const & Emrys::Mixture< Component_, Allocator_ >::space ( ) const

inlinenodiscard

Returns: the source's space

◆ valueDimension()

template<internal::ComponentOrInfoForm Component_, typename Allocator_ = DefaultAllocator>

Index Emrys::Mixture< Component_, Allocator_ >::valueDimension ( ) const

inlinenodiscard

Returns: the number of coordinates of every component's mean

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

EmrysFilter/Distributions/Mixture.h

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ begin()

◆ collapsed()

◆ conditional()

◆ density()

◆ differenceDimension()

◆ end()

◆ ess()

◆ get_allocator()

◆ logDensity()

◆ logTotalWeight()

◆ moments()

◆ mostProbable()

◆ operator[]()

◆ size()

◆ space()

◆ valueDimension()