A conditional of gaussian mixtures indexed by discrete variables, as part of a Bayes Network. This is the result of the elimination of a continuous variable in a hybrid scheme, such that the remaining variables are discrete+continuous. More...

#include <GaussianMixture.h>

Inheritance diagram for gtsam::GaussianMixture:

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Collaboration diagram for gtsam::GaussianMixture:

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Public Types
using	This = GaussianMixture

using	shared_ptr = std::shared_ptr< GaussianMixture >

using	BaseFactor = HybridFactor

using	BaseConditional = Conditional< HybridFactor, GaussianMixture >

using	Conditionals = DecisionTree< Key, GaussianConditional::shared_ptr >
	typedef for Decision Tree of Gaussian Conditionals

typedef Factor	Base
	Our base class.

typedef KeyVector::iterator	iterator
	Iterator over keys.

typedef KeyVector::const_iterator	const_iterator
	Const iterator over keys.

typedef std::pair< typename HybridFactor ::const_iterator, typename HybridFactor ::const_iterator >	ConstFactorRange

typedef ConstFactorRangeIterator	Frontals

typedef ConstFactorRangeIterator	Parents

Public Member Functions
Constructors
	GaussianMixture ()=default
	Default constructor, mainly for serialization.

	GaussianMixture (const KeyVector &continuousFrontals, const KeyVector &continuousParents, const DiscreteKeys &discreteParents, const Conditionals &conditionals)
	Construct a new GaussianMixture object. More...

	GaussianMixture (KeyVector &&continuousFrontals, KeyVector &&continuousParents, DiscreteKeys &&discreteParents, std::vector< GaussianConditional::shared_ptr > &&conditionals)
	Make a Gaussian Mixture from a list of Gaussian conditionals. More...

	GaussianMixture (const KeyVector &continuousFrontals, const KeyVector &continuousParents, const DiscreteKeys &discreteParents, const std::vector< GaussianConditional::shared_ptr > &conditionals)
	Make a Gaussian Mixture from a list of Gaussian conditionals. More...

Testable
bool	equals (const HybridFactor &lf, double tol=1e-9) const override
	Test equality with base HybridFactor.

void	print (const std::string &s="GaussianMixture\, const KeyFormatter &formatter=DefaultKeyFormatter) const override
	Print utility.

Standard API
GaussianConditional::shared_ptr	operator() (const DiscreteValues &discreteValues) const
	Return the conditional Gaussian for the given discrete assignment.

size_t	nrComponents () const
	Returns the total number of continuous components.

KeyVector	continuousParents () const
	Returns the continuous keys among the parents.

double	logNormalizationConstant () const override

std::shared_ptr< GaussianMixtureFactor >	likelihood (const VectorValues &given) const

const Conditionals &	conditionals () const
	Getter for the underlying Conditionals DecisionTree.

AlgebraicDecisionTree< Key >	logProbability (const VectorValues &continuousValues) const
	Compute logProbability of the GaussianMixture as a tree. More...

double	error (const HybridValues &values) const override
	Compute the error of this Gaussian Mixture. More...

AlgebraicDecisionTree< Key >	error (const VectorValues &continuousValues) const
	Compute error of the GaussianMixture as a tree. More...

double	logProbability (const HybridValues &values) const override
	Compute the logProbability of this Gaussian Mixture. More...

double	evaluate (const HybridValues &values) const override
	Calculate probability density for given `values`.

double	operator() (const HybridValues &values) const
	Evaluate probability density, sugar.

void	prune (const DecisionTreeFactor &decisionTree)
	Prune the decision tree of Gaussian factors as per the discrete `decisionTree`. More...

GaussianFactorGraphTree	add (const GaussianFactorGraphTree &sum) const
	Merge the Gaussian Factor Graphs in `this` and `sum` while maintaining the decision tree structure. More...

Testable
bool	equals (const This &other, double tol=1e-9) const
	check equality

virtual void	printKeys (const std::string &s="Factor", const KeyFormatter &formatter=DefaultKeyFormatter) const
	print only keys

Standard Interface
bool	isDiscrete () const
	True if this is a factor of discrete variables only.

bool	isContinuous () const
	True if this is a factor of continuous variables only.

bool	isHybrid () const
	True is this is a Discrete-Continuous factor.

size_t	nrContinuous () const
	Return the number of continuous variables in this factor.

const DiscreteKeys &	discreteKeys () const
	Return the discrete keys for this factor.

const KeyVector &	continuousKeys () const
	Return only the continuous keys for this factor.

Standard Interface
bool	empty () const
	Whether the factor is empty (involves zero variables).

Key	front () const
	First key.

Key	back () const
	Last key.

const_iterator	find (Key key) const
	find

const KeyVector &	keys () const
	Access the factor's involved variable keys.

const_iterator	begin () const

const_iterator	end () const

size_t	size () const

Advanced Interface
KeyVector &	keys ()

iterator	begin ()

iterator	end ()

Testable
bool	equals (const This &c, double tol=1e-9) const

Standard Interface
size_t	nrFrontals () const

size_t	nrParents () const

Key	firstFrontalKey () const

Frontals	frontals () const

Parents	parents () const

double	normalizationConstant () const

Static Protected Member Functions
Standard Constructors
template<typename CONTAINER >
static Factor	FromKeys (const CONTAINER &keys)

template<typename ITERATOR >
static Factor	FromIterators (ITERATOR first, ITERATOR last)

Protected Attributes
DiscreteKeys	discreteKeys_

KeyVector	continuousKeys_
	Record continuous keys for book-keeping.

KeyVector	keys_
	The keys involved in this factor.

size_t	nrFrontals_

Advanced Interface
size_t &	nrFrontals ()

HybridFactor ::const_iterator	beginFrontals () const

HybridFactor ::iterator	beginFrontals ()

HybridFactor ::const_iterator	endFrontals () const

HybridFactor ::iterator	endFrontals ()

HybridFactor ::const_iterator	beginParents () const

HybridFactor ::iterator	beginParents ()

HybridFactor ::const_iterator	endParents () const

HybridFactor ::iterator	endParents ()

static bool	CheckInvariants (const GaussianMixture &conditional, const VALUES &x)

Detailed Description

A conditional of gaussian mixtures indexed by discrete variables, as part of a Bayes Network. This is the result of the elimination of a continuous variable in a hybrid scheme, such that the remaining variables are discrete+continuous.

Represents the conditional density P(X | M, Z) where X is the set of continuous random variables, M is the selection of discrete variables corresponding to a subset of the Gaussian variables and Z is parent of this node .

The probability P(x|y,z,...) is proportional to \( \sum_i k_i \exp - \frac{1}{2} |R_i x - (d_i - S_i y - T_i z - ...)|^2 \) where i indexes the components and k_i is a component-wise normalization constant.

a density over continuous variables given discrete/continuous parents.

Symbolic factors, used to represent a graph structure, implemented in

Member Typedef Documentation

◆ ConstFactorRange

typedef std::pair<typename HybridFactor ::const_iterator, typename HybridFactor ::const_iterator> gtsam::Conditional< HybridFactor , GaussianMixture >::ConstFactorRange

inherited

A mini implementation of an iterator range, to share const views of frontals and parents.

◆ Frontals

typedef ConstFactorRangeIterator gtsam::Conditional< HybridFactor , GaussianMixture >::Frontals

inherited

View of the frontal keys (call frontals())

◆ Parents

typedef ConstFactorRangeIterator gtsam::Conditional< HybridFactor , GaussianMixture >::Parents

inherited

View of the separator keys (call parents())

Constructor & Destructor Documentation

◆ GaussianMixture() [1/3]

gtsam::GaussianMixture::GaussianMixture	(	const KeyVector &	continuousFrontals,
		const KeyVector &	continuousParents,
		const DiscreteKeys &	discreteParents,
		const Conditionals &	conditionals
	)

Construct a new GaussianMixture object.

Parameters

continuousFrontals	the continuous frontals.
continuousParents	the continuous parents.
discreteParents	the discrete parents. Will be placed last.
conditionals	a decision tree of GaussianConditionals. The number of conditionals should be C^(number of discrete parents), where C is the cardinality of the DiscreteKeys in discreteParents, since the discreteParents will be used as the labels in the decision tree.

◆ GaussianMixture() [2/3]

gtsam::GaussianMixture::GaussianMixture	(	KeyVector &&	continuousFrontals,
		KeyVector &&	continuousParents,
		DiscreteKeys &&	discreteParents,
		std::vector< GaussianConditional::shared_ptr > &&	conditionals
	)

Make a Gaussian Mixture from a list of Gaussian conditionals.

Parameters

continuousFrontals	The continuous frontal variables
continuousParents	The continuous parent variables
discreteParents	Discrete parents variables
conditionals	List of conditionals

◆ GaussianMixture() [3/3]

gtsam::GaussianMixture::GaussianMixture	(	const KeyVector &	continuousFrontals,
		const KeyVector &	continuousParents,
		const DiscreteKeys &	discreteParents,
		const std::vector< GaussianConditional::shared_ptr > &	conditionals
	)

Make a Gaussian Mixture from a list of Gaussian conditionals.

Parameters

continuousFrontals	The continuous frontal variables
continuousParents	The continuous parent variables
discreteParents	Discrete parents variables
conditionals	List of conditionals

Member Function Documentation

◆ add()

GaussianFactorGraphTree gtsam::GaussianMixture::add ( const GaussianFactorGraphTree & sum ) const

Merge the Gaussian Factor Graphs in this and sum while maintaining the decision tree structure.

Parameters

sum	Decision Tree of Gaussian Factor Graphs

Returns: GaussianFactorGraphTree

◆ begin() [1/2]

const_iterator gtsam::Factor::begin ( ) const

inlineinherited

Iterator at beginning of involved variable keys

◆ begin() [2/2]

iterator gtsam::Factor::begin ( )

inlineinherited

Iterator at beginning of involved variable keys

◆ beginFrontals() [1/2]

HybridFactor ::const_iterator gtsam::Conditional< HybridFactor , GaussianMixture >::beginFrontals ( ) const

inlineinherited

Iterator pointing to first frontal key.

◆ beginFrontals() [2/2]

HybridFactor ::iterator gtsam::Conditional< HybridFactor , GaussianMixture >::beginFrontals ( )

inlineinherited

Mutable iterator pointing to first frontal key.

◆ beginParents() [1/2]

HybridFactor ::const_iterator gtsam::Conditional< HybridFactor , GaussianMixture >::beginParents ( ) const

inlineinherited

Iterator pointing to the first parent key.

◆ beginParents() [2/2]

HybridFactor ::iterator gtsam::Conditional< HybridFactor , GaussianMixture >::beginParents ( )

inlineinherited

Mutable iterator pointing to the first parent key.

◆ CheckInvariants()

bool gtsam::Conditional< HybridFactor , GaussianMixture >::CheckInvariants	(	const GaussianMixture &	conditional,
		const VALUES &	x
	)

staticinherited

Check invariants of this conditional, given the values x. It tests:

evaluate >= 0.0
evaluate(x) == conditional(x)
exp(logProbability(x)) == evaluate(x)
logNormalizationConstant() = log(normalizationConstant())
error >= 0.0
logProbability(x) == logNormalizationConstant() - error(x)

Parameters

conditional The conditional to test, as a reference to the derived type.

Template Parameters

VALUES HybridValues, or a more narrow type like DiscreteValues.

◆ end() [1/2]

const_iterator gtsam::Factor::end ( ) const

inlineinherited

Iterator at end of involved variable keys

◆ end() [2/2]

iterator gtsam::Factor::end ( )

inlineinherited

Iterator at end of involved variable keys

◆ endFrontals() [1/2]

HybridFactor ::const_iterator gtsam::Conditional< HybridFactor , GaussianMixture >::endFrontals ( ) const

inlineinherited

Iterator pointing past the last frontal key.

◆ endFrontals() [2/2]

HybridFactor ::iterator gtsam::Conditional< HybridFactor , GaussianMixture >::endFrontals ( )

inlineinherited

Mutable iterator pointing past the last frontal key.

◆ endParents() [1/2]

HybridFactor ::const_iterator gtsam::Conditional< HybridFactor , GaussianMixture >::endParents ( ) const

inlineinherited

Iterator pointing past the last parent key.

◆ endParents() [2/2]

HybridFactor ::iterator gtsam::Conditional< HybridFactor , GaussianMixture >::endParents ( )

inlineinherited

Mutable iterator pointing past the last parent key.

◆ equals()

bool gtsam::Conditional< HybridFactor , GaussianMixture >::equals	(	const This &	c,
		double	tol = `1e-9`
	)		const

inherited

check equality

◆ error() [1/2]

double gtsam::GaussianMixture::error ( const HybridValues & values ) const

overridevirtual

Compute the error of this Gaussian Mixture.

This requires some care, as different mixture components may have different normalization constants. Let's consider p(x|y,m), where m is discrete. We need the error to satisfy the invariant:

error(x;y,m) = K - log(probability(x;y,m))

For all x,y,m. But note that K, the (log) normalization constant defined in Conditional.h, should not depend on x, y, or m, only on the parameters of the density. Hence, we delegate to the underlying Gaussian conditionals, indexed by m, which do satisfy:

log(probability_m(x;y)) = K_m - error_m(x;y)

We resolve by having K == max(K_m) and

error(x;y,m) = error_m(x;y) + K - K_m

which also makes error(x;y,m) >= 0 for all x,y,m.

Parameters

values Continuous values and discrete assignment.

Returns: double

Reimplemented from gtsam::Factor.

◆ error() [2/2]

AlgebraicDecisionTree<Key> gtsam::GaussianMixture::error ( const VectorValues & continuousValues ) const

Compute error of the GaussianMixture as a tree.

Parameters

continuousValues The continuous VectorValues.

Returns: AlgebraicDecisionTree<Key> A decision tree on the discrete keys only, with the leaf values as the error for each assignment.

◆ firstFrontalKey()

Key gtsam::Conditional< HybridFactor , GaussianMixture >::firstFrontalKey ( ) const

inlineinherited

Convenience function to get the first frontal key

◆ FromIterators()

template<typename ITERATOR >

static Factor gtsam::Factor::FromIterators	(	ITERATOR	first,
		ITERATOR	last
	)

inlinestaticprotectedinherited

Construct factor from iterator keys. This is called internally from derived factor static factor methods, as a workaround for not being able to call the protected constructors above.

◆ FromKeys()

template<typename CONTAINER >

static Factor gtsam::Factor::FromKeys ( const CONTAINER & keys )

inlinestaticprotectedinherited

Construct factor from container of keys. This is called internally from derived factor static factor methods, as a workaround for not being able to call the protected constructors above.

◆ frontals()

Frontals gtsam::Conditional< HybridFactor , GaussianMixture >::frontals ( ) const

inlineinherited

return a view of the frontal keys

◆ keys()

KeyVector& gtsam::Factor::keys ( )

inlineinherited

Returns: keys involved in this factor

◆ likelihood()

std::shared_ptr<GaussianMixtureFactor> gtsam::GaussianMixture::likelihood ( const VectorValues & given ) const

Create a likelihood factor for a Gaussian mixture, return a Mixture factor on the parents.

◆ logNormalizationConstant()

double gtsam::GaussianMixture::logNormalizationConstant ( ) const

inlineoverridevirtual

The log normalization constant is max of the the individual log-normalization constants.

Reimplemented from gtsam::Conditional< HybridFactor, GaussianMixture >.

◆ logProbability() [1/2]

AlgebraicDecisionTree<Key> gtsam::GaussianMixture::logProbability ( const VectorValues & continuousValues ) const

Compute logProbability of the GaussianMixture as a tree.

Parameters

continuousValues The continuous VectorValues.

Returns: AlgebraicDecisionTree<Key> A decision tree with the same keys as the conditionals, and leaf values as the logProbability.

◆ logProbability() [2/2]

double gtsam::GaussianMixture::logProbability ( const HybridValues & values ) const

overridevirtual

Compute the logProbability of this Gaussian Mixture.

Parameters

values Continuous values and discrete assignment.

Returns: double

Reimplemented from gtsam::Conditional< HybridFactor, GaussianMixture >.

◆ normalizationConstant()

double gtsam::Conditional< HybridFactor , GaussianMixture >::normalizationConstant ( ) const

inherited

Non-virtual, exponentiate logNormalizationConstant.

◆ nrFrontals() [1/2]

size_t gtsam::Conditional< HybridFactor , GaussianMixture >::nrFrontals ( ) const

inlineinherited

return the number of frontals

◆ nrFrontals() [2/2]

size_t& gtsam::Conditional< HybridFactor , GaussianMixture >::nrFrontals ( )

inlineinherited

Mutable version of nrFrontals

◆ nrParents()

size_t gtsam::Conditional< HybridFactor , GaussianMixture >::nrParents ( ) const

inlineinherited

return the number of parents

◆ parents()

Parents gtsam::Conditional< HybridFactor , GaussianMixture >::parents ( ) const

inlineinherited

return a view of the parent keys

◆ prune()

void gtsam::GaussianMixture::prune ( const DecisionTreeFactor & decisionTree )

Prune the decision tree of Gaussian factors as per the discrete decisionTree.

Parameters

decisionTree A pruned decision tree of discrete keys where the leaves are probabilities.

◆ size()

size_t gtsam::Factor::size ( ) const

inlineinherited

Returns: the number of variables involved in this factor

Member Data Documentation

◆ nrFrontals_

size_t gtsam::Conditional< HybridFactor , GaussianMixture >::nrFrontals_

protectedinherited

The first nrFrontal variables are frontal and the rest are parents.

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

/home/docs/checkouts/readthedocs.org/user_builds/gtsam-jlblanco-docs/checkouts/latest/gtsam/hybrid/GaussianMixture.h

Public Types

Public Member Functions

Static Protected Member Functions

Protected Attributes

Advanced Interface

Detailed Description

Member Typedef Documentation

◆ ConstFactorRange

◆ Frontals

◆ Parents

Constructor & Destructor Documentation

◆ GaussianMixture() [1/3]

◆ GaussianMixture() [2/3]

◆ GaussianMixture() [3/3]

Member Function Documentation

◆ add()

◆ begin() [1/2]

◆ begin() [2/2]

◆ beginFrontals() [1/2]

◆ beginFrontals() [2/2]

◆ beginParents() [1/2]

◆ beginParents() [2/2]

◆ CheckInvariants()

◆ end() [1/2]

◆ end() [2/2]

◆ endFrontals() [1/2]

◆ endFrontals() [2/2]

◆ endParents() [1/2]

◆ endParents() [2/2]

◆ equals()

◆ error() [1/2]

◆ error() [2/2]

◆ firstFrontalKey()

◆ FromIterators()

◆ FromKeys()

◆ frontals()

◆ keys()

◆ likelihood()

◆ logNormalizationConstant()

◆ logProbability() [1/2]

◆ logProbability() [2/2]

◆ normalizationConstant()

◆ nrFrontals() [1/2]

◆ nrFrontals() [2/2]

◆ nrParents()

◆ parents()

◆ prune()

◆ size()

Member Data Documentation

◆ nrFrontals_