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:

[legend]

Public Types
using	BaseConditional = Conditional< HybridFactor, GaussianMixture >

using	BaseFactor = HybridFactor

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

using	shared_ptr = std::shared_ptr< GaussianMixture >

using	This = GaussianMixture

Public Types inherited from gtsam::HybridFactor
typedef Factor	Base
	Our base class. More...

typedef std::shared_ptr< HybridFactor >	shared_ptr
	shared_ptr to this class More...

typedef HybridFactor	This
	This class. More...

Public Types inherited from gtsam::Factor
typedef KeyVector::const_iterator	const_iterator
	Const iterator over keys. More...

typedef KeyVector::iterator	iterator
	Iterator over keys. More...

Public Types inherited from gtsam::Conditional< HybridFactor, GaussianMixture >
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. More...

	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. More...

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

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

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

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

double	logNormalizationConstant () const override

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

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

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`. More...

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

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...

Public Member Functions inherited from gtsam::HybridFactor
	HybridFactor ()=default

	HybridFactor (const KeyVector &keys)
	Construct hybrid factor from continuous keys. More...

	HybridFactor (const DiscreteKeys &discreteKeys)
	Construct hybrid factor from discrete keys. More...

	HybridFactor (const KeyVector &continuousKeys, const DiscreteKeys &discreteKeys)
	Construct a new Hybrid Factor object. More...

void	print (const std::string &s="HybridFactor\, const KeyFormatter &formatter=DefaultKeyFormatter) const override
	print More...

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

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

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

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

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

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

Public Member Functions inherited from gtsam::Factor
virtual	~Factor ()=default
	Default destructor. More...

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

Key	front () const
	First key. More...

Key	back () const
	Last key. More...

const_iterator	find (Key key) const
	find More...

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

const_iterator	begin () const

const_iterator	end () const

size_t	size () const

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

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

KeyVector &	keys ()

iterator	begin ()

iterator	end ()

Public Member Functions inherited from gtsam::Conditional< HybridFactor, GaussianMixture >
void	print (const std::string &s="Conditional", const KeyFormatter &formatter=DefaultKeyFormatter) const

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

virtual	~Conditional ()

size_t	nrFrontals () const

size_t	nrParents () const

Key	firstFrontalKey () const

Frontals	frontals () const

Parents	parents () const

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

double	normalizationConstant () const

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 ()

Private Member Functions
bool	allFrontalsGiven (const VectorValues &given) const
	Check whether `given` has values for all frontal keys. More...

GaussianFactorGraphTree	asGaussianFactorGraphTree () const
	Convert a DecisionTree of factors into a DT of Gaussian FGs. More...

std::function< GaussianConditional::shared_ptr(const Assignment< Key > &, const GaussianConditional::shared_ptr &)>	prunerFunc (const DecisionTreeFactor &decisionTree)
	Helper function to get the pruner functor. More...

Private Attributes
Conditionals	conditionals_
	a decision tree of Gaussian conditionals. More...

double	logConstant_
	log of the normalization constant. More...

Additional Inherited Members
Static Public Member Functions inherited from gtsam::Conditional< HybridFactor, GaussianMixture >
static bool	CheckInvariants (const GaussianMixture &conditional, const VALUES &x)

Protected Member Functions inherited from gtsam::Factor
	Factor ()

template<typename CONTAINER >
	Factor (const CONTAINER &keys)

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

Protected Member Functions inherited from gtsam::Conditional< HybridFactor, GaussianMixture >
	Conditional ()

	Conditional (size_t nrFrontals)

Static Protected Member Functions inherited from gtsam::Factor
template<typename CONTAINER >
static Factor	FromKeys (const CONTAINER &keys)

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

Protected Attributes inherited from gtsam::HybridFactor
KeyVector	continuousKeys_
	Record continuous keys for book-keeping. More...

DiscreteKeys	discreteKeys_

Protected Attributes inherited from gtsam::Factor
KeyVector	keys_
	The keys involved in this factor. More...

Protected Attributes inherited from gtsam::Conditional< HybridFactor, GaussianMixture >
size_t	nrFrontals_

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

Definition at line 53 of file GaussianMixture.h.

Member Typedef Documentation

◆ BaseConditional

using gtsam::GaussianMixture::BaseConditional = Conditional<HybridFactor, GaussianMixture>

Definition at line 60 of file GaussianMixture.h.

◆ BaseFactor

using gtsam::GaussianMixture::BaseFactor = HybridFactor

Definition at line 59 of file GaussianMixture.h.

◆ Conditionals

using gtsam::GaussianMixture::Conditionals = DecisionTree<Key, GaussianConditional::shared_ptr>

typedef for Decision Tree of Gaussian Conditionals

Definition at line 63 of file GaussianMixture.h.

◆ shared_ptr

using gtsam::GaussianMixture::shared_ptr = std::shared_ptr<GaussianMixture>

Definition at line 58 of file GaussianMixture.h.

◆ This

using gtsam::GaussianMixture::This = GaussianMixture

Definition at line 57 of file GaussianMixture.h.

Constructor & Destructor Documentation

◆ GaussianMixture() [1/4]

gtsam::GaussianMixture::GaussianMixture ( )

default

Default constructor, mainly for serialization.

◆ GaussianMixture() [2/4]

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.

Definition at line 31 of file GaussianMixture.cpp.

◆ GaussianMixture() [3/4]

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

Definition at line 57 of file GaussianMixture.cpp.

◆ GaussianMixture() [4/4]

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

Definition at line 65 of file GaussianMixture.cpp.

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

Definition at line 75 of file GaussianMixture.cpp.

◆ allFrontalsGiven()

bool gtsam::GaussianMixture::allFrontalsGiven ( const VectorValues & given ) const

private

Check whether given has values for all frontal keys.

Definition at line 178 of file GaussianMixture.cpp.

◆ asGaussianFactorGraphTree()

GaussianFactorGraphTree gtsam::GaussianMixture::asGaussianFactorGraphTree ( ) const

private

Convert a DecisionTree of factors into a DT of Gaussian FGs.

Definition at line 88 of file GaussianMixture.cpp.

◆ conditionals()

const GaussianMixture::Conditionals & gtsam::GaussianMixture::conditionals ( ) const

Getter for the underlying Conditionals DecisionTree.

Definition at line 52 of file GaussianMixture.cpp.

◆ continuousParents()

KeyVector gtsam::GaussianMixture::continuousParents ( ) const

Returns the continuous keys among the parents.

Definition at line 162 of file GaussianMixture.cpp.

◆ equals()

bool gtsam::GaussianMixture::equals	(	const HybridFactor &	lf,
		double	tol = `1e-9`
	)		const

overridevirtual

Test equality with base HybridFactor.

Reimplemented from gtsam::HybridFactor.

Definition at line 118 of file GaussianMixture.cpp.

◆ 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.

Definition at line 329 of file GaussianMixture.cpp.

◆ 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.

Definition at line 318 of file GaussianMixture.cpp.

◆ evaluate()

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

overridevirtual

Calculate probability density for given values.

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

Definition at line 343 of file GaussianMixture.cpp.

◆ 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.

Definition at line 188 of file GaussianMixture.cpp.

◆ 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 >.

Definition at line 161 of file GaussianMixture.h.

◆ 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.

Definition at line 300 of file GaussianMixture.cpp.

◆ 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 >.

Definition at line 337 of file GaussianMixture.cpp.

◆ nrComponents()

size_t gtsam::GaussianMixture::nrComponents ( ) const

Returns the total number of continuous components.

Definition at line 96 of file GaussianMixture.cpp.

◆ operator()() [1/2]

GaussianConditional::shared_ptr gtsam::GaussianMixture::operator() ( const DiscreteValues & discreteValues ) const

Return the conditional Gaussian for the given discrete assignment.

Definition at line 105 of file GaussianMixture.cpp.

◆ operator()() [2/2]

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

inline

Evaluate probability density, sugar.

Definition at line 231 of file GaussianMixture.h.

◆ print()

void gtsam::GaussianMixture::print	(	const std::string &	s = `"GaussianMixture\n"`,
		const KeyFormatter &	formatter = `DefaultKeyFormatter`
	)		const

overridevirtual

Print utility.

Reimplemented from gtsam::Factor.

Definition at line 136 of file GaussianMixture.cpp.

◆ 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.

Definition at line 288 of file GaussianMixture.cpp.

◆ prunerFunc()

std::function< GaussianConditional::shared_ptr(const Assignment< Key > &, const GaussianConditional::shared_ptr &)> gtsam::GaussianMixture::prunerFunc ( const DecisionTreeFactor & decisionTree )

private

Helper function to get the pruner functor.

Helper function to get the pruner functional.

Parameters

decisionTree The pruned discrete probability decision tree.

Returns: std::function<GaussianConditional::shared_ptr( const Assignment<Key> &, const GaussianConditional::shared_ptr &)>

Parameters

decisionTree The probability decision tree of only discrete keys.

Returns: std::function<GaussianConditional::shared_ptr( const Assignment<Key> &, const GaussianConditional::shared_ptr &)>

Definition at line 237 of file GaussianMixture.cpp.

Member Data Documentation

◆ conditionals_

Conditionals gtsam::GaussianMixture::conditionals_

private

a decision tree of Gaussian conditionals.

Definition at line 66 of file GaussianMixture.h.

◆ logConstant_

double gtsam::GaussianMixture::logConstant_

private

log of the normalization constant.

Definition at line 67 of file GaussianMixture.h.

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

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ BaseConditional

◆ BaseFactor

◆ Conditionals

◆ shared_ptr

◆ This

Constructor & Destructor Documentation

◆ GaussianMixture() [1/4]

◆ GaussianMixture() [2/4]

◆ GaussianMixture() [3/4]

◆ GaussianMixture() [4/4]

Member Function Documentation

◆ add()

◆ allFrontalsGiven()

◆ asGaussianFactorGraphTree()

◆ conditionals()

◆ continuousParents()

◆ equals()

◆ error() [1/2]

◆ error() [2/2]

◆ evaluate()

◆ likelihood()

◆ logNormalizationConstant()

◆ logProbability() [1/2]

◆ logProbability() [2/2]

◆ nrComponents()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ print()

◆ prune()

◆ prunerFunc()

Member Data Documentation

◆ conditionals_

◆ logConstant_