Multivariate Gaussian Distribution. More...

#include <xmmGaussianDistribution.hpp>

Inheritance diagram for xmm::GaussianDistribution:

Collaboration diagram for xmm::GaussianDistribution:

Public Types
enum	CovarianceMode { CovarianceMode::Full = 0, CovarianceMode::Diagonal = 1 }
	Covariance Mode. More...

Public Member Functions
	GaussianDistribution (bool bimodal=false, unsigned int dimension=1, unsigned int dimension_input=0, CovarianceMode covariance_mode=CovarianceMode::Full)
	Default Constructor. More...

	GaussianDistribution (GaussianDistribution const &src)
	Copy constructor. More...

	GaussianDistribution (Json::Value const &root)
	Constructor from Json Structure. More...

GaussianDistribution &	operator= (GaussianDistribution const &src)
	Assignment. More...

Likelihood & Regression
double	likelihood (const float *observation) const
	Get Likelihood of a data vector. More...

double	likelihood_input (const float *observation_input) const
	Get Likelihood of a data vector for input modality. More...

double	likelihood_bimodal (const float observation_input, const float observation_output) const
	Get Likelihood of a data vector for bimodal mode. More...

void	regression (std::vector< float > const &observation_input, std::vector< float > &predicted_output) const
	Linear Regression using the Gaussian Distribution (covariance-based) More...

Utilities
void	regularize (std::vector< double > regularization)
	Add offset to the diagonal of the covariance matrix. More...

void	updateInverseCovariance ()
	Compute inverse covariance matrix. More...

Ellipse	toEllipse (unsigned int dimension1, unsigned int dimension2)
	Compute the 68%?? Confidence Interval ellipse of the Gaussian. More...

void	fromEllipse (Ellipse const &gaussian_ellipse, unsigned int dimension1, unsigned int dimension2)
	Sets the parameters of the Gaussian distribution according to the 68%?? Confidence Interval ellipse. More...

JSON I/O
Json::Value	toJson () const
	Write the object to a JSON Structure. More...

void	fromJson (Json::Value const &root)
	Read the object from a JSON Structure. More...

Python File I/O
void	writeFile (char *fileName) const
	write method for python wrapping ('write' keyword forbidden, name has to be different) More...

void	readFile (char *fileName)
	read method for python wrapping ('read' keyword forbidden, name has to be different) More...

std::string	__str__ () const
	"print" method for python => returns the results of write method More...

Conversion & Extraction
Attribute< unsigned int >	dimension
	Convert to bimodal distribution in place. More...

Attribute< unsigned int >	dimension_input
	Input Dimension of the multivariate normal. More...

std::vector< double >	mean
	Mean of the Gaussian Distribution. More...

Attribute< CovarianceMode >	covariance_mode
	Covariance Mode. More...

std::vector< double >	covariance
	Covariance Matrix of the Gaussian Distribution. More...

std::vector< double >	output_covariance
	Conditional Output Variance (updated when covariances matrices are inverted) More...

bool	bimodal_
	Defines if regression parameters need to be computed. More...

double	covariance_determinant_
	Determinant of the covariance matrix. More...

std::vector< double >	inverse_covariance_
	Inverse covariance matrix. More...

double	covariance_determinant_input_
	Determinant of the covariance matrix of the input modality. More...

std::vector< double >	inverse_covariance_input_
	Inverse covariance matrix of the input modality. More...

void	allocate ()
	Resize Mean and Covariance Vectors to appropriate dimension. More...

virtual void	onAttributeChange (AttributeBase *attr_pointer)
	notification function called when a member attribute is changed More...

void	updateOutputCovariance ()
	Compute the conditional variance vector of the output modality (conditioned over the input). More...

Detailed Description

Multivariate Gaussian Distribution.

Full covariance, optionally multimodal with support for regression

Member Enumeration Documentation

enum xmm::GaussianDistribution::CovarianceMode

strong

Covariance Mode.

Enumerator
Full	Full covariance.
Diagonal	Diagonal covariance (diagonal matrix)

Constructor & Destructor Documentation

xmm::GaussianDistribution::GaussianDistribution	(	bool	bimodal = `false`,
		unsigned int	dimension = `1`,
		unsigned int	dimension_input = `0`,
		CovarianceMode	covariance_mode = `CovarianceMode::Full`
	)

Default Constructor.

Parameters

bimodal	specify if the distribution is bimodal for use in regression
dimension	dimension of the distribution
dimension_input	dimension of the input modality in bimodal mode.
covariance_mode	covariance mode (full vs diagonal)

xmm::GaussianDistribution::GaussianDistribution ( GaussianDistribution const & src )

Copy constructor.

Parameters

src	source distribution

xmm::GaussianDistribution::GaussianDistribution ( Json::Value const & root )

explicit

Constructor from Json Structure.

Parameters

root	Json Value

Member Function Documentation

std::string xmm::Writable::__str__ ( ) const

inlineinherited

"print" method for python => returns the results of write method

Warning: only defined if SWIGPYTHON is defined

void xmm::GaussianDistribution::allocate ( )

protected

Resize Mean and Covariance Vectors to appropriate dimension.

void xmm::GaussianDistribution::fromEllipse	(	Ellipse const &	gaussian_ellipse,
		unsigned int	dimension1,
		unsigned int	dimension2
	)

Sets the parameters of the Gaussian distribution according to the 68%?? Confidence Interval ellipse.

the ellipse is 2D, and is therefore projected over 2 axes

Parameters

gaussian_ellipse	68% Confidence Interval ellipse parameters (1x std)
dimension1	index of the first axis
dimension2	index of the second axis

Exceptions

out_of_range if the dimensions are out of bounds

void xmm::GaussianDistribution::fromJson ( Json::Value const & root )

virtual

Read the object from a JSON Structure.

Parameters

root	JSON value containing the object's information

Exceptions

JsonException if the JSON value has a wrong format

Implements xmm::Writable.

double xmm::GaussianDistribution::likelihood ( const float * observation ) const

Get Likelihood of a data vector.

Parameters

observation data observation (must be of size dimension)

Returns: likelihood

Exceptions

runtime_error if the Covariance Matrix is not invertible

double xmm::GaussianDistribution::likelihood_bimodal	(	const float *	observation_input,
		const float *	observation_output
	)		const

Get Likelihood of a data vector for bimodal mode.

Parameters

observation_input	observation of the input modality
observation_output	observation of the output modality

Exceptions

runtime_error	if the Covariance Matrix is not invertible
runtime_error	if the model is not bimodal

Returns: likelihood

double xmm::GaussianDistribution::likelihood_input ( const float * observation_input ) const

Get Likelihood of a data vector for input modality.

Parameters

observation_input observation (must be of size dimension_input)

Returns: likelihood

Exceptions

runtime_error	if the Covariance Matrix of the input modality is not invertible
runtime_error	if the model is not bimodal

void xmm::GaussianDistribution::onAttributeChange ( AttributeBase * attr_pointer )

protectedvirtual

notification function called when a member attribute is changed

xmm::GaussianDistribution & xmm::GaussianDistribution::operator= ( GaussianDistribution const & src )

Assignment.

Parameters

src	source distribution

void xmm::Writable::readFile ( char * fileName )

inlineinherited

read method for python wrapping ('read' keyword forbidden, name has to be different)

Warning: only defined if SWIGPYTHON is defined

void xmm::GaussianDistribution::regression	(	std::vector< float > const &	observation_input,
		std::vector< float > &	predicted_output
	)		const

Linear Regression using the Gaussian Distribution (covariance-based)

Parameters

observation_input	input observation (must be of size: dimension_input)
predicted_output	predicted output vector (size: dimension-dimension_input)

Exceptions

runtime_error if the model is not bimodal

void xmm::GaussianDistribution::regularize ( std::vector< double > regularization )

Add offset to the diagonal of the covariance matrix.

Ensures convergence + generalization on few examples

xmm::Ellipse xmm::GaussianDistribution::toEllipse	(	unsigned int	dimension1,
		unsigned int	dimension2
	)

Compute the 68%?? Confidence Interval ellipse of the Gaussian.

the ellipse is 2D, and is therefore projected over 2 axes

Parameters

dimension1	index of the first axis
dimension2	index of the second axis

Exceptions

out_of_range if the dimensions are out of bounds

Returns: ellipse parameters

Json::Value xmm::GaussianDistribution::toJson ( ) const

virtual

Write the object to a JSON Structure.

Returns: Json value containing the object's information

Implements xmm::Writable.

void xmm::GaussianDistribution::updateInverseCovariance ( )

Compute inverse covariance matrix.

Exceptions

runtime_error if the covariance matrix is not invertible

void xmm::GaussianDistribution::updateOutputCovariance ( )

protected

Compute the conditional variance vector of the output modality (conditioned over the input).

Exceptions

runtime_error if the model is not bimodal

void xmm::Writable::writeFile ( char * fileName ) const

inlineinherited

write method for python wrapping ('write' keyword forbidden, name has to be different)

Warning: only defined if SWIGPYTHON is defined

Member Data Documentation

bool xmm::GaussianDistribution::bimodal_

protected

Defines if regression parameters need to be computed.

std::vector<double> xmm::GaussianDistribution::covariance

Covariance Matrix of the Gaussian Distribution.

double xmm::GaussianDistribution::covariance_determinant_

protected

Determinant of the covariance matrix.

double xmm::GaussianDistribution::covariance_determinant_input_

protected

Determinant of the covariance matrix of the input modality.

Attribute<CovarianceMode> xmm::GaussianDistribution::covariance_mode

Covariance Mode.

Attribute<unsigned int> xmm::GaussianDistribution::dimension

Convert to bimodal distribution in place.

Parameters

dimension_input dimension of the input modality

Exceptions

runtime_error	if the model is already bimodal
out_of_range	if the requested input dimension is too large Convert to unimodal distribution in place
runtime_error	if the model is already unimodal extract a sub-distribution with the given columns

Parameters

columns columns indices in the target order

Exceptions

runtime_error	if the model is training
out_of_range	if the number or indices of the requested columns exceeds the current dimension

Returns: a Gaussian Distribution from the current model considering only the target columns extract the sub-distribution of the input modality

Exceptions

runtime_error if the model is training or if it is not bimodal

Returns: a unimodal Gaussian Distribution of the input modality from the current bimodal model extract the sub-distribution of the output modality

Exceptions

runtime_error if the model is training or if it is not bimodal

Returns: a unimodal Gaussian Distribution of the output modality from the current bimodal model extract the model with reversed input and output modalities

Exceptions

runtime_error if the model is training or if it is not bimodal

Returns: a bimodal Gaussian Distribution that swaps the input and output modalities Total Dimension of the multivariate normal

Attribute<unsigned int> xmm::GaussianDistribution::dimension_input

Input Dimension of the multivariate normal.

std::vector<double> xmm::GaussianDistribution::inverse_covariance_

protected

Inverse covariance matrix.

std::vector<double> xmm::GaussianDistribution::inverse_covariance_input_

protected

Inverse covariance matrix of the input modality.

std::vector<double> xmm::GaussianDistribution::mean

Mean of the Gaussian Distribution.

std::vector<double> xmm::GaussianDistribution::output_covariance

Conditional Output Variance (updated when covariances matrices are inverted)

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

XMM - Probabilistic Models for Motion Recognition and Mapping

Public Types

Public Member Functions

Conversion & Extraction

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation