The multivariate Laplace distribution centered at 0 has pdf. More...

Public Member Functions
	LaplaceDistribution ()
	Default constructor, which creates a Laplace distribution with zero dimension and zero scale parameter. More...

	LaplaceDistribution (const size_t dimensionality, const double scale)
	Construct the Laplace distribution with the given scale and dimensionality. More...

	LaplaceDistribution (const arma::vec &mean, const double scale)
	Construct the Laplace distribution with the given mean and scale parameter. More...

size_t	Dimensionality () const
	Return the dimensionality of this distribution. More...

void	Estimate (const arma::mat &observations)
	Estimate the Laplace distribution directly from the given observations. More...

void	Estimate (const arma::mat &observations, const arma::vec &probabilities)
	Estimate the Laplace distribution from the given observations, taking into account the probability of each observation actually being from this distribution. More...

double	LogProbability (const arma::vec &observation) const
	Return the log probability of the given observation. More...

void	LogProbability (const arma::mat &x, arma::vec &logProbabilities) const
	Evaluate log probability density function of given observation. More...

const arma::vec &	Mean () const
	Return the mean. More...

arma::vec &	Mean ()
	Modify the mean. More...

double	Probability (const arma::vec &observation) const
	Return the probability of the given observation. More...

void	Probability (const arma::mat &x, arma::vec &probabilities) const
	Evaluate probability density function of given observation. More...

arma::vec	Random () const
	Return a randomly generated observation according to the probability distribution defined by this object. More...

double	Scale () const
	Return the scale parameter. More...

double &	Scale ()
	Modify the scale parameter. More...

template < typename Archive >
void	serialize (Archive &ar, const uint32_t)
	Serialize the distribution. More...

Detailed Description

The multivariate Laplace distribution centered at 0 has pdf.

$f(x|\theta) = \frac{1}{2 \theta}\exp\left(-\frac{\|x - \mu\|}{\theta}\right)$

given scale parameter $\theta$ and mean $\mu$ . This implementation assumes a diagonal covariance, but a rewrite to support arbitrary covariances is possible.

See the following paper for more information on the non-diagonal-covariance Laplace distribution and estimation techniques:

@article{eltoft2006multivariate,
  title={{On the Multivariate Laplace Distribution}},
  author={Eltoft, Torbj\orn and Kim, Taesu and Lee, Te-Won},
  journal={IEEE Signal Processing Letters},
  volume={13},
  number={5},
  pages={300--304},
  year={2006}
}

Note that because of the diagonal covariance restriction, much of the algebra in the paper above becomes simplified, and the PDF takes roughly the same form as the univariate case.

Definition at line 50 of file laplace_distribution.hpp.

Constructor & Destructor Documentation

◆ LaplaceDistribution() [1/3]

LaplaceDistribution ( )

inline

Default constructor, which creates a Laplace distribution with zero dimension and zero scale parameter.

Definition at line 57 of file laplace_distribution.hpp.

◆ LaplaceDistribution() [2/3]

LaplaceDistribution	(	const size_t	dimensionality,
		const double	scale
	)

inline

Construct the Laplace distribution with the given scale and dimensionality.

The mean is initialized to zero.

Parameters

dimensionality	Dimensionality of distribution.
scale	Scale of distribution.

Definition at line 66 of file laplace_distribution.hpp.

◆ LaplaceDistribution() [3/3]

LaplaceDistribution	(	const arma::vec &	mean,
		const double	scale
	)

inline

Construct the Laplace distribution with the given mean and scale parameter.

Parameters

mean	Mean of distribution.
scale	Scale of distribution.

Definition at line 76 of file laplace_distribution.hpp.

Member Function Documentation

◆ Dimensionality()

size_t Dimensionality ( ) const

inline

Return the dimensionality of this distribution.

Definition at line 80 of file laplace_distribution.hpp.

◆ Estimate() [1/2]

void Estimate ( const arma::mat & observations )

Estimate the Laplace distribution directly from the given observations.

Parameters

observations List of observations.

Referenced by LaplaceDistribution::Random().

◆ Estimate() [2/2]

void Estimate	(	const arma::mat &	observations,
		const arma::vec &	probabilities
	)

Estimate the Laplace distribution from the given observations, taking into account the probability of each observation actually being from this distribution.

◆ LogProbability() [1/2]

double LogProbability ( const arma::vec & observation ) const

Return the log probability of the given observation.

Parameters

observation Point to evaluate logarithm of probability.

Referenced by LaplaceDistribution::LogProbability(), and LaplaceDistribution::Probability().

◆ LogProbability() [2/2]

void LogProbability	(	const arma::mat &	x,
		arma::vec &	logProbabilities
	)		const

inline

Evaluate log probability density function of given observation.

Parameters

x	List of observations.
logProbabilities	Output probabilities for each input observation.

Definition at line 113 of file laplace_distribution.hpp.

References LaplaceDistribution::LogProbability().

◆ Mean() [1/2]

const arma::vec& Mean ( ) const

inline

Return the mean.

Definition at line 163 of file laplace_distribution.hpp.

◆ Mean() [2/2]

arma::vec& Mean ( )

inline

Modify the mean.

Definition at line 165 of file laplace_distribution.hpp.

◆ Probability() [1/2]

double Probability ( const arma::vec & observation ) const

inline

Return the probability of the given observation.

Parameters

observation Point to evaluate probability at.

Definition at line 87 of file laplace_distribution.hpp.

References LaplaceDistribution::LogProbability().

◆ Probability() [2/2]

void Probability	(	const arma::mat &	x,
		arma::vec &	probabilities
	)		const

Evaluate probability density function of given observation.

Parameters

x	List of observations.
probabilities	Output probabilities for each input observation.

◆ Random()

arma::vec Random ( ) const

inline

Return a randomly generated observation according to the probability distribution defined by this object.

This is inlined for speed.

Returns: Random observation from this Laplace distribution.

Definition at line 128 of file laplace_distribution.hpp.

References LaplaceDistribution::Estimate().

◆ Scale() [1/2]

double Scale ( ) const

inline

Return the scale parameter.

Definition at line 168 of file laplace_distribution.hpp.

◆ Scale() [2/2]

double& Scale ( )

inline

Modify the scale parameter.

Definition at line 170 of file laplace_distribution.hpp.

◆ serialize()

void serialize	(	Archive &	ar,
		const uint32_t
	)

inline

Serialize the distribution.

Definition at line 176 of file laplace_distribution.hpp.

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

/home/ryan/src/mlpack.org/_src/mlpack-git/src/mlpack/core/dists/laplace_distribution.hpp

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ LaplaceDistribution() [1/3]

◆ LaplaceDistribution() [2/3]

◆ LaplaceDistribution() [3/3]

Member Function Documentation

◆ Dimensionality()

◆ Estimate() [1/2]

◆ Estimate() [2/2]

◆ LogProbability() [1/2]

◆ LogProbability() [2/2]

◆ Mean() [1/2]

◆ Mean() [2/2]

◆ Probability() [1/2]

◆ Probability() [2/2]

◆ Random()

◆ Scale() [1/2]

◆ Scale() [2/2]

◆ serialize()