jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter > Class Reference

Inherits java::io::Serializable.

List of all members.

Public Member Functions

abstract double F (ParamD T)
 Computes the log normalizer $ F( \mathbf{\Theta} ) $.
abstract ParamD gradF (ParamD T)
 Computes $ \nabla F ( \mathbf{\Theta} )$.
double DivergenceF (ParamD TP, ParamD TQ)
 Computes $ div F $.
abstract double G (ParamD H)
 Computes $ G(\mathbf{H})$.
abstract ParamD gradG (ParamD H)
 Computes $ \nabla G (\mathbf{H})$.
double DivergenceG (ParamD HP, ParamD HQ)
 Computes $ div G $.
abstract ParamD t (ParamX x)
 Computes the sufficient statistic $ t(x)$.
abstract double k (ParamX x)
 Computes the carrier measure $ k(x) $.
abstract ParamD Lambda2Theta (ParamD L)
 Converts source parameters to natural parameters.
abstract ParamD Theta2Lambda (ParamD T)
 Converts natural parameters to source parameters.
abstract ParamD Lambda2Eta (ParamD L)
 Converts source parameters to expectation parameters.
abstract ParamD Eta2Lambda (ParamD H)
 Converts expectation parameters to source parameters.
ParamD Theta2Eta (ParamD T)
 Converts natural parameters to expectation parameters.
ParamD Eta2Theta (ParamD H)
 Converts expectation parameters to natural parameters.
double density (ParamX x, ParamD T)
 Computes the density value $ f(x;\mathbf{\Theta}) $ of an exponential family member.
double BD (ParamD T1, ParamD T2)
 Computes the Bregman divergence between two members of a same exponential family.
abstract double KLD (ParamD LP, ParamD LQ)
 Computes the Kullback-Leibler divergence between two members of a same exponential family.
ParamD GeodesicPoint (ParamD T1, ParamD T2, double alpha)
 Computes the geodesic point.
abstract ParamX drawRandomPoint (ParamD L)
 Draws a random point from the considered distribution.

Detailed Description

Author:
Vincent Garcia

Frank Nielsen

Version:
1.0

License

See file LICENSE.txt

Description

This class integrates the Kullback-Leibler divergence and conversion procedures inside the exponential family.

Member Function Documentation

double jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.BD ( ParamD  T1,
ParamD  T2 
)

Computes the Bregman divergence between two members of a same exponential family.

Parameters:
T1 natural parameters $ \mathbf{\Theta}_1$
T2 natural parameters $ \mathbf{\Theta}_2$
Returns:
$ BD( \mathbf{\Theta_1} \| \mathbf{\Theta_2} ) = F(\mathbf{\Theta_1}) - F(\mathbf{\Theta_2}) - \langle \mathbf{\Theta_1} - \mathbf{\Theta_2} , \nabla F(\mathbf{\Theta_2}) \rangle $

double jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.density ( ParamX  x,
ParamD  T 
)

Computes the density value $ f(x;\mathbf{\Theta}) $ of an exponential family member.

Parameters:
x a point
T natural parameters $ \mathbf{\Theta} $
Returns:
$ f(x) = \exp \left( \langle \mathbf{\Theta} \ , \ t(x) \rangle - F(\mathbf{\Theta}) + k(x) \right) $

double jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.DivergenceF ( ParamD  TP,
ParamD  TQ 
)

Computes $ div F $.

Parameters:
TP natural parameters $ \mathbf{\Theta}_P$
TQ natural parameters $ \mathbf{\Theta}_Q$
Returns:
$ div F( \mathbf{\Theta}_P \| \mathbf{\Theta}_Q ) = F(\mathbf{\Theta}_P) - F(\mathbf{\Theta}_Q) - \langle \mathbf{\Theta}_P-\mathbf{\Theta}_Q , \nabla F(\mathbf{\Theta}_Q) \rangle$

double jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.DivergenceG ( ParamD  HP,
ParamD  HQ 
)

Computes $ div G $.

Parameters:
HP expectation parameters $ \mathbf{H}_P$
HQ expectation parameters $ \mathbf{H}_Q$
Returns:
$ div G( \mathbf{H}_P \| \mathbf{H}_Q ) = G(\mathbf{H}_P) - G(\mathbf{H}_Q) - \langle \mathbf{H}_P-\mathbf{H}_Q , \nabla G(\mathbf{H}_Q) \rangle$

abstract ParamX jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.drawRandomPoint ( ParamD  L  )  [pure virtual]

Draws a random point from the considered distribution.

Parameters:
L source parameters $ \mathbf{\Lambda}$
Returns:
a point

abstract ParamD jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.Eta2Lambda ( ParamD  H  )  [pure virtual]

Converts expectation parameters to source parameters.

Parameters:
H expectation parameters $ \mathbf{H} $
Returns:
source parameters $ \mathbf{\Lambda} $

ParamD jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.Eta2Theta ( ParamD  H  ) 

Converts expectation parameters to natural parameters.

Parameters:
H expectation parameters $ \mathbf{H} $
Returns:
natural parameters $ \mathbf{\Theta} $

abstract double jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.F ( ParamD  T  )  [pure virtual]

Computes the log normalizer $ F( \mathbf{\Theta} ) $.

Parameters:
T natural parameters $ \mathbf{\Theta}$
Returns:
$ F(\mathbf{\Theta}) $

abstract double jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.G ( ParamD  H  )  [pure virtual]

Computes $ G(\mathbf{H})$.

Parameters:
H expectation parameters $ \mathbf{H} $
Returns:
$ G(\mathbf{H}) $

ParamD jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.GeodesicPoint ( ParamD  T1,
ParamD  T2,
double  alpha 
)

Computes the geodesic point.

Parameters:
T1 natural parameters $ \mathbf{\Theta}_1$
T2 natural parameters $ \mathbf{\Theta}_2$
alpha position $ \alpha $ of the point on the geodesic link
Returns:
$ \nabla G \left( (1-\alpha) \nabla F (\mathbf{\Theta}_1) + \alpha \nabla F (\mathbf{\Theta}_2) \right) $

abstract ParamD jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.gradF ( ParamD  T  )  [pure virtual]

Computes $ \nabla F ( \mathbf{\Theta} )$.

Parameters:
T expectation parameters $ \mathbf{\Theta} $
Returns:
$ \nabla F( \mathbf{\Theta} ) $

abstract ParamD jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.gradG ( ParamD  H  )  [pure virtual]

Computes $ \nabla G (\mathbf{H})$.

Parameters:
H expectation parameters $ \mathbf{H} $
Returns:
$ \nabla G(\mathbf{H}) $

abstract double jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.k ( ParamX  x  )  [pure virtual]

Computes the carrier measure $ k(x) $.

Parameters:
x a point
Returns:
$ k(x) $

abstract double jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.KLD ( ParamD  LP,
ParamD  LQ 
) [pure virtual]

Computes the Kullback-Leibler divergence between two members of a same exponential family.

Parameters:
LP source parameters $ \mathbf{\Lambda}_P $
LQ source parameters $ \mathbf{\Lambda}_Q $
Returns:
$ D_{\mathrm{KL}}(f_P\|f_Q) $

abstract ParamD jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.Lambda2Eta ( ParamD  L  )  [pure virtual]

Converts source parameters to expectation parameters.

Parameters:
L source parameters $ \mathbf{\Lambda} $
Returns:
expected parameters $ \mathbf{H} $

abstract ParamD jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.Lambda2Theta ( ParamD  L  )  [pure virtual]

Converts source parameters to natural parameters.

Parameters:
L source parameters $ \mathbf{\Lambda} $
Returns:
natural parameters $ \mathbf{\Theta} $

abstract ParamD jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.t ( ParamX  x  )  [pure virtual]

Computes the sufficient statistic $ t(x)$.

Parameters:
x a point
Returns:
$ t(x) $

ParamD jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.Theta2Eta ( ParamD  T  ) 

Converts natural parameters to expectation parameters.

Parameters:
T natural parameters $ \mathbf{\Theta}$
Returns:
expectation parameters $ \mathbf{H} $

abstract ParamD jMEF.ExponentialFamily< ParamX extends Parameter, ParamD extends Parameter >.Theta2Lambda ( ParamD  T  )  [pure virtual]

Converts natural parameters to source parameters.

Parameters:
T natural parameters $ \mathbf{\Theta}$
Returns:
source parameters $ \mathbf{\Lambda} $

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