SHOGUN
4.1.0
|
Class that models a Student's-t likelihood.
\[ p(y|f)=\prod_{i=1}^{n} \frac{\Gamma(\frac{\nu+1}{2})} {\Gamma(\frac{\nu}{2})\sqrt{\nu\pi}\sigma} \left(1+\frac{(y_i-f_i)^2}{\nu\sigma^2} \right)^{-\frac{\nu+1}{2}} \]
The hyperparameters of the Student's t-likelihood model are \(\sigma\) - scale parameter, and \(\nu\) - degrees of freedom.
Definition at line 58 of file StudentsTLikelihood.h.
Static Public Member Functions | |
static CStudentsTLikelihood * | obtain_from_generic (CLikelihoodModel *likelihood) |
Public Attributes | |
SGIO * | io |
Parallel * | parallel |
Version * | version |
Parameter * | m_parameters |
Parameter * | m_model_selection_parameters |
Parameter * | m_gradient_parameters |
uint32_t | m_hash |
Protected Member Functions | |
virtual void | load_serializable_pre () throw (ShogunException) |
virtual void | load_serializable_post () throw (ShogunException) |
virtual void | save_serializable_pre () throw (ShogunException) |
virtual void | save_serializable_post () throw (ShogunException) |
default constructor
Definition at line 263 of file StudentsTLikelihood.cpp.
CStudentsTLikelihood | ( | float64_t | sigma, |
float64_t | df | ||
) |
constructor
sigma | noise variance |
df | degrees of freedom |
Definition at line 268 of file StudentsTLikelihood.cpp.
|
virtual |
Definition at line 284 of file StudentsTLikelihood.cpp.
|
inherited |
Builds a dictionary of all parameters in SGObject as well of those of SGObjects that are parameters of this object. Dictionary maps parameters to the objects that own them.
dict | dictionary of parameters to be built. |
Definition at line 597 of file SGObject.cpp.
|
virtualinherited |
Creates a clone of the current object. This is done via recursively traversing all parameters, which corresponds to a deep copy. Calling equals on the cloned object always returns true although none of the memory of both objects overlaps.
Definition at line 714 of file SGObject.cpp.
|
virtualinherited |
A deep copy. All the instance variables will also be copied.
Definition at line 198 of file SGObject.cpp.
Recursively compares the current SGObject to another one. Compares all registered numerical parameters, recursion upon complex (SGObject) parameters. Does not compare pointers!
May be overwritten but please do with care! Should not be necessary in most cases.
other | object to compare with |
accuracy | accuracy to use for comparison (optional) |
tolerant | allows linient check on float equality (within accuracy) |
Definition at line 618 of file SGObject.cpp.
float64_t get_degrees_freedom | ( | ) | const |
get degrees of freedom
Definition at line 99 of file StudentsTLikelihood.h.
|
virtual |
get derivative of log likelihood \(log(P(y|f))\) with respect to given parameter
lab | labels used |
func | function location |
param | parameter |
Reimplemented from CLikelihoodModel.
Definition at line 411 of file StudentsTLikelihood.cpp.
|
virtual |
returns the first moment of a given (unnormalized) probability distribution \(q(f_i) = Z_i^-1 p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2)\), where \( Z_i=\int p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2) df_i\).
This method is useful for EP local likelihood approximation.
mu | mean of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
s2 | variance of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
lab | labels \(y_i\) |
i | index i |
Implements CLikelihoodModel.
Definition at line 634 of file StudentsTLikelihood.cpp.
|
virtualinherited |
returns the first moment of a given (unnormalized) probability distribution \(q(f_i) = Z_i^-1 p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2)\) for each \(f_i\), where \( Z_i=\int p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2) df_i\).
Wrapper method which calls get_first_moment multiple times.
mu | mean of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
s2 | variance of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
lab | labels \(y_i\) |
Definition at line 72 of file LikelihoodModel.cpp.
|
inherited |
|
inherited |
|
inherited |
|
virtual |
get derivative of log likelihood \(log(P(y|f))\) with respect to function location \(f\)
lab | labels used |
func | function location |
i | index, choices are 1, 2, and 3 for first, second, and third derivatives respectively |
Implements CLikelihoodModel.
Definition at line 356 of file StudentsTLikelihood.cpp.
|
virtual |
returns the logarithm of the point-wise likelihood \(log(p(y_i|f_i))\) for each label \(y_i\).
One can evaluate log-likelihood like: \(log(p(y|f)) = \sum_{i=1}^{n} log(p(y_i|f_i))\)
lab | labels \(y_i\) |
func | values of the function \(f_i\) |
Implements CLikelihoodModel.
Definition at line 323 of file StudentsTLikelihood.cpp.
|
virtualinherited |
Returns the log-likelihood \(log(p(y|f)) = \sum_{i=1}^{n} log(p(y_i|f_i))\) for each of the provided functions \( f \) in the given matrix.
Wrapper method which calls get_log_probability_f multiple times.
lab | labels \(y_i\) |
F | values of the function \(f_i\) where each column of the matrix is one function \( f \). |
Definition at line 51 of file LikelihoodModel.cpp.
|
virtual |
returns the zeroth moment of a given (unnormalized) probability distribution:
\[ log(Z_i) = log\left(\int p(y_i|f_i) \mathcal{N}(f_i|\mu,\sigma^2) df_i\right) \]
for each \(f_i\).
mu | mean of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
s2 | variance of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
lab | labels \(y_i\) |
Implements CLikelihoodModel.
Definition at line 570 of file StudentsTLikelihood.cpp.
|
virtual |
get model type
Reimplemented from CLikelihoodModel.
Definition at line 156 of file StudentsTLikelihood.h.
|
inherited |
Definition at line 498 of file SGObject.cpp.
|
inherited |
Returns description of a given parameter string, if it exists. SG_ERROR otherwise
param_name | name of the parameter |
Definition at line 522 of file SGObject.cpp.
|
inherited |
Returns index of model selection parameter with provided index
param_name | name of model selection parameter |
Definition at line 535 of file SGObject.cpp.
|
virtual |
returns the name of the likelihood model
Implements CSGObject.
Definition at line 77 of file StudentsTLikelihood.h.
|
virtualinherited |
returns the logarithm of the predictive density of \(y_*\):
\[ log(p(y_*|X,y,x_*)) = log\left(\int p(y_*|f_*) p(f_*|X,y,x_*) df_*\right) \]
which approximately equals to
\[ log\left(\int p(y_*|f_*) \mathcal{N}(f_*|\mu,\sigma^2) df_*\right) \]
where normal distribution \(\mathcal{N}(\mu,\sigma^2)\) is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\).
NOTE: if lab equals to NULL, then each \(y_*\) equals to one.
mu | posterior mean of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
s2 | posterior variance of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
lab | labels \(y_*\) |
Reimplemented in CSoftMaxLikelihood.
Definition at line 45 of file LikelihoodModel.cpp.
|
virtual |
returns mean of the predictive marginal \(p(y_*|X,y,x_*)\).
NOTE: if lab equals to NULL, then each \(y_*\) equals to one.
mu | posterior mean of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
s2 | posterior variance of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
lab | labels \(y_*\) |
Implements CLikelihoodModel.
Definition at line 300 of file StudentsTLikelihood.cpp.
|
virtual |
returns variance of the predictive marginal \(p(y_*|X,y,x_*)\).
NOTE: if lab equals to NULL, then each \(y_*\) equals to one.
mu | posterior mean of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
s2 | posterior variance of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
lab | labels \(y_*\) |
Implements CLikelihoodModel.
Definition at line 306 of file StudentsTLikelihood.cpp.
|
virtual |
get derivative of the first derivative of log likelihood with respect to function location, i.e. \(\frac{\partial log(P(y|f))}{\partial f}\) with respect to given parameter
lab | labels used |
func | function location |
param | parameter |
Reimplemented from CLikelihoodModel.
Definition at line 466 of file StudentsTLikelihood.cpp.
|
virtual |
returns the second moment of a given (unnormalized) probability distribution \(q(f_i) = Z_i^-1 p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2)\), where \( Z_i=\int p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2) df_i\).
This method is useful for EP local likelihood approximation.
mu | mean of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
s2 | variance of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
lab | labels \(y_i\) |
i | index i |
Implements CLikelihoodModel.
Definition at line 676 of file StudentsTLikelihood.cpp.
|
virtualinherited |
returns the second moment of a given (unnormalized) probability distribution \(q(f_i) = Z_i^-1 p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2)\) for each \(f_i\), where \( Z_i=\int p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2) df_i\).
Wrapper method which calls get_second_moment multiple times.
mu | mean of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
s2 | variance of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
lab | labels \(y_i\) |
Definition at line 89 of file LikelihoodModel.cpp.
float64_t get_sigma | ( | ) | const |
returns the scale paramter
Definition at line 83 of file StudentsTLikelihood.h.
|
virtual |
get derivative of the second derivative of log likelihood with respect to function location, i.e. \(\frac{\partial^{2} log(P(y|f))}{\partial f^{2}}\) with respect to given parameter
lab | labels used |
func | function location |
param | parameter |
Reimplemented from CLikelihoodModel.
Definition at line 516 of file StudentsTLikelihood.cpp.
|
virtualinherited |
If the SGSerializable is a class template then TRUE will be returned and GENERIC is set to the type of the generic.
generic | set to the type of the generic if returning TRUE |
Definition at line 296 of file SGObject.cpp.
|
virtualinherited |
Load this object from file. If it will fail (returning FALSE) then this object will contain inconsistent data and should not be used!
file | where to load from |
prefix | prefix for members |
Definition at line 369 of file SGObject.cpp.
|
protectedvirtualinherited |
Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_POST is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.
Definition at line 426 of file SGObject.cpp.
|
protectedvirtualinherited |
Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_PRE is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 421 of file SGObject.cpp.
|
static |
helper method used to specialize a base class instance
likelihood | likelihood model |
Definition at line 288 of file StudentsTLikelihood.cpp.
|
virtualinherited |
Definition at line 262 of file SGObject.cpp.
|
inherited |
prints all parameter registered for model selection and their type
Definition at line 474 of file SGObject.cpp.
|
virtualinherited |
prints registered parameters out
prefix | prefix for members |
Definition at line 308 of file SGObject.cpp.
|
virtualinherited |
Save this object to file.
file | where to save the object; will be closed during returning if PREFIX is an empty string. |
prefix | prefix for members |
Definition at line 314 of file SGObject.cpp.
|
protectedvirtualinherited |
Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_POST is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel.
Definition at line 436 of file SGObject.cpp.
|
protectedvirtualinherited |
Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_PRE is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 431 of file SGObject.cpp.
void set_degrees_freedom | ( | float64_t | df | ) |
set degrees of freedom
df | degrees of freedom |
Definition at line 105 of file StudentsTLikelihood.h.
|
inherited |
Definition at line 41 of file SGObject.cpp.
|
inherited |
Definition at line 46 of file SGObject.cpp.
|
inherited |
Definition at line 51 of file SGObject.cpp.
|
inherited |
Definition at line 56 of file SGObject.cpp.
|
inherited |
Definition at line 61 of file SGObject.cpp.
|
inherited |
Definition at line 66 of file SGObject.cpp.
|
inherited |
Definition at line 71 of file SGObject.cpp.
|
inherited |
Definition at line 76 of file SGObject.cpp.
|
inherited |
Definition at line 81 of file SGObject.cpp.
|
inherited |
Definition at line 86 of file SGObject.cpp.
|
inherited |
Definition at line 91 of file SGObject.cpp.
|
inherited |
Definition at line 96 of file SGObject.cpp.
|
inherited |
Definition at line 101 of file SGObject.cpp.
|
inherited |
Definition at line 106 of file SGObject.cpp.
|
inherited |
Definition at line 111 of file SGObject.cpp.
|
inherited |
set generic type to T
|
inherited |
|
inherited |
set the parallel object
parallel | parallel object to use |
Definition at line 241 of file SGObject.cpp.
|
inherited |
set the version object
version | version object to use |
Definition at line 283 of file SGObject.cpp.
void set_sigma | ( | float64_t | sigma | ) |
sets the scale parameter
sigma | scale parameter |
Definition at line 89 of file StudentsTLikelihood.h.
|
virtualinherited |
A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.
Reimplemented in CGaussianKernel.
Definition at line 192 of file SGObject.cpp.
|
virtualinherited |
return whether likelihood function supports binary classification
Reimplemented in CVariationalLikelihood, CProbitLikelihood, and CLogitLikelihood.
Definition at line 329 of file LikelihoodModel.h.
|
virtualinherited |
return whether likelihood function supports multiclass classification
Reimplemented in CSoftMaxLikelihood, and CVariationalLikelihood.
Definition at line 335 of file LikelihoodModel.h.
|
virtual |
return whether Student's likelihood function supports regression
Reimplemented from CLikelihoodModel.
Definition at line 280 of file StudentsTLikelihood.h.
|
inherited |
unset generic type
this has to be called in classes specializing a template class
Definition at line 303 of file SGObject.cpp.
|
virtualinherited |
Updates the hash of current parameter combination
Definition at line 248 of file SGObject.cpp.
|
inherited |
io
Definition at line 369 of file SGObject.h.
|
inherited |
parameters wrt which we can compute gradients
Definition at line 384 of file SGObject.h.
|
inherited |
Hash of parameter values
Definition at line 387 of file SGObject.h.
|
inherited |
model selection parameters
Definition at line 381 of file SGObject.h.
|
inherited |
parameters
Definition at line 378 of file SGObject.h.
|
inherited |
parallel
Definition at line 372 of file SGObject.h.
|
inherited |
version
Definition at line 375 of file SGObject.h.