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CFITCInferenceMethod Class Reference

Detailed Description

The Fully Independent Conditional Training inference method class.

This inference method computes the Cholesky and Alpha vectors approximately with the help of inducing variables. For more details, see "Sparse Gaussian Process using Pseudo-inputs", Edward Snelson, Zoubin Ghahramani, NIPS 18, MIT Press, 2005.

This specific implementation was inspired by the infFITC.m file in the GPML toolbox.

NOTE: The Gaussian Likelihood Function must be used for this inference method.

Note that the number of inducing points (m) is usually far less than the number of input points (n). (the time complexity is computed based on the assumption m < n)

Warning: the time complexity of method, CSingleFITCLaplacianBase::get_derivative_wrt_kernel(const TParameter* param), depends on the implementation of virtual kernel method, CKernel::get_parameter_gradient_diagonal(param, i). The default time complexity of the kernel method can be O(n^2)

Warning: the the time complexity increases from O(m^2*n) to O(n^2*m) if method CFITCInferenceMethod::get_posterior_covariance() is called

Definition at line 54 of file FITCInferenceMethod.h.

Inheritance diagram for CFITCInferenceMethod:
Inheritance graph
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Public Member Functions

 CFITCInferenceMethod ()
 
 CFITCInferenceMethod (CKernel *kernel, CFeatures *features, CMeanFunction *mean, CLabels *labels, CLikelihoodModel *model, CFeatures *inducing_features)
 
virtual ~CFITCInferenceMethod ()
 
virtual const char * get_name () const
 
virtual EInferenceType get_inference_type () const
 
virtual float64_t get_negative_log_marginal_likelihood ()
 
virtual SGVector< float64_tget_diagonal_vector ()
 
virtual bool supports_regression () const
 
virtual SGVector< float64_tget_posterior_mean ()
 
virtual SGMatrix< float64_tget_posterior_covariance ()
 
virtual void update ()
 
virtual void set_kernel (CKernel *kern)
 
virtual void optimize_inducing_features ()
 
virtual void set_lower_bound_of_inducing_features (SGVector< float64_t > bound)
 
virtual void set_upper_bound_of_inducing_features (SGVector< float64_t > bound)
 
virtual void set_tolearance_for_inducing_features (float64_t tol)
 
virtual void set_max_iterations_for_inducing_features (int32_t it)
 
virtual void enable_optimizing_inducing_features (bool is_optmization)
 
virtual void set_inducing_features (CFeatures *feat)
 
virtual CFeaturesget_inducing_features ()
 
virtual SGVector< float64_tget_alpha ()
 
virtual SGMatrix< float64_tget_cholesky ()
 
virtual void set_inducing_noise (float64_t noise)
 
virtual float64_t get_inducing_noise ()
 
float64_t get_marginal_likelihood_estimate (int32_t num_importance_samples=1, float64_t ridge_size=1e-15)
 
virtual CMap< TParameter
*, SGVector< float64_t > > * 
get_negative_log_marginal_likelihood_derivatives (CMap< TParameter *, CSGObject * > *parameters)
 
virtual CMap< TParameter
*, SGVector< float64_t > > * 
get_gradient (CMap< TParameter *, CSGObject * > *parameters)
 
virtual SGVector< float64_tget_value ()
 
virtual CFeaturesget_features ()
 
virtual void set_features (CFeatures *feat)
 
virtual CKernelget_kernel ()
 
virtual CMeanFunctionget_mean ()
 
virtual void set_mean (CMeanFunction *m)
 
virtual CLabelsget_labels ()
 
virtual void set_labels (CLabels *lab)
 
CLikelihoodModelget_model ()
 
virtual void set_model (CLikelihoodModel *mod)
 
virtual float64_t get_scale () const
 
virtual void set_scale (float64_t scale)
 
virtual bool supports_binary () const
 
virtual bool supports_multiclass () const
 
virtual SGMatrix< float64_tget_multiclass_E ()
 
virtual CSGObjectshallow_copy () const
 
virtual CSGObjectdeep_copy () const
 
virtual bool is_generic (EPrimitiveType *generic) const
 
template<class T >
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
template<>
void set_generic ()
 
void unset_generic ()
 
virtual void print_serializable (const char *prefix="")
 
virtual bool save_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=Version::get_version_parameter())
 
virtual bool load_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=Version::get_version_parameter())
 
DynArray< TParameter * > * load_file_parameters (const SGParamInfo *param_info, int32_t file_version, CSerializableFile *file, const char *prefix="")
 
DynArray< TParameter * > * load_all_file_parameters (int32_t file_version, int32_t current_version, CSerializableFile *file, const char *prefix="")
 
void map_parameters (DynArray< TParameter * > *param_base, int32_t &base_version, DynArray< const SGParamInfo * > *target_param_infos)
 
void set_global_io (SGIO *io)
 
SGIOget_global_io ()
 
void set_global_parallel (Parallel *parallel)
 
Parallelget_global_parallel ()
 
void set_global_version (Version *version)
 
Versionget_global_version ()
 
SGStringList< char > get_modelsel_names ()
 
void print_modsel_params ()
 
char * get_modsel_param_descr (const char *param_name)
 
index_t get_modsel_param_index (const char *param_name)
 
void build_gradient_parameter_dictionary (CMap< TParameter *, CSGObject * > *dict)
 
virtual void update_parameter_hash ()
 
virtual bool parameter_hash_changed ()
 
virtual bool equals (CSGObject *other, float64_t accuracy=0.0, bool tolerant=false)
 
virtual CSGObjectclone ()
 

Static Public Member Functions

static CFITCInferenceMethodobtain_from_generic (CInferenceMethod *inference)
 

Public Attributes

SGIOio
 
Parallelparallel
 
Versionversion
 
Parameterm_parameters
 
Parameterm_model_selection_parameters
 
Parameterm_gradient_parameters
 
ParameterMapm_parameter_map
 
uint32_t m_hash
 

Protected Member Functions

virtual void check_members () const
 
virtual void update_alpha ()
 
virtual void update_chol ()
 
virtual void update_deriv ()
 
virtual SGVector< float64_tget_derivative_wrt_likelihood_model (const TParameter *param)
 
virtual void compute_gradient ()
 
virtual float64_t get_derivative_related_cov (SGVector< float64_t > ddiagKi, SGMatrix< float64_t > dKuui, SGMatrix< float64_t > dKui)
 
virtual float64_t get_derivative_related_cov (SGVector< float64_t > ddiagKi, SGMatrix< float64_t > dKuui, SGMatrix< float64_t > dKui, SGVector< float64_t > v, SGMatrix< float64_t > R)
 
virtual float64_t get_derivative_related_cov_helper (SGMatrix< float64_t > dKuui, SGVector< float64_t > v, SGMatrix< float64_t > R)
 
virtual SGVector< float64_tget_derivative_wrt_inducing_noise (const TParameter *param)
 
virtual SGVector< float64_tget_derivative_related_cov_diagonal ()
 
virtual float64_t get_derivative_related_mean (SGVector< float64_t > dmu)
 
virtual SGVector< float64_tget_derivative_related_inducing_features (SGMatrix< float64_t > BdK, const TParameter *param)
 
virtual SGVector< float64_tget_derivative_wrt_mean (const TParameter *param)
 
virtual SGVector< float64_tget_derivative_wrt_inducing_features (const TParameter *param)
 
virtual SGVector< float64_tget_derivative_wrt_inference_method (const TParameter *param)
 
virtual SGVector< float64_tget_derivative_wrt_kernel (const TParameter *param)
 
virtual void check_bound (SGVector< float64_t > bound)
 
virtual void check_fully_sparse ()
 
virtual void convert_features ()
 
virtual void check_features ()
 
virtual void update_train_kernel ()
 
virtual TParametermigrate (DynArray< TParameter * > *param_base, const SGParamInfo *target)
 
virtual void one_to_one_migration_prepare (DynArray< TParameter * > *param_base, const SGParamInfo *target, TParameter *&replacement, TParameter *&to_migrate, char *old_name=NULL)
 
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)
 

Static Protected Member Functions

static void * get_derivative_helper (void *p)
 

Protected Attributes

SGMatrix< float64_tm_chol_uu
 
SGMatrix< float64_tm_chol_utr
 
SGVector< float64_tm_r
 
SGVector< float64_tm_be
 
SGVector< float64_tm_al
 
SGVector< float64_tm_t
 
SGMatrix< float64_tm_B
 
SGVector< float64_tm_w
 
SGMatrix< float64_tm_Rvdd
 
SGMatrix< float64_tm_V
 
SGVector< float64_tm_lower_bound
 
SGVector< float64_tm_upper_bound
 
float64_t m_max_ind_iterations
 
float64_t m_ind_tolerance
 
bool m_opt_inducing_features
 
bool m_fully_sparse
 
CLockm_lock
 
SGMatrix< float64_tm_inducing_features
 
float64_t m_log_ind_noise
 
SGMatrix< float64_tm_kuu
 
SGMatrix< float64_tm_ktru
 
SGMatrix< float64_tm_Sigma
 
SGVector< float64_tm_mu
 
SGVector< float64_tm_ktrtr_diag
 
CKernelm_kernel
 
CMeanFunctionm_mean
 
CLikelihoodModelm_model
 
CFeaturesm_features
 
CLabelsm_labels
 
SGVector< float64_tm_alpha
 
SGMatrix< float64_tm_L
 
float64_t m_log_scale
 
SGMatrix< float64_tm_ktrtr
 
SGMatrix< float64_tm_E
 
bool m_gradient_update
 

Constructor & Destructor Documentation

default constructor

Definition at line 44 of file FITCInferenceMethod.cpp.

CFITCInferenceMethod ( CKernel kernel,
CFeatures features,
CMeanFunction mean,
CLabels labels,
CLikelihoodModel model,
CFeatures inducing_features 
)

constructor

Parameters
kernelcovariance function
featuresfeatures to use in inference
meanmean function
labelslabels of the features
modellikelihood model to use
inducing_featuresfeatures to use

Definition at line 49 of file FITCInferenceMethod.cpp.

~CFITCInferenceMethod ( )
virtual

Definition at line 60 of file FITCInferenceMethod.cpp.

Member Function Documentation

void build_gradient_parameter_dictionary ( CMap< TParameter *, CSGObject * > *  dict)
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.

Parameters
dictdictionary of parameters to be built.

Definition at line 1244 of file SGObject.cpp.

void check_bound ( SGVector< float64_t bound)
protectedvirtualinherited

check the bound constraint is vailid or not

Parameters
boundbound constrains of inducing features

Definition at line 206 of file SingleSparseInferenceBase.cpp.

void check_features ( )
protectedvirtualinherited

check whether features and inducing features are set

Definition at line 49 of file SparseInferenceBase.cpp.

void check_fully_sparse ( )
protectedvirtualinherited

check whether the provided kernel can compute the gradient wrt inducing features

Note that currently we check the name of the provided kernel to determine whether the kernel can compute the derivatives wrt inducing_features

The name of a supported Kernel must end with "SparseKernel"

Definition at line 98 of file SingleSparseInferenceBase.cpp.

void check_members ( ) const
protectedvirtual

check if members of object are valid for inference

Reimplemented from CSparseInferenceBase.

Definition at line 101 of file FITCInferenceMethod.cpp.

CSGObject * clone ( )
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.

Returns
an identical copy of the given object, which is disjoint in memory. NULL if the clone fails. Note that the returned object is SG_REF'ed

Definition at line 1361 of file SGObject.cpp.

void compute_gradient ( )
protectedvirtual

update gradients

Reimplemented from CInferenceMethod.

Definition at line 63 of file FITCInferenceMethod.cpp.

void convert_features ( )
protectedvirtualinherited

convert inducing features and features to the same represention

Note that these two kinds of features can be different types. The reasons are listed below.

  1. The type of the gradient wrt inducing features is float64_t, which is used to update inducing features
  2. Reason 1 implies that the type of inducing features can be float64_t while the type of features does not required as float64_t
  3. Reason 2 implies that the type of features must be a subclass of CDotFeatures, which can represent features as float64_t

Definition at line 54 of file SparseInferenceBase.cpp.

CSGObject * deep_copy ( ) const
virtualinherited

A deep copy. All the instance variables will also be copied.

Definition at line 200 of file SGObject.cpp.

void enable_optimizing_inducing_features ( bool  is_optmization)
virtualinherited

whether enable to opitmize inducing features

Parameters
is_optmizationenable optimization

Definition at line 255 of file SingleSparseInferenceBase.cpp.

bool equals ( CSGObject other,
float64_t  accuracy = 0.0,
bool  tolerant = false 
)
virtualinherited

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.

Parameters
otherobject to compare with
accuracyaccuracy to use for comparison (optional)
tolerantallows linient check on float equality (within accuracy)
Returns
true if all parameters were equal, false if not

Definition at line 1265 of file SGObject.cpp.

SGVector< float64_t > get_alpha ( )
virtualinherited

get alpha vector

Returns
vector to compute posterior mean of Gaussian Process:

\[ \mu = K\alpha \]

where \(\mu\) is the mean and \(K\) is the prior covariance matrix.

Definition at line 136 of file SparseInferenceBase.cpp.

SGMatrix< float64_t > get_cholesky ( )
virtualinherited

get Cholesky decomposition matrix

Returns
Cholesky decomposition of matrix:

\[ L = Cholesky(sW*K*sW+I) \]

where \(K\) is the prior covariance matrix, \(sW\) is the vector returned by get_diagonal_vector(), and \(I\) is the identity matrix.

Definition at line 145 of file SparseInferenceBase.cpp.

void * get_derivative_helper ( void *  p)
staticprotectedinherited

pthread helper method to compute negative log marginal likelihood derivatives wrt hyperparameter

Definition at line 235 of file InferenceMethod.cpp.

float64_t get_derivative_related_cov ( SGVector< float64_t ddiagKi,
SGMatrix< float64_t dKuui,
SGMatrix< float64_t dKui 
)
protectedvirtualinherited

compute variables which are required to compute negative log marginal likelihood full derivatives wrt cov-like hyperparameter \(\theta\)

Note that scale, which is a hyperparameter in inference_method, is a cov-like hyperparameter hyperparameters in cov function are cov-like hyperparameters

Parameters
ddiagKi\(\textbf{diag}(\frac{\partial {\Sigma_{n}}}{\partial {\theta}})\)
dKuui\(\frac{\partial {\Sigma_{m}}}{\partial {\theta}}\)
dKui\(\frac{\partial {\Sigma_{m,n}}}{\partial {\theta}}\)
Returns
derivative of negative log marginal likelihood

Implements CSingleSparseInferenceBase.

Reimplemented in CSingleFITCLaplacianInferenceMethod.

Definition at line 110 of file SingleFITCLaplacianBase.cpp.

float64_t get_derivative_related_cov ( SGVector< float64_t ddiagKi,
SGMatrix< float64_t dKuui,
SGMatrix< float64_t dKui,
SGVector< float64_t v,
SGMatrix< float64_t R 
)
protectedvirtualinherited

compute variables which are required to compute negative log marginal likelihood derivatives wrt cov-like hyperparameter \(\theta\)

Note that scale, which is a hyperparameter in inference_method, is a cov-like hyperparameter hyperparameters in cov function are cov-like hyperparameters

Parameters
ddiagKi\(\textbf{diag}(\frac{\partial {\Sigma_{n}}}{\partial {\theta}})\)
dKuui\(\frac{\partial {\Sigma_{m}}}{\partial {\theta}}\)
dKui\(\frac{\partial {\Sigma_{m,n}}}{\partial {\theta}}\)
vauxiliary variable related to explicit derivative
Rauxiliary variable related to explicit derivative
Returns
derivative of negative log marginal likelihood

Definition at line 132 of file SingleFITCLaplacianBase.cpp.

SGVector< float64_t > get_derivative_related_cov_diagonal ( )
protectedvirtualinherited

helper function to compute variables which are required to compute negative log marginal likelihood derivatives wrt the diagonal part of cov-like hyperparameter \(\theta\)

Returns
derivative of negative log marginal likelihood

Definition at line 74 of file SingleFITCLaplacianBase.cpp.

float64_t get_derivative_related_cov_helper ( SGMatrix< float64_t dKuui,
SGVector< float64_t v,
SGMatrix< float64_t R 
)
protectedvirtualinherited

helper function to compute variables which are required to compute negative log marginal likelihood derivatives wrt cov-like hyperparameter \(\theta\)

Note that scale, which is a hyperparameter in inference_method, is a cov-like hyperparameter hyperparameters in cov function are cov-like hyperparameters what is more, derivative wrt inducing_noise will also use this function

Parameters
dKuui\(\frac{\partial {\Sigma_{m}}}{\partial {\theta}}\)
vauxiliary variable related to explicit derivative
Rauxiliary variable related to explicit derivative
Returns
derivative of negative log marginal likelihood

Definition at line 87 of file SingleFITCLaplacianBase.cpp.

SGVector< float64_t > get_derivative_related_inducing_features ( SGMatrix< float64_t BdK,
const TParameter param 
)
protectedvirtualinherited

helper function to compute variables which are required to compute negative log marginal likelihood derivatives wrt inducing features

Note that the kernel must support to compute the derivatives wrt inducing features

Parameters
BdKauxiliary variable related to explicit derivative or implicit derivative
paramparameter of given kernel
Returns
derivative of negative log marginal likelihood

Definition at line 216 of file SingleFITCLaplacianBase.cpp.

float64_t get_derivative_related_mean ( SGVector< float64_t dmu)
protectedvirtualinherited

helper function to compute variables which are required to compute negative log marginal likelihood derivatives wrt mean \(\lambda\)

Parameters
dmu\(\frac{\partial {\mu_{n}}}{\partial {\lambda}}\)
Returns
derivative of negative log marginal likelihood

Reimplemented in CSingleFITCLaplacianInferenceMethod.

Definition at line 155 of file SingleFITCLaplacianBase.cpp.

SGVector< float64_t > get_derivative_wrt_inducing_features ( const TParameter param)
protectedvirtualinherited

returns derivative of negative log marginal likelihood wrt inducing features (input) Note that in order to call this method, kernel must support FITC inference, which means derivatives wrt inducing features can be computed

Note that the kernel must support to compute the derivatives wrt inducing features

Parameters
paramparameter of given kernel
Returns
derivative of negative log marginal likelihood

Implements CSingleSparseInferenceBase.

Reimplemented in CSingleFITCLaplacianInferenceMethod.

Definition at line 264 of file SingleFITCLaplacianBase.cpp.

SGVector< float64_t > get_derivative_wrt_inducing_noise ( const TParameter param)
protectedvirtualinherited

returns derivative of negative log marginal likelihood wrt inducing noise

Parameters
paramparameter of given inference class
Returns
derivative of negative log marginal likelihood

Implements CSingleSparseInferenceBase.

Reimplemented in CSingleFITCLaplacianInferenceMethod.

Definition at line 185 of file SingleFITCLaplacianBase.cpp.

SGVector< float64_t > get_derivative_wrt_inference_method ( const TParameter param)
protectedvirtualinherited

returns derivative of negative log marginal likelihood wrt parameter of CInferenceMethod class

Parameters
paramparameter of CInferenceMethod class
Returns
derivative of negative log marginal likelihood

Implements CSparseInferenceBase.

Reimplemented in CSingleFITCLaplacianInferenceMethod.

Definition at line 110 of file SingleSparseInferenceBase.cpp.

SGVector< float64_t > get_derivative_wrt_kernel ( const TParameter param)
protectedvirtualinherited

returns derivative of negative log marginal likelihood wrt kernel's parameter

Parameters
paramparameter of given kernel
Returns
derivative of negative log marginal likelihood

Implements CSparseInferenceBase.

Reimplemented in CSingleFITCLaplacianInferenceMethod.

Definition at line 162 of file SingleSparseInferenceBase.cpp.

SGVector< float64_t > get_derivative_wrt_likelihood_model ( const TParameter param)
protectedvirtual

returns derivative of negative log marginal likelihood wrt parameter of likelihood model

Parameters
paramparameter of given likelihood model
Returns
derivative of negative log marginal likelihood

Implements CSingleFITCLaplacianBase.

Definition at line 402 of file FITCInferenceMethod.cpp.

SGVector< float64_t > get_derivative_wrt_mean ( const TParameter param)
protectedvirtualinherited

returns derivative of negative log marginal likelihood wrt mean function's parameter

Parameters
paramparameter of given mean function
Returns
derivative of negative log marginal likelihood

Implements CSparseInferenceBase.

Reimplemented in CSingleFITCLaplacianInferenceMethod.

Definition at line 163 of file SingleFITCLaplacianBase.cpp.

SGVector< float64_t > get_diagonal_vector ( )
virtual

get diagonal vector

Returns
diagonal of matrix used to calculate posterior covariance matrix:

\[ Cov = (K^{-1}+sW^{2})^{-1} \]

where \(Cov\) is the posterior covariance matrix, \(K\) is the prior covariance matrix, and \(sW\) is the diagonal vector.

Definition at line 111 of file FITCInferenceMethod.cpp.

virtual CFeatures* get_features ( )
virtualinherited

get features

Returns
features

Definition at line 246 of file InferenceMethod.h.

SGIO * get_global_io ( )
inherited

get the io object

Returns
io object

Definition at line 237 of file SGObject.cpp.

Parallel * get_global_parallel ( )
inherited

get the parallel object

Returns
parallel object

Definition at line 279 of file SGObject.cpp.

Version * get_global_version ( )
inherited

get the version object

Returns
version object

Definition at line 292 of file SGObject.cpp.

virtual CMap<TParameter*, SGVector<float64_t> >* get_gradient ( CMap< TParameter *, CSGObject * > *  parameters)
virtualinherited

get the gradient

Parameters
parametersparameter's dictionary
Returns
map of gradient. Keys are names of parameters, values are values of derivative with respect to that parameter.

Implements CDifferentiableFunction.

Definition at line 225 of file InferenceMethod.h.

virtual CFeatures* get_inducing_features ( )
virtualinherited

get inducing features

Returns
features

Definition at line 122 of file SparseInferenceBase.h.

float64_t get_inducing_noise ( )
virtualinherited

get the noise for inducing points

Returns
noise noise for inducing points

Definition at line 119 of file SparseInferenceBase.cpp.

virtual EInferenceType get_inference_type ( ) const
virtual

return what type of inference we are

Returns
inference type FITC_REGRESSION

Reimplemented from CSparseInferenceBase.

Definition at line 85 of file FITCInferenceMethod.h.

virtual CKernel* get_kernel ( )
virtualinherited

get kernel

Returns
kernel

Definition at line 263 of file InferenceMethod.h.

virtual CLabels* get_labels ( )
virtualinherited

get labels

Returns
labels

Definition at line 297 of file InferenceMethod.h.

float64_t get_marginal_likelihood_estimate ( int32_t  num_importance_samples = 1,
float64_t  ridge_size = 1e-15 
)
inherited

Computes an unbiased estimate of the marginal-likelihood (in log-domain),

\[ p(y|X,\theta), \]

where \(y\) are the labels, \(X\) are the features (omitted from in the following expressions), and \(\theta\) represent hyperparameters.

This is done via a Gaussian approximation to the posterior \(q(f|y, \theta)\approx p(f|y, \theta)\), which is computed by the underlying CInferenceMethod instance (if implemented, otherwise error), and then using an importance sample estimator

\[ p(y|\theta)=\int p(y|f)p(f|\theta)df =\int p(y|f)\frac{p(f|\theta)}{q(f|y, \theta)}q(f|y, \theta)df \approx\frac{1}{n}\sum_{i=1}^n p(y|f^{(i)})\frac{p(f^{(i)}|\theta)} {q(f^{(i)}|y, \theta)}, \]

where \( f^{(i)} \) are samples from the posterior approximation \( q(f|y, \theta) \). The resulting estimator has a low variance if \( q(f|y, \theta) \) is a good approximation. It has large variance otherwise (while still being consistent). Storing all number of log-domain ensures numerical stability.

Parameters
num_importance_samplesthe number of importance samples \(n\) from \( q(f|y, \theta) \).
ridge_sizescalar that is added to the diagonal of the involved Gaussian distribution's covariance of GP prior and posterior approximation to stabilise things. Increase if covariance matrix is not numerically positive semi-definite.
Returns
unbiased estimate of the marginal likelihood function \( p(y|\theta),\) in log-domain.

Definition at line 106 of file InferenceMethod.cpp.

virtual CMeanFunction* get_mean ( )
virtualinherited

get mean

Returns
mean

Definition at line 280 of file InferenceMethod.h.

CLikelihoodModel* get_model ( )
inherited

get likelihood model

Returns
likelihood

Definition at line 314 of file InferenceMethod.h.

SGStringList< char > get_modelsel_names ( )
inherited
Returns
vector of names of all parameters which are registered for model selection

Definition at line 1136 of file SGObject.cpp.

char * get_modsel_param_descr ( const char *  param_name)
inherited

Returns description of a given parameter string, if it exists. SG_ERROR otherwise

Parameters
param_namename of the parameter
Returns
description of the parameter

Definition at line 1160 of file SGObject.cpp.

index_t get_modsel_param_index ( const char *  param_name)
inherited

Returns index of model selection parameter with provided index

Parameters
param_namename of model selection parameter
Returns
index of model selection parameter with provided name, -1 if there is no such

Definition at line 1173 of file SGObject.cpp.

SGMatrix< float64_t > get_multiclass_E ( )
virtualinherited

get the E matrix used for multi classification

Returns
the matrix for multi classification

Definition at line 52 of file InferenceMethod.cpp.

virtual const char* get_name ( ) const
virtual

returns the name of the inference method

Returns
name FITC

Reimplemented from CSingleFITCLaplacianBase.

Definition at line 79 of file FITCInferenceMethod.h.

float64_t get_negative_log_marginal_likelihood ( )
virtual

get negative log marginal likelihood

Returns
the negative log of the marginal likelihood function:

\[ -log(p(y|X, \theta)) \]

where \(y\) are the labels, \(X\) are the features, and \(\theta\) represent hyperparameters.

Implements CInferenceMethod.

Definition at line 128 of file FITCInferenceMethod.cpp.

CMap< TParameter *, SGVector< float64_t > > * get_negative_log_marginal_likelihood_derivatives ( CMap< TParameter *, CSGObject * > *  parameters)
virtualinherited

get log marginal likelihood gradient

Returns
vector of the marginal likelihood function gradient with respect to hyperparameters (under the current approximation to the posterior \(q(f|y)\approx p(f|y)\):

\[ -\frac{\partial log(p(y|X, \theta))}{\partial \theta} \]

where \(y\) are the labels, \(X\) are the features, and \(\theta\) represent hyperparameters.

Definition at line 165 of file InferenceMethod.cpp.

SGMatrix< float64_t > get_posterior_covariance ( )
virtual

returns covariance matrix \(\Sigma\) of the Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\), which is an approximation to the posterior:

\[ p(f|y) \approx q(f|y) = \mathcal{N}(\mu,\Sigma) \]

in case if particular inference method doesn't compute posterior \(p(f|y)\) exactly, and it returns covariance matrix \(\Sigma\) of the posterior Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\) otherwise.

Returns
covariance matrix

Implements CSparseInferenceBase.

Definition at line 360 of file FITCInferenceMethod.cpp.

SGVector< float64_t > get_posterior_mean ( )
virtual

returns mean vector \(\mu\) of the Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\), which is an approximation to the posterior:

\[ p(f|y) \approx q(f|y) = \mathcal{N}(\mu,\Sigma) \]

in case if particular inference method doesn't compute posterior \(p(f|y)\) exactly, and it returns covariance matrix \(\Sigma\) of the posterior Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\) otherwise.

Returns
mean vector

Implements CSparseInferenceBase.

Definition at line 330 of file FITCInferenceMethod.cpp.

float64_t get_scale ( ) const
virtualinherited

get kernel scale

Returns
kernel scale

Definition at line 41 of file InferenceMethod.cpp.

virtual SGVector<float64_t> get_value ( )
virtualinherited

get the function value

Returns
vector that represents the function value

Implements CDifferentiableFunction.

Definition at line 235 of file InferenceMethod.h.

bool is_generic ( EPrimitiveType *  generic) const
virtualinherited

If the SGSerializable is a class template then TRUE will be returned and GENERIC is set to the type of the generic.

Parameters
genericset to the type of the generic if returning TRUE
Returns
TRUE if a class template.

Definition at line 298 of file SGObject.cpp.

DynArray< TParameter * > * load_all_file_parameters ( int32_t  file_version,
int32_t  current_version,
CSerializableFile file,
const char *  prefix = "" 
)
inherited

maps all parameters of this instance to the provided file version and loads all parameter data from the file into an array, which is sorted (basically calls load_file_parameter(...) for all parameters and puts all results into a sorted array)

Parameters
file_versionparameter version of the file
current_versionversion from which mapping begins (you want to use Version::get_version_parameter() for this in most cases)
filefile to load from
prefixprefix for members
Returns
(sorted) array of created TParameter instances with file data

Definition at line 705 of file SGObject.cpp.

DynArray< TParameter * > * load_file_parameters ( const SGParamInfo param_info,
int32_t  file_version,
CSerializableFile file,
const char *  prefix = "" 
)
inherited

loads some specified parameters from a file with a specified version The provided parameter info has a version which is recursively mapped until the file parameter version is reached. Note that there may be possibly multiple parameters in the mapping, therefore, a set of TParameter instances is returned

Parameters
param_infoinformation of parameter
file_versionparameter version of the file, must be <= provided parameter version
filefile to load from
prefixprefix for members
Returns
new array with TParameter instances with the attached data

Definition at line 546 of file SGObject.cpp.

bool load_serializable ( CSerializableFile file,
const char *  prefix = "",
int32_t  param_version = Version::get_version_parameter() 
)
virtualinherited

Load this object from file. If it will fail (returning FALSE) then this object will contain inconsistent data and should not be used!

Parameters
filewhere to load from
prefixprefix for members
param_version(optional) a parameter version different to (this is mainly for testing, better do not use)
Returns
TRUE if done, otherwise FALSE

Definition at line 375 of file SGObject.cpp.

void load_serializable_post ( )
throw (ShogunException
)
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.

Exceptions
ShogunExceptionwill be thrown if an error occurs.

Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.

Definition at line 1063 of file SGObject.cpp.

void load_serializable_pre ( )
throw (ShogunException
)
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.

Exceptions
ShogunExceptionwill 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 1058 of file SGObject.cpp.

void map_parameters ( DynArray< TParameter * > *  param_base,
int32_t &  base_version,
DynArray< const SGParamInfo * > *  target_param_infos 
)
inherited

Takes a set of TParameter instances (base) with a certain version and a set of target parameter infos and recursively maps the base level wise to the current version using CSGObject::migrate(...). The base is replaced. After this call, the base version containing parameters should be of same version/type as the initial target parameter infos. Note for this to work, the migrate methods and all the internal parameter mappings have to match

Parameters
param_baseset of TParameter instances that are mapped to the provided target parameter infos
base_versionversion of the parameter base
target_param_infosset of SGParamInfo instances that specify the target parameter base

Definition at line 743 of file SGObject.cpp.

TParameter * migrate ( DynArray< TParameter * > *  param_base,
const SGParamInfo target 
)
protectedvirtualinherited

creates a new TParameter instance, which contains migrated data from the version that is provided. The provided parameter data base is used for migration, this base is a collection of all parameter data of the previous version. Migration is done FROM the data in param_base TO the provided param info Migration is always one version step. Method has to be implemented in subclasses, if no match is found, base method has to be called.

If there is an element in the param_base which equals the target, a copy of the element is returned. This represents the case when nothing has changed and therefore, the migrate method is not overloaded in a subclass

Parameters
param_baseset of TParameter instances to use for migration
targetparameter info for the resulting TParameter
Returns
a new TParameter instance with migrated data from the base of the type which is specified by the target parameter

Definition at line 950 of file SGObject.cpp.

CFITCInferenceMethod * obtain_from_generic ( CInferenceMethod inference)
static

helper method used to specialize a base class instance

Parameters
inferenceinference method
Returns
casted CFITCInferenceMethod object

Definition at line 88 of file FITCInferenceMethod.cpp.

void one_to_one_migration_prepare ( DynArray< TParameter * > *  param_base,
const SGParamInfo target,
TParameter *&  replacement,
TParameter *&  to_migrate,
char *  old_name = NULL 
)
protectedvirtualinherited

This method prepares everything for a one-to-one parameter migration. One to one here means that only ONE element of the parameter base is needed for the migration (the one with the same name as the target). Data is allocated for the target (in the type as provided in the target SGParamInfo), and a corresponding new TParameter instance is written to replacement. The to_migrate pointer points to the single needed TParameter instance needed for migration. If a name change happened, the old name may be specified by old_name. In addition, the m_delete_data flag of to_migrate is set to true. So if you want to migrate data, the only thing to do after this call is converting the data in the m_parameter fields. If unsure how to use - have a look into an example for this. (base_migration_type_conversion.cpp for example)

Parameters
param_baseset of TParameter instances to use for migration
targetparameter info for the resulting TParameter
replacement(used as output) here the TParameter instance which is returned by migration is created into
to_migratethe only source that is used for migration
old_namewith this parameter, a name change may be specified

Definition at line 890 of file SGObject.cpp.

void optimize_inducing_features ( )
virtualinherited

opitmize inducing features

Definition at line 260 of file SingleSparseInferenceBase.cpp.

bool parameter_hash_changed ( )
virtualinherited
Returns
whether parameter combination has changed since last update

Definition at line 264 of file SGObject.cpp.

void print_modsel_params ( )
inherited

prints all parameter registered for model selection and their type

Definition at line 1112 of file SGObject.cpp.

void print_serializable ( const char *  prefix = "")
virtualinherited

prints registered parameters out

Parameters
prefixprefix for members

Definition at line 310 of file SGObject.cpp.

bool save_serializable ( CSerializableFile file,
const char *  prefix = "",
int32_t  param_version = Version::get_version_parameter() 
)
virtualinherited

Save this object to file.

Parameters
filewhere to save the object; will be closed during returning if PREFIX is an empty string.
prefixprefix for members
param_version(optional) a parameter version different to (this is mainly for testing, better do not use)
Returns
TRUE if done, otherwise FALSE

Definition at line 316 of file SGObject.cpp.

void save_serializable_post ( )
throw (ShogunException
)
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.

Exceptions
ShogunExceptionwill be thrown if an error occurs.

Reimplemented in CKernel.

Definition at line 1073 of file SGObject.cpp.

void save_serializable_pre ( )
throw (ShogunException
)
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.

Exceptions
ShogunExceptionwill 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 1068 of file SGObject.cpp.

virtual void set_features ( CFeatures feat)
virtualinherited

set features

Parameters
featfeatures to set

Definition at line 252 of file InferenceMethod.h.

void set_generic ( )
inherited

Definition at line 42 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 47 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 52 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 57 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 62 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 67 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 72 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 77 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 82 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 87 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 92 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 97 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 102 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 107 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 112 of file SGObject.cpp.

void set_generic ( )
inherited

set generic type to T

void set_global_io ( SGIO io)
inherited

set the io object

Parameters
ioio object to use

Definition at line 230 of file SGObject.cpp.

void set_global_parallel ( Parallel parallel)
inherited

set the parallel object

Parameters
parallelparallel object to use

Definition at line 243 of file SGObject.cpp.

void set_global_version ( Version version)
inherited

set the version object

Parameters
versionversion object to use

Definition at line 285 of file SGObject.cpp.

virtual void set_inducing_features ( CFeatures feat)
virtualinherited

set inducing features

Parameters
featfeatures to set

Definition at line 109 of file SparseInferenceBase.h.

void set_inducing_noise ( float64_t  noise)
virtualinherited

set the noise for inducing points

Parameters
noisenoise for inducing points

The noise is used to enfore the kernel matrix about the inducing points are positive definite

Definition at line 113 of file SparseInferenceBase.cpp.

void set_kernel ( CKernel kern)
virtualinherited

set kernel

Parameters
kernkernel to set

Reimplemented from CInferenceMethod.

Definition at line 87 of file SingleSparseInferenceBase.cpp.

virtual void set_labels ( CLabels lab)
virtualinherited

set labels

Parameters
lablabel to set

Definition at line 303 of file InferenceMethod.h.

void set_lower_bound_of_inducing_features ( SGVector< float64_t bound)
virtualinherited

set the lower bound of inducing features

Parameters
boundlower bound constrains of inducing features

Note that if the length of the bound can be 1, it means the bound constraint applies to each dimension of inducing features

Note that if the length of the bound is greater than 1, it means each dimension of the bound constraint applies to the corresponding dimension of inducing features

Definition at line 217 of file SingleSparseInferenceBase.cpp.

void set_max_iterations_for_inducing_features ( int32_t  it)
virtualinherited

set the max number of iterations used in optimization of inducing features

Parameters
itmax number of iterations

Definition at line 228 of file SingleSparseInferenceBase.cpp.

virtual void set_mean ( CMeanFunction m)
virtualinherited

set mean

Parameters
mmean function to set

Definition at line 286 of file InferenceMethod.h.

virtual void set_model ( CLikelihoodModel mod)
virtualinherited

set likelihood model

Parameters
modmodel to set

Reimplemented in CKLInferenceMethod, and CKLDualInferenceMethod.

Definition at line 320 of file InferenceMethod.h.

void set_scale ( float64_t  scale)
virtualinherited

set kernel scale

Parameters
scalescale to be set

Definition at line 46 of file InferenceMethod.cpp.

void set_tolearance_for_inducing_features ( float64_t  tol)
virtualinherited

set the tolearance used in optimization of inducing features

Parameters
toltolearance

Definition at line 233 of file SingleSparseInferenceBase.cpp.

void set_upper_bound_of_inducing_features ( SGVector< float64_t bound)
virtualinherited

set the upper bound of inducing features

Parameters
boundupper bound constrains of inducing features

Note that if the length of the bound can be 1, it means the bound constraint applies to each dimension of inducing features

Note that if the length of the bound is greater than 1, it means each dimension of the bound constraint applies to the corresponding dimension of inducing features

Definition at line 222 of file SingleSparseInferenceBase.cpp.

CSGObject * shallow_copy ( ) const
virtualinherited

A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.

Reimplemented in CGaussianKernel.

Definition at line 194 of file SGObject.cpp.

virtual bool supports_binary ( ) const
virtualinherited

whether combination of inference method and given likelihood function supports binary classification

Returns
false

Reimplemented in CEPInferenceMethod, CKLInferenceMethod, CSingleFITCLaplacianInferenceMethod, and CSingleLaplacianInferenceMethod.

Definition at line 351 of file InferenceMethod.h.

virtual bool supports_multiclass ( ) const
virtualinherited

whether combination of inference method and given likelihood function supports multiclass classification

Returns
false

Definition at line 358 of file InferenceMethod.h.

virtual bool supports_regression ( ) const
virtual
Returns
whether combination of FITC inference method and given likelihood function supports regression

Reimplemented from CInferenceMethod.

Definition at line 125 of file FITCInferenceMethod.h.

void unset_generic ( )
inherited

unset generic type

this has to be called in classes specializing a template class

Definition at line 305 of file SGObject.cpp.

void update ( )
virtual

update all matrices

Implements CSparseInferenceBase.

Definition at line 75 of file FITCInferenceMethod.cpp.

void update_alpha ( )
protectedvirtual

update alpha matrix

Implements CSingleFITCLaplacianBase.

Definition at line 248 of file FITCInferenceMethod.cpp.

void update_chol ( )
protectedvirtual

update cholesky Matrix.

Implements CSingleFITCLaplacianBase.

Definition at line 151 of file FITCInferenceMethod.cpp.

void update_deriv ( )
protectedvirtual

update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter

Implements CSingleFITCLaplacianBase.

Definition at line 267 of file FITCInferenceMethod.cpp.

void update_parameter_hash ( )
virtualinherited

Updates the hash of current parameter combination

Definition at line 250 of file SGObject.cpp.

void update_train_kernel ( )
protectedvirtualinherited

update train kernel matrix

Reimplemented from CInferenceMethod.

Definition at line 154 of file SparseInferenceBase.cpp.

Member Data Documentation

SGIO* io
inherited

io

Definition at line 496 of file SGObject.h.

SGVector<float64_t> m_al
protectedinherited

Note that alpha is NOT post.alpha alpha and post.alpha are defined in infFITC.m and infFITC_Laplace.m

Definition at line 232 of file SingleFITCLaplacianBase.h.

SGVector<float64_t> m_alpha
protectedinherited

alpha vector used in process mean calculation

Definition at line 455 of file InferenceMethod.h.

SGMatrix<float64_t> m_B
protectedinherited

Definition at line 241 of file SingleFITCLaplacianBase.h.

SGVector<float64_t> m_be
protected

solves the equation V * r = m_chol_utr

Definition at line 206 of file FITCInferenceMethod.h.

SGMatrix<float64_t> m_chol_utr
protected

Cholesky of covariance of inducing features and training features

Definition at line 200 of file FITCInferenceMethod.h.

SGMatrix<float64_t> m_chol_uu
protected

Cholesky of covariance of inducing features

Definition at line 197 of file FITCInferenceMethod.h.

SGMatrix<float64_t> m_E
protectedinherited

the matrix used for multi classification

Definition at line 467 of file InferenceMethod.h.

CFeatures* m_features
protectedinherited

features to use

Definition at line 449 of file InferenceMethod.h.

bool m_fully_sparse
protectedinherited

Definition at line 221 of file SingleSparseInferenceBase.h.

Parameter* m_gradient_parameters
inherited

parameters wrt which we can compute gradients

Definition at line 511 of file SGObject.h.

bool m_gradient_update
protectedinherited

Whether gradients are updated

Definition at line 470 of file InferenceMethod.h.

uint32_t m_hash
inherited

Hash of parameter values

Definition at line 517 of file SGObject.h.

float64_t m_ind_tolerance
protectedinherited

tolearance used in optimizing inducing_features

Definition at line 194 of file SingleSparseInferenceBase.h.

SGMatrix<float64_t> m_inducing_features
protectedinherited

inducing features for approximation

Definition at line 305 of file SparseInferenceBase.h.

CKernel* m_kernel
protectedinherited

covariance function

Definition at line 440 of file InferenceMethod.h.

SGMatrix<float64_t> m_ktrtr
protectedinherited

kernel matrix from features (non-scalled by inference scalling)

Definition at line 464 of file InferenceMethod.h.

SGVector<float64_t> m_ktrtr_diag
protectedinherited

diagonal elements of kernel matrix m_ktrtr

Definition at line 323 of file SparseInferenceBase.h.

SGMatrix<float64_t> m_ktru
protectedinherited

covariance matrix of inducing features and training features

Definition at line 314 of file SparseInferenceBase.h.

SGMatrix<float64_t> m_kuu
protectedinherited

covariance matrix of inducing features

Definition at line 311 of file SparseInferenceBase.h.

SGMatrix<float64_t> m_L
protectedinherited

upper triangular factor of Cholesky decomposition

Definition at line 458 of file InferenceMethod.h.

CLabels* m_labels
protectedinherited

labels of features

Definition at line 452 of file InferenceMethod.h.

CLock* m_lock
protectedinherited

Definition at line 224 of file SingleSparseInferenceBase.h.

float64_t m_log_ind_noise
protectedinherited

noise of the inducing variables

Definition at line 308 of file SparseInferenceBase.h.

float64_t m_log_scale
protectedinherited

kernel scale

Definition at line 461 of file InferenceMethod.h.

SGVector<float64_t> m_lower_bound
protectedinherited

lower bound of inducing features

Definition at line 185 of file SingleSparseInferenceBase.h.

float64_t m_max_ind_iterations
protectedinherited

max number of iterations

Definition at line 191 of file SingleSparseInferenceBase.h.

CMeanFunction* m_mean
protectedinherited

mean function

Definition at line 443 of file InferenceMethod.h.

CLikelihoodModel* m_model
protectedinherited

likelihood function to use

Definition at line 446 of file InferenceMethod.h.

Parameter* m_model_selection_parameters
inherited

model selection parameters

Definition at line 508 of file SGObject.h.

SGVector<float64_t> m_mu
protectedinherited

mean vector of the the posterior Gaussian distribution

Definition at line 320 of file SparseInferenceBase.h.

bool m_opt_inducing_features
protectedinherited

whether optimize inducing features

Definition at line 197 of file SingleSparseInferenceBase.h.

ParameterMap* m_parameter_map
inherited

map for different parameter versions

Definition at line 514 of file SGObject.h.

Parameter* m_parameters
inherited

parameters

Definition at line 505 of file SGObject.h.

SGVector<float64_t> m_r
protected

labels adjusted for noise and means

Definition at line 203 of file FITCInferenceMethod.h.

SGMatrix<float64_t> m_Rvdd
protectedinherited

Rvdd=W where W is defined in infFITC.m and Rvdd is defined in infFITC_Laplace.m Note that W is NOT the diagonal matrix

Definition at line 250 of file SingleFITCLaplacianBase.h.

SGMatrix<float64_t> m_Sigma
protectedinherited

covariance matrix of the the posterior Gaussian distribution

Definition at line 317 of file SparseInferenceBase.h.

SGVector<float64_t> m_t
protectedinherited

t=1/g_sn2 in regression, where g_sn2 is defined in infFITC.m t=W.*dd in Laplace for binary classification, where W and dd are defined in infFITC_Laplace.m

Definition at line 238 of file SingleFITCLaplacianBase.h.

SGVector<float64_t> m_upper_bound
protectedinherited

upper bound of inducing features

Definition at line 188 of file SingleSparseInferenceBase.h.

SGMatrix<float64_t> m_V
protectedinherited

Definition at line 253 of file SingleFITCLaplacianBase.h.

SGVector<float64_t> m_w
protectedinherited

Definition at line 244 of file SingleFITCLaplacianBase.h.

Parallel* parallel
inherited

parallel

Definition at line 499 of file SGObject.h.

Version* version
inherited

version

Definition at line 502 of file SGObject.h.


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

SHOGUN Machine Learning Toolbox - Documentation