Detailed Description

The Laplace approximation FITC inference method with LBFGS class for regression and binary classification.

We use the Limited-memory BFGS (LBFGS) method to obtain the maximum of likelihood. Here L-BFGS only uses the last m (m<<n) function/gradient pairs to find the optimal pointer

For more details of LBFGS, see Nocedal, Jorge, and Stephen J. Wright. "Numerical Optimization 2nd." (2006), Pages 177-180.

This specific implementation was based on the idea from Murphy, Kevin P. "Machine learning: a probabilistic perspective." (2012), Pages 251-252.

Definition at line 58 of file SingleFITCLaplacianInferenceMethodWithLBFGS.h.

Inheritance diagram for CSingleFITCLaplacianInferenceMethodWithLBFGS:

[legend]

Public Member Functions
	CSingleFITCLaplacianInferenceMethodWithLBFGS ()

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

virtual	~CSingleFITCLaplacianInferenceMethodWithLBFGS ()

virtual const char *	get_name () const

virtual void	set_lbfgs_parameters (int m=100, int max_linesearch=1000, int linesearch=LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE, int max_iterations=1000, float64_t delta=0.0, int past=0, float64_t epsilon=1e-5, float64_t min_step=1e-20, float64_t max_step=1e+20, float64_t ftol=1e-4, float64_t wolfe=0.9, float64_t gtol=0.9, float64_t xtol=1e-16, float64_t orthantwise_c=0.0, int orthantwise_start=0, int orthantwise_end=1)

virtual void	set_newton_method (bool enable_newton_if_fail)

virtual EInferenceType	get_inference_type () const

virtual bool	supports_regression () const

virtual bool	supports_binary () const

virtual SGVector< float64_t >	get_diagonal_vector ()

virtual SGVector< float64_t >	get_posterior_mean ()

virtual SGMatrix< float64_t >	get_posterior_covariance ()

virtual float64_t	get_newton_tolerance ()

virtual void	set_newton_tolerance (float64_t tol)

virtual int32_t	get_newton_iterations ()

virtual void	set_newton_iterations (int32_t iter)

virtual float64_t	get_minimization_tolerance ()

virtual void	set_minimization_tolerance (float64_t tol)

virtual float64_t	get_minimization_max ()

virtual void	set_minimization_max (float64_t max)

virtual void	update ()

virtual float64_t	get_negative_log_marginal_likelihood ()

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 CFeatures *	get_inducing_features ()

virtual SGVector< float64_t >	get_alpha ()

virtual SGMatrix< float64_t >	get_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_t >	get_value ()

virtual CFeatures *	get_features ()

virtual void	set_features (CFeatures *feat)

virtual CKernel *	get_kernel ()

virtual CMeanFunction *	get_mean ()

virtual void	set_mean (CMeanFunction *m)

virtual CLabels *	get_labels ()

virtual void	set_labels (CLabels *lab)

CLikelihoodModel *	get_model ()

virtual void	set_model (CLikelihoodModel *mod)

virtual float64_t	get_scale () const

virtual void	set_scale (float64_t scale)

virtual bool	supports_multiclass () const

virtual SGMatrix< float64_t >	get_multiclass_E ()

virtual CSGObject *	shallow_copy () const

virtual CSGObject *	deep_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="")

virtual bool	load_serializable (CSerializableFile file, const char prefix="")

void	set_global_io (SGIO *io)

SGIO *	get_global_io ()

void	set_global_parallel (Parallel *parallel)

Parallel *	get_global_parallel ()

void	set_global_version (Version *version)

Version *	get_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 CSGObject *	clone ()

Static Public Member Functions
static CSingleFITCLaplacianInferenceMethod *	obtain_from_generic (CInferenceMethod *inference)

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	update_alpha ()

virtual void	compute_gradient ()

virtual void	update_init ()

virtual void	update_chol ()

virtual void	update_approx_cov ()

virtual void	update_deriv ()

virtual SGVector< float64_t >	get_derivative_wrt_inference_method (const TParameter *param)

virtual SGVector< float64_t >	get_derivative_wrt_likelihood_model (const TParameter *param)

virtual SGVector< float64_t >	get_derivative_wrt_kernel (const TParameter *param)

virtual SGVector< float64_t >	get_derivative_wrt_mean (const TParameter *param)

virtual SGMatrix< float64_t >	get_chol_inv (SGMatrix< float64_t > mtx)

virtual SGVector< float64_t >	compute_mvmK (SGVector< float64_t > al)

virtual SGVector< float64_t >	compute_mvmZ (SGVector< float64_t > x)

virtual SGVector< float64_t >	get_derivative_wrt_inducing_features (const TParameter *param)

virtual SGVector< float64_t >	get_derivative_wrt_inducing_noise (const TParameter *param)

virtual SGVector< float64_t >	derivative_helper_when_Wneg (SGVector< float64_t > res, const TParameter *param)

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_mean (SGVector< float64_t > dmu)

virtual float64_t	get_derivative_implicit_term_helper (SGVector< float64_t > d)

virtual float64_t	get_derivative_related_cov_helper (SGMatrix< float64_t > dKuui, SGVector< float64_t > v, SGMatrix< float64_t > R)

virtual SGVector< float64_t >	get_derivative_related_cov_diagonal ()

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

virtual void	check_bound (SGVector< float64_t > bound, const char *name)

virtual void	check_fully_sparse ()

virtual void	convert_features ()

virtual void	check_features ()

virtual void	check_members () const

virtual void	update_train_kernel ()

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
SGVector< float64_t >	m_sW

SGVector< float64_t >	m_d2lp

SGVector< float64_t >	m_d3lp

SGVector< float64_t >	m_dlp

SGVector< float64_t >	m_W

float64_t	m_tolerance

index_t	m_iter

float64_t	m_opt_tolerance

float64_t	m_opt_max

SGMatrix< float64_t >	m_chol_R0

SGVector< float64_t >	m_dfhat

SGVector< float64_t >	m_g

float64_t	m_Psi

SGVector< float64_t >	m_dg

bool	m_Wneg

SGVector< float64_t >	m_al

SGVector< float64_t >	m_t

SGMatrix< float64_t >	m_B

SGVector< float64_t >	m_w

SGMatrix< float64_t >	m_Rvdd

SGMatrix< float64_t >	m_V

SGVector< float64_t >	m_lower_bound

SGVector< float64_t >	m_upper_bound

float64_t	m_max_ind_iterations

float64_t	m_ind_tolerance

bool	m_opt_inducing_features

bool	m_fully_sparse

CLock *	m_lock

SGMatrix< float64_t >	m_inducing_features

float64_t	m_log_ind_noise

SGMatrix< float64_t >	m_kuu

SGMatrix< float64_t >	m_ktru

SGMatrix< float64_t >	m_Sigma

SGVector< float64_t >	m_mu

SGVector< float64_t >	m_ktrtr_diag

CKernel *	m_kernel

CMeanFunction *	m_mean

CLikelihoodModel *	m_model

CFeatures *	m_features

CLabels *	m_labels

SGVector< float64_t >	m_alpha

SGMatrix< float64_t >	m_L

float64_t	m_log_scale

SGMatrix< float64_t >	m_ktrtr

SGMatrix< float64_t >	m_E

bool	m_gradient_update

Constructor & Destructor Documentation

CSingleFITCLaplacianInferenceMethodWithLBFGS ( )

Definition at line 44 of file SingleFITCLaplacianInferenceMethodWithLBFGS.cpp.

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

Definition at line 50 of file SingleFITCLaplacianInferenceMethodWithLBFGS.cpp.

~CSingleFITCLaplacianInferenceMethodWithLBFGS ( )

virtual

Definition at line 158 of file SingleFITCLaplacianInferenceMethodWithLBFGS.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

dict	dictionary of parameters to be built.

Definition at line 597 of file SGObject.cpp.

void check_bound	(	SGVector< float64_t >	bound,
		const char *	name
	)

protectedvirtualinherited

check the bound constraint is vailid or not

Parameters

bound	bound constrains of inducing features
name	the name of the bound

Definition at line 202 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 96 of file SingleSparseInferenceBase.cpp.

void check_members ( ) const

protectedvirtualinherited

check if members of object are valid for inference

Reimplemented from CInferenceMethod.

Reimplemented in CFITCInferenceMethod, and CSparseVGInferenceMethod.

Definition at line 128 of file SparseInferenceBase.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 714 of file SGObject.cpp.

void compute_gradient ( )

protectedvirtualinherited

update gradients

Reimplemented from CInferenceMethod.

Definition at line 133 of file SingleFITCLaplacianInferenceMethod.cpp.

SGVector< float64_t > compute_mvmK ( SGVector< float64_t > al )

protectedvirtualinherited

efficiently compute the matrix-vector product $\Sigma \times al$\f, where $$ is the FITC equivalent covariance n-by-n matrix (prior) of f_n

Parameters

al	input vector

Returns: the matrix-vector product

Definition at line 187 of file SingleFITCLaplacianInferenceMethod.cpp.

SGVector< float64_t > compute_mvmZ ( SGVector< float64_t > x )

protectedvirtualinherited

efficiently compute the matrix-vector product $ \inv{\inv{W}+\Sigma} \times x$\f, where $$ is the FITC equivalent covariance n-by-n matrix (prior) of f_n

Parameters

x	input vector

Returns: the matrix-vector product

Definition at line 172 of file SingleFITCLaplacianInferenceMethod.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.

The type of the gradient wrt inducing features is float64_t, which is used to update inducing features
Reason 1 implies that the type of inducing features can be float64_t while the type of features does not required as float64_t
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 198 of file SGObject.cpp.

SGVector< float64_t > derivative_helper_when_Wneg	(	SGVector< float64_t >	res,
		const TParameter *	param
	)

protectedvirtualinherited

returns derivative of negative log marginal likelihood wrt param when W has at least one negative element

Parameters

res	raw derivative
param	parameter

Returns: derivative when W has negative element(s)

Definition at line 817 of file SingleFITCLaplacianInferenceMethod.cpp.

void enable_optimizing_inducing_features ( bool is_optmization )

virtualinherited

whether enable to opitmize inducing features

Parameters

is_optmization enable optimization

Definition at line 257 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

other	object to compare with
accuracy	accuracy to use for comparison (optional)
tolerant	allows linient check on float equality (within accuracy)

Returns: true if all parameters were equal, false if not

Definition at line 618 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_chol_inv ( SGMatrix< float64_t > mtx )

protectedvirtualinherited

efficiently compute the Cholesky decomposition of inverse of the input matrix chol(inv(mtx))

Parameters

mtx	symmetric positive definite matrix

Returns: Cholesky decomposition of inverse of the input matrix

Definition at line 214 of file SingleFITCLaplacianInferenceMethod.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 255 of file InferenceMethod.cpp.

float64_t get_derivative_implicit_term_helper ( SGVector< float64_t > d )

protectedvirtualinherited

helper function to compute variables which are required to compute negative log marginal likelihood implicit derivatives

Parameters

d	raw derivative

Returns: derivative of negative log marginal likelihood

Definition at line 785 of file SingleFITCLaplacianInferenceMethod.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	$\frac{\partial {\Sigma_{m,n}}}{\partial {\theta}}$
v	auxiliary variable related to explicit derivative
R	auxiliary variable related to explicit derivative

Returns: derivative of negative log marginal likelihood

Definition at line 132 of file SingleFITCLaplacianBase.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

Reimplemented from CSingleFITCLaplacianBase.

Definition at line 587 of file SingleFITCLaplacianInferenceMethod.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	$\frac{\partial {\Sigma_{m}}}{\partial {\theta}}$
v	auxiliary variable related to explicit derivative
R	auxiliary 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

BdK	auxiliary variable related to explicit derivative or implicit derivative
param	parameter 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 from CSingleFITCLaplacianBase.

Definition at line 770 of file SingleFITCLaplacianInferenceMethod.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

param parameter of given kernel

Returns: derivative of negative log marginal likelihood

Reimplemented from CSingleFITCLaplacianBase.

Definition at line 827 of file SingleFITCLaplacianInferenceMethod.cpp.

SGVector< float64_t > get_derivative_wrt_inducing_noise ( const TParameter * param )

protectedvirtualinherited

returns derivative of negative log marginal likelihood wrt inducing noise

Parameters

param parameter of given inference class

Returns: derivative of negative log marginal likelihood

Reimplemented from CSingleFITCLaplacianBase.

Definition at line 874 of file SingleFITCLaplacianInferenceMethod.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

param parameter of CInferenceMethod class

Returns: derivative of negative log marginal likelihood

Reimplemented from CSingleSparseInferenceBase.

Definition at line 631 of file SingleFITCLaplacianInferenceMethod.cpp.

SGVector< float64_t > get_derivative_wrt_kernel ( const TParameter * param )

protectedvirtualinherited

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

Parameters

param parameter of given kernel

Returns: derivative of negative log marginal likelihood

Reimplemented from CSingleSparseInferenceBase.

Definition at line 725 of file SingleFITCLaplacianInferenceMethod.cpp.

SGVector< float64_t > get_derivative_wrt_likelihood_model ( const TParameter * param )

protectedvirtualinherited

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

Parameters

param parameter of given likelihood model

Returns: derivative of negative log marginal likelihood

Implements CSingleFITCLaplacianBase.

Definition at line 690 of file SingleFITCLaplacianInferenceMethod.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

param parameter of given mean function

Returns: derivative of negative log marginal likelihood

Reimplemented from CSingleFITCLaplacianBase.

Definition at line 795 of file SingleFITCLaplacianInferenceMethod.cpp.

SGVector< float64_t > get_diagonal_vector ( )

virtualinherited

get diagonal vector

Returns: diagonal of matrix used to calculate posterior covariance matrix:

Definition at line 160 of file SingleFITCLaplacianInferenceMethod.cpp.

virtual CFeatures* get_features ( )

virtualinherited

get features

Returns: features

Definition at line 266 of file InferenceMethod.h.

SGIO * get_global_io ( )

inherited

get the io object

Returns: io object

Definition at line 235 of file SGObject.cpp.

Parallel * get_global_parallel ( )

inherited

get the parallel object

Returns: parallel object

Definition at line 277 of file SGObject.cpp.

Version * get_global_version ( )

inherited

get the version object

Returns: version object

Definition at line 290 of file SGObject.cpp.

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

virtualinherited

get the gradient

Parameters

parameters parameter'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 245 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

virtualinherited

return what type of inference we are

Returns: inference type FITC

Reimplemented from CSparseInferenceBase.

Definition at line 94 of file SingleFITCLaplacianInferenceMethod.h.

virtual CKernel* get_kernel ( )

virtualinherited

get kernel

Returns: kernel

Definition at line 283 of file InferenceMethod.h.

virtual CLabels* get_labels ( )

virtualinherited

get labels

Returns: labels

Definition at line 317 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_samples	the number of importance samples $n$ from $ q(f\|y, \theta) $.
ridge_size	scalar 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 126 of file InferenceMethod.cpp.

virtual CMeanFunction* get_mean ( )

virtualinherited

get mean

Returns: mean

Definition at line 300 of file InferenceMethod.h.

virtual float64_t get_minimization_max ( )

virtualinherited

get maximum for Brent's minimization method

Returns: maximum for Brent's minimization method

Definition at line 199 of file SingleFITCLaplacianInferenceMethod.h.

virtual float64_t get_minimization_tolerance ( )

virtualinherited

get tolerance for Brent's minimization method

Returns: tolerance for Brent's minimization method

Definition at line 187 of file SingleFITCLaplacianInferenceMethod.h.

CLikelihoodModel* get_model ( )

inherited

get likelihood model

Returns: likelihood

Definition at line 334 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 498 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_name name of the parameter

Returns: description of the parameter

Definition at line 522 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_name name of model selection parameter

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

Definition at line 535 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 72 of file InferenceMethod.cpp.

virtual const char* get_name ( ) const

virtual

returns the name of the inference method

Returns: name SingleFITCLaplacian

Reimplemented from CSingleFITCLaplacianInferenceMethod.

Definition at line 87 of file SingleFITCLaplacianInferenceMethodWithLBFGS.h.

float64_t get_negative_log_marginal_likelihood ( )

virtualinherited

get negative log marginal likelihood

Returns: the negative log of the (approximated) 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 231 of file SingleFITCLaplacianInferenceMethod.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 185 of file InferenceMethod.cpp.

virtual int32_t get_newton_iterations ( )

virtualinherited

get max Newton iterations

Returns: max Newton iterations

Definition at line 175 of file SingleFITCLaplacianInferenceMethod.h.

virtual float64_t get_newton_tolerance ( )

virtualinherited

get tolerance for newton iterations

Returns: tolerance for newton iterations

Definition at line 163 of file SingleFITCLaplacianInferenceMethod.h.

SGMatrix< float64_t > get_posterior_covariance ( )

virtualinherited

returns covariance matrix $\Sigma=(K^{-1}+W)^{-1}$ of the Gaussian distribution $\mathcal{N}(\mu,\Sigma)$, which is an approximation to the posterior:

Note that the time complexity of this method is O(n^3), where n is the number of samples

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

Returns: covariance matrix

Implements CSparseInferenceBase.

Definition at line 928 of file SingleFITCLaplacianInferenceMethod.cpp.

SGVector< float64_t > get_posterior_mean ( )

virtualinherited

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

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

Mean vector $\mu$ is evaluated using FITC inference and Newton's method.

Returns: mean vector

Implements CSparseInferenceBase.

Definition at line 903 of file SingleFITCLaplacianInferenceMethod.cpp.

float64_t get_scale ( ) const

virtualinherited

get kernel scale

Returns: kernel scale

Definition at line 61 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 255 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

generic set to the type of the generic if returning TRUE

Returns: TRUE if a class template.

Definition at line 296 of file SGObject.cpp.

bool load_serializable	(	CSerializableFile *	file,
		const char *	prefix = `""`
	)

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

file	where to load from
prefix	prefix for members

Returns: TRUE if done, otherwise FALSE

Definition at line 369 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

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.

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

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.

CSingleFITCLaplacianInferenceMethod * obtain_from_generic ( CInferenceMethod * inference )

staticinherited

helper method used to specialize a base class instance

Parameters

inference inference method

Returns: casted CSingleFITCLaplacianInferenceMethod object

Definition at line 202 of file SingleFITCLaplacianInferenceMethod.cpp.

void optimize_inducing_features ( )

virtualinherited

opitmize inducing features

Definition at line 262 of file SingleSparseInferenceBase.cpp.

bool parameter_hash_changed ( )

virtualinherited

Returns: whether parameter combination has changed since last update

Definition at line 262 of file SGObject.cpp.

void print_modsel_params ( )

inherited

prints all parameter registered for model selection and their type

Definition at line 474 of file SGObject.cpp.

void print_serializable ( const char * prefix = "" )

virtualinherited

prints registered parameters out

Parameters

prefix prefix for members

Definition at line 308 of file SGObject.cpp.

bool save_serializable	(	CSerializableFile *	file,
		const char *	prefix = `""`
	)

virtualinherited

Save this object to file.

Parameters

file	where to save the object; will be closed during returning if PREFIX is an empty string.
prefix	prefix for members

Returns: TRUE if done, otherwise FALSE

Definition at line 314 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

ShogunException will be thrown if an error occurs.

Reimplemented in CKernel.

Definition at line 436 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

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.

virtual void set_features ( CFeatures * feat )

virtualinherited

set features

Parameters

feat	features to set

Definition at line 272 of file InferenceMethod.h.

void set_generic ( )

inherited

Definition at line 41 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 46 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 51 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 56 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 61 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 66 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 71 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 76 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 81 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 86 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 91 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 96 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 101 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 106 of file SGObject.cpp.

void set_generic ( )

inherited

Definition at line 111 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

io	io object to use

Definition at line 228 of file SGObject.cpp.

void set_global_parallel ( Parallel * parallel )

inherited

set the parallel object

Parameters

parallel parallel object to use

Definition at line 241 of file SGObject.cpp.

void set_global_version ( Version * version )

inherited

set the version object

Parameters

version version object to use

Definition at line 283 of file SGObject.cpp.

virtual void set_inducing_features ( CFeatures * feat )

virtualinherited

set inducing features

Parameters

feat	features 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

noise noise 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

kern	kernel to set

Reimplemented from CInferenceMethod.

Definition at line 85 of file SingleSparseInferenceBase.cpp.

virtual void set_labels ( CLabels * lab )

virtualinherited

set labels

Parameters

lab	label to set

Definition at line 323 of file InferenceMethod.h.

void set_lbfgs_parameters	(	int	m = `100`,
		int	max_linesearch = `1000`,
		int	linesearch = `LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE`,
		int	max_iterations = `1000`,
		float64_t	delta = `0.0`,
		int	past = `0`,
		float64_t	epsilon = `1e-5`,
		float64_t	min_step = `1e-20`,
		float64_t	max_step = `1e+20`,
		float64_t	ftol = `1e-4`,
		float64_t	wolfe = `0.9`,
		float64_t	gtol = `0.9`,
		float64_t	xtol = `1e-16`,
		float64_t	orthantwise_c = `0.0`,
		int	orthantwise_start = `0`,
		int	orthantwise_end = `1`
	)

virtual

Definition at line 64 of file SingleFITCLaplacianInferenceMethodWithLBFGS.cpp.

void set_lower_bound_of_inducing_features ( SGVector< float64_t > bound )

virtualinherited

set the lower bound of inducing features

Parameters

bound lower bound constrains of inducing features

Note that if the length of the bound is 1, it means the bound constraint applies to each dimension of all 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 219 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

it	max number of iterations

Definition at line 230 of file SingleSparseInferenceBase.cpp.

virtual void set_mean ( CMeanFunction * m )

virtualinherited

set mean

Parameters

m	mean function to set

Definition at line 306 of file InferenceMethod.h.

virtual void set_minimization_max ( float64_t max )

virtualinherited

set maximum for Brent's minimization method

Parameters

max	maximum for Brent's minimization method

Definition at line 205 of file SingleFITCLaplacianInferenceMethod.h.

virtual void set_minimization_tolerance ( float64_t tol )

virtualinherited

set tolerance for Brent's minimization method

Parameters

tol	tolerance for Brent's minimization method

Definition at line 193 of file SingleFITCLaplacianInferenceMethod.h.

virtual void set_model ( CLikelihoodModel * mod )

virtualinherited

set likelihood model

Parameters

mod	model to set

Reimplemented in CKLInferenceMethod, and CKLDualInferenceMethod.

Definition at line 340 of file InferenceMethod.h.

virtual void set_newton_iterations ( int32_t iter )

virtualinherited

set max Newton iterations

Parameters

iter	max Newton iterations

Definition at line 181 of file SingleFITCLaplacianInferenceMethod.h.

void set_newton_method ( bool enable_newton_if_fail )

virtual

Definition at line 58 of file SingleFITCLaplacianInferenceMethodWithLBFGS.cpp.

virtual void set_newton_tolerance ( float64_t tol )

virtualinherited

set tolerance for newton iterations

Parameters

tol	tolerance for newton iterations to set

Definition at line 169 of file SingleFITCLaplacianInferenceMethod.h.

void set_scale ( float64_t scale )

virtualinherited

set kernel scale

Parameters

scale scale to be set

Definition at line 66 of file InferenceMethod.cpp.

void set_tolearance_for_inducing_features ( float64_t tol )

virtualinherited

set the tolearance used in optimization of inducing features

Parameters

tol	tolearance

Definition at line 235 of file SingleSparseInferenceBase.cpp.

void set_upper_bound_of_inducing_features ( SGVector< float64_t > bound )

virtualinherited

set the upper bound of inducing features

Parameters

bound upper bound constrains of inducing features

Note that if the length of the bound is 1, it means the bound constraint applies to each dimension of all 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 224 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 192 of file SGObject.cpp.

virtual bool supports_binary ( ) const

virtualinherited

Returns: whether combination of Laplace approximation inference method and given likelihood function supports binary classification

Reimplemented from CInferenceMethod.

Definition at line 117 of file SingleFITCLaplacianInferenceMethod.h.

virtual bool supports_multiclass ( ) const

virtualinherited

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

Returns: false

Definition at line 378 of file InferenceMethod.h.

virtual bool supports_regression ( ) const

virtualinherited

Returns: whether combination of Laplace approximation inference method and given likelihood function supports regression

Reimplemented from CInferenceMethod.

Definition at line 107 of file SingleFITCLaplacianInferenceMethod.h.

void unset_generic ( )

inherited

unset generic type

this has to be called in classes specializing a template class

Definition at line 303 of file SGObject.cpp.

void update ( )

virtualinherited

update matrices except gradients

Implements CSparseInferenceBase.

Definition at line 146 of file SingleFITCLaplacianInferenceMethod.cpp.

void update_alpha ( )

protectedvirtual

update alpha matrix

Reimplemented from CSingleFITCLaplacianInferenceMethod.

Definition at line 184 of file SingleFITCLaplacianInferenceMethodWithLBFGS.cpp.

void update_approx_cov ( )

protectedvirtualinherited

update covariance matrix of the approximation to the posterior

Definition at line 267 of file SingleFITCLaplacianInferenceMethod.cpp.

void update_chol ( )

protectedvirtualinherited

update cholesky matrix

Implements CSingleFITCLaplacianBase.

Definition at line 458 of file SingleFITCLaplacianInferenceMethod.cpp.

void update_deriv ( )

protectedvirtualinherited

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

Implements CSingleFITCLaplacianBase.

Definition at line 555 of file SingleFITCLaplacianInferenceMethod.cpp.

void update_init ( )

protectedvirtualinherited

pre-compution for Newton's method

Definition at line 271 of file SingleFITCLaplacianInferenceMethod.cpp.

void update_parameter_hash ( )

virtualinherited

Updates the hash of current parameter combination

Definition at line 248 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 369 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 475 of file InferenceMethod.h.

SGMatrix<float64_t> m_B

protectedinherited

Definition at line 241 of file SingleFITCLaplacianBase.h.

SGMatrix<float64_t> m_chol_R0

protectedinherited

Cholesky of inverse covariance of inducing features

Definition at line 405 of file SingleFITCLaplacianInferenceMethod.h.

SGVector<float64_t> m_d2lp

protectedinherited

second derivative of log likelihood with respect to function location

Definition at line 381 of file SingleFITCLaplacianInferenceMethod.h.

SGVector<float64_t> m_d3lp

protectedinherited

third derivative of log likelihood with respect to function location

Definition at line 384 of file SingleFITCLaplacianInferenceMethod.h.

SGVector<float64_t> m_dfhat

protectedinherited

derivative of negative log (approximated) marginal likelihood wrt f

Definition at line 408 of file SingleFITCLaplacianInferenceMethod.h.

SGVector<float64_t> m_dg

protectedinherited

d0 defined in infFITC_Laplace.m

Definition at line 422 of file SingleFITCLaplacianInferenceMethod.h.

SGVector<float64_t> m_dlp

protectedinherited

derivative of log likelihood with respect to function location

Definition at line 387 of file SingleFITCLaplacianInferenceMethod.h.

SGMatrix<float64_t> m_E

protectedinherited

the matrix used for multi classification

Definition at line 487 of file InferenceMethod.h.

CFeatures* m_features

protectedinherited

features to use

Definition at line 469 of file InferenceMethod.h.

bool m_fully_sparse

protectedinherited

Definition at line 219 of file SingleSparseInferenceBase.h.

SGVector<float64_t> m_g

protectedinherited

g defined in infFITC_Laplace.m

Definition at line 411 of file SingleFITCLaplacianInferenceMethod.h.

Parameter* m_gradient_parameters

inherited

parameters wrt which we can compute gradients

Definition at line 384 of file SGObject.h.

bool m_gradient_update

protectedinherited

Whether gradients are updated

Definition at line 490 of file InferenceMethod.h.

uint32_t m_hash

inherited

Hash of parameter values

Definition at line 387 of file SGObject.h.

float64_t m_ind_tolerance

protectedinherited

tolearance used in optimizing inducing_features

Definition at line 193 of file SingleSparseInferenceBase.h.

SGMatrix<float64_t> m_inducing_features

protectedinherited

inducing features for approximation

Definition at line 305 of file SparseInferenceBase.h.

index_t m_iter

protectedinherited

max Newton's iterations

Definition at line 396 of file SingleFITCLaplacianInferenceMethod.h.

CKernel* m_kernel

protectedinherited

covariance function

Definition at line 460 of file InferenceMethod.h.

SGMatrix<float64_t> m_ktrtr

protectedinherited

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

Definition at line 484 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 478 of file InferenceMethod.h.

CLabels* m_labels

protectedinherited

labels of features

Definition at line 472 of file InferenceMethod.h.

CLock* m_lock

protectedinherited

Definition at line 222 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 481 of file InferenceMethod.h.

SGVector<float64_t> m_lower_bound

protectedinherited

lower bound of inducing features

Definition at line 184 of file SingleSparseInferenceBase.h.

float64_t m_max_ind_iterations

protectedinherited

max number of iterations

Definition at line 190 of file SingleSparseInferenceBase.h.

CMeanFunction* m_mean

protectedinherited

mean function

Definition at line 463 of file InferenceMethod.h.

CLikelihoodModel* m_model

protectedinherited

likelihood function to use

Definition at line 466 of file InferenceMethod.h.

Parameter* m_model_selection_parameters

inherited

model selection parameters

Definition at line 381 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 196 of file SingleSparseInferenceBase.h.

float64_t m_opt_max

protectedinherited

max iterations for Brent's minimization method

Definition at line 402 of file SingleFITCLaplacianInferenceMethod.h.

float64_t m_opt_tolerance

protectedinherited

amount of tolerance for Brent's minimization method

Definition at line 399 of file SingleFITCLaplacianInferenceMethod.h.

Parameter* m_parameters

inherited

parameters

Definition at line 378 of file SGObject.h.

float64_t m_Psi

protectedinherited

the negative log likelihood without constant terms of

\[ -log(p(f_n|y)) \]

used in Newton's method

Definition at line 419 of file SingleFITCLaplacianInferenceMethod.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_sW

protectedinherited

square root of W

Definition at line 378 of file SingleFITCLaplacianInferenceMethod.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.

float64_t m_tolerance

protectedinherited

amount of tolerance for Newton's iterations

Definition at line 393 of file SingleFITCLaplacianInferenceMethod.h.

SGVector<float64_t> m_upper_bound

protectedinherited

upper bound of inducing features

Definition at line 187 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.

SGVector<float64_t> m_W

protectedinherited

noise matrix

Definition at line 390 of file SingleFITCLaplacianInferenceMethod.h.

bool m_Wneg

protectedinherited

whether W contains negative elements

Definition at line 425 of file SingleFITCLaplacianInferenceMethod.h.

Parallel* parallel

inherited

parallel

Definition at line 372 of file SGObject.h.

Version* version

inherited

version

Definition at line 375 of file SGObject.h.

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

ddiagKi	\(\textbf{diag}(\frac{\partial {\Sigma_{n}}}{\partial {\theta}})\)
dKuui	\(\frac{\partial {\Sigma_{m}}}{\partial {\theta}}\)
dKui	\(\frac{\partial {\Sigma_{m,n}}}{\partial {\theta}}\)
v	auxiliary variable related to explicit derivative
R	auxiliary variable related to explicit derivative

num_importance_samples	the number of importance samples \(n\) from \( q(f\|y, \theta) \).
ridge_size	scalar 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.

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation