Detailed Description

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

This inference method approximates the posterior likelihood function by using Laplace's method. Here, we compute a Gaussian approximation to the posterior via a Taylor expansion around the maximum of the posterior likelihood function. We use the Limited-memory BFGS method to obtain the maximum of likelihood. Note that due to the Laplace approximation, the time complexity of the class still is O(n^3), where n is the number of training data points. However, in the optimization step we use L-BFGS method, which of the time complexity is O(n*m) to replace the Newton method, which of the time complexity is O(n^3). Here L-BFGS only uses the last m (m<<n) function/gradient pairs to find the optimal pointer

For more details, 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 65 of file SingleLaplacianInferenceMethodWithLBFGS.h.

Inheritance diagram for CSingleLaplacianInferenceMethodWithLBFGS:

[legend]

Public Member Functions
	CSingleLaplacianInferenceMethodWithLBFGS ()

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

virtual	~CSingleLaplacianInferenceMethodWithLBFGS ()

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 float64_t	get_negative_log_marginal_likelihood ()

virtual bool	supports_regression () const

virtual bool	supports_binary () const

virtual SGVector< float64_t >	get_diagonal_vector ()

virtual void	update ()

virtual SGVector< float64_t >	get_posterior_mean ()

virtual SGMatrix< float64_t >	get_cholesky ()

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)

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 void	set_kernel (CKernel *kern)

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 CSingleLaplacianInferenceMethod *	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	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 void	compute_gradient ()

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_dfhat

SGMatrix< float64_t >	m_Z

SGVector< float64_t >	m_g

float64_t	m_Psi

SGVector< float64_t >	m_dlp

SGVector< float64_t >	m_W

SGVector< float64_t >	m_mu

SGMatrix< float64_t >	m_Sigma

float64_t	m_tolerance

index_t	m_iter

float64_t	m_opt_tolerance

float64_t	m_opt_max

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

CSingleLaplacianInferenceMethodWithLBFGS ( )

Definition at line 43 of file SingleLaplacianInferenceMethodWithLBFGS.cpp.

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

Definition at line 49 of file SingleLaplacianInferenceMethodWithLBFGS.cpp.

~CSingleLaplacianInferenceMethodWithLBFGS ( )

virtual

Definition at line 160 of file SingleLaplacianInferenceMethodWithLBFGS.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_members ( ) const

protectedvirtualinherited

check if members of object are valid for inference

Reimplemented in CSparseInferenceBase, CExactInferenceMethod, CFITCInferenceMethod, CSparseVGInferenceMethod, and CMultiLaplacianInferenceMethod.

Definition at line 309 of file InferenceMethod.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 80 of file LaplacianInferenceBase.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.

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.

SGMatrix< float64_t > get_cholesky ( )

virtualinherited

get alpha vector

Returns: vector to compute posterior mean of Gaussian Process:

\[ \mu = K\alpha+meanf \]

where $\mu$ is the mean, $K$ is the prior covariance matrix, and $meanf$\f is the mean prior fomr MeanFunction */ virtual SGVector<float64_t> get_alpha(); /** get Cholesky decomposition matrix @return Cholesky decomposition of matrix: for binary and regression case \f[ L = Cholesky(W^{\frac{1}{2}}*K*W^{\frac{1}{2}}+I) \f] where $ $ is the prior covariance matrix, $sW $ is the vector returned by get_diagonal_vector(), and $ $ is the identity matrix. for multiclass case \f[ M = Cholesky(\sum_\text{c}{E_\text{c}) \f] where ${c}

Definition at line 115 of file LaplacianInferenceBase.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.

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

Implements CInferenceMethod.

Definition at line 450 of file SingleLaplacianInferenceMethod.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

Implements CInferenceMethod.

Definition at line 515 of file SingleLaplacianInferenceMethod.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 CInferenceMethod.

Definition at line 481 of file SingleLaplacianInferenceMethod.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

Implements CInferenceMethod.

Definition at line 557 of file SingleLaplacianInferenceMethod.cpp.

SGVector< float64_t > get_diagonal_vector ( )

virtualinherited

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 95 of file SingleLaplacianInferenceMethod.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 EInferenceType get_inference_type ( ) const

virtualinherited

return what type of inference we are

Returns: inference type Laplacian_Single

Reimplemented from CLaplacianInferenceBase.

Definition at line 72 of file SingleLaplacianInferenceMethod.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 177 of file LaplacianInferenceBase.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 165 of file LaplacianInferenceBase.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 SingleLaplacian

Reimplemented from CSingleLaplacianInferenceMethod.

Definition at line 91 of file SingleLaplacianInferenceMethodWithLBFGS.h.

float64_t get_negative_log_marginal_likelihood ( )

virtualinherited

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 121 of file SingleLaplacianInferenceMethod.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 153 of file LaplacianInferenceBase.h.

virtual float64_t get_newton_tolerance ( )

virtualinherited

get tolerance for newton iterations

Returns: tolerance for newton iterations

Definition at line 141 of file LaplacianInferenceBase.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:

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

Returns: covariance matrix

Implements CInferenceMethod.

Definition at line 124 of file LaplacianInferenceBase.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:

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

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

Returns: mean vector

Implements CInferenceMethod.

Definition at line 590 of file SingleLaplacianInferenceMethod.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.

CSingleLaplacianInferenceMethod * obtain_from_generic ( CInferenceMethod * inference )

staticinherited

helper method used to specialize a base class instance

Parameters

inference inference method

Returns: casted CSingleLaplacianInferenceMethod object

Definition at line 104 of file SingleLaplacianInferenceMethod.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_kernel ( CKernel * kern )

virtualinherited

set kernel

Parameters

kern	kernel to set

Reimplemented in CSingleSparseInferenceBase.

Definition at line 289 of file InferenceMethod.h.

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 66 of file SingleLaplacianInferenceMethodWithLBFGS.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 183 of file LaplacianInferenceBase.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 171 of file LaplacianInferenceBase.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 159 of file LaplacianInferenceBase.h.

void set_newton_method ( bool enable_newton_if_fail )

virtual

Definition at line 60 of file SingleLaplacianInferenceMethodWithLBFGS.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 147 of file LaplacianInferenceBase.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.

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 108 of file SingleLaplacianInferenceMethod.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 98 of file SingleLaplacianInferenceMethod.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 all matrices except gradients

Reimplemented from CLaplacianInferenceBase.

Definition at line 234 of file SingleLaplacianInferenceMethod.cpp.

void update_alpha ( )

protectedvirtual

update alpha matrix

Reimplemented from CSingleLaplacianInferenceMethod.

Definition at line 185 of file SingleLaplacianInferenceMethodWithLBFGS.cpp.

void update_approx_cov ( )

protectedvirtualinherited

update covariance matrix of the approximation to the posterior

Implements CLaplacianInferenceBase.

Definition at line 162 of file SingleLaplacianInferenceMethod.cpp.

void update_chol ( )

protectedvirtualinherited

update cholesky matrix

Implements CInferenceMethod.

Definition at line 182 of file SingleLaplacianInferenceMethod.cpp.

void update_deriv ( )

protectedvirtualinherited

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

Implements CInferenceMethod.

Definition at line 394 of file SingleLaplacianInferenceMethod.cpp.

void update_init ( )

protectedvirtualinherited

Definition at line 249 of file SingleLaplacianInferenceMethod.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 in CSparseInferenceBase.

Definition at line 324 of file InferenceMethod.cpp.

Member Data Documentation

SGIO* io

inherited

io

Definition at line 369 of file SGObject.h.

SGVector<float64_t> m_alpha

protectedinherited

alpha vector used in process mean calculation

Definition at line 475 of file InferenceMethod.h.

SGVector<float64_t> m_d2lp

protectedinherited

second derivative of log likelihood with respect to function location

Definition at line 208 of file SingleLaplacianInferenceMethod.h.

SGVector<float64_t> m_d3lp

protectedinherited

third derivative of log likelihood with respect to function location

Definition at line 211 of file SingleLaplacianInferenceMethod.h.

SGVector<float64_t> m_dfhat

protectedinherited

Definition at line 213 of file SingleLaplacianInferenceMethod.h.

SGVector<float64_t> m_dlp

protectedinherited

derivative of log likelihood with respect to function location

Definition at line 197 of file LaplacianInferenceBase.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.

SGVector<float64_t> m_g

protectedinherited

Definition at line 217 of file SingleLaplacianInferenceMethod.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.

index_t m_iter

protectedinherited

max Newton's iterations

Definition at line 212 of file LaplacianInferenceBase.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.

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.

float64_t m_log_scale

protectedinherited

kernel scale

Definition at line 481 of file InferenceMethod.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 approximation to the posterior

Definition at line 203 of file LaplacianInferenceBase.h.

float64_t m_opt_max

protectedinherited

max iterations for Brent's minimization method

Definition at line 218 of file LaplacianInferenceBase.h.

float64_t m_opt_tolerance

protectedinherited

amount of tolerance for Brent's minimization method

Definition at line 215 of file LaplacianInferenceBase.h.

Parameter* m_parameters

inherited

parameters

Definition at line 378 of file SGObject.h.

float64_t m_Psi

protectedinherited

Definition at line 219 of file SingleLaplacianInferenceMethod.h.

SGMatrix<float64_t> m_Sigma

protectedinherited

covariance matrix of the approximation to the posterior

Definition at line 206 of file LaplacianInferenceBase.h.

SGVector<float64_t> m_sW

protectedinherited

square root of W

Definition at line 205 of file SingleLaplacianInferenceMethod.h.

float64_t m_tolerance

protectedinherited

amount of tolerance for Newton's iterations

Definition at line 209 of file LaplacianInferenceBase.h.

SGVector<float64_t> m_W

protectedinherited

noise matrix

Definition at line 200 of file LaplacianInferenceBase.h.

SGMatrix<float64_t> m_Z

protectedinherited

Definition at line 215 of file SingleLaplacianInferenceMethod.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:

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