SHOGUN
4.2.0
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The Gaussian exact form inference method class.
This inference method computes the Gaussian Method exactly using matrix equations.
\[ L = cholesky(K + \sigma^{2}I) \]
\(L\) is the cholesky decomposition of \(K\), the covariance matrix, plus a diagonal matrix with entries \(\sigma^{2}\), the observation noise.
\[ \boldsymbol{\alpha} = L^{T} \backslash(L \backslash \boldsymbol{y}}) \]
where \(L\) is the matrix mentioned above, \(\boldsymbol{y}\) are the labels, and \(\backslash\) is an operator ( \(x = A \backslash B\) means \(Ax=B\).)
NOTE: The Gaussian Likelihood Function must be used for this inference method.
Definition at line 66 of file ExactInferenceMethod.h.
Public Member Functions | |
CExactInferenceMethod () | |
CExactInferenceMethod (CKernel *kernel, CFeatures *features, CMeanFunction *mean, CLabels *labels, CLikelihoodModel *model) | |
virtual | ~CExactInferenceMethod () |
virtual EInferenceType | get_inference_type () const |
virtual const char * | get_name () const |
virtual float64_t | get_negative_log_marginal_likelihood () |
virtual SGVector< float64_t > | get_alpha () |
virtual SGMatrix< float64_t > | get_cholesky () |
virtual SGVector< float64_t > | get_diagonal_vector () |
virtual SGVector< float64_t > | get_posterior_mean () |
virtual SGMatrix< float64_t > | get_posterior_covariance () |
virtual bool | supports_regression () const |
virtual void | update () |
virtual void | register_minimizer (Minimizer *minimizer) |
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_binary () const |
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) |
bool | has (const std::string &name) const |
template<typename T > | |
bool | has (const Tag< T > &tag) const |
template<typename T , typename U = void> | |
bool | has (const std::string &name) const |
template<typename T > | |
void | set (const Tag< T > &_tag, const T &value) |
template<typename T , typename U = void> | |
void | set (const std::string &name, const T &value) |
template<typename T > | |
T | get (const Tag< T > &_tag) const |
template<typename T , typename U = void> | |
T | get (const std::string &name) const |
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 CExactInferenceMethod * | obtain_from_generic (CInference *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 | check_members () const |
virtual void | update_alpha () |
virtual void | update_chol () |
virtual void | update_mean () |
virtual void | update_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 | 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) |
template<typename T > | |
void | register_param (Tag< T > &_tag, const T &value) |
template<typename T > | |
void | register_param (const std::string &name, const T &value) |
Static Protected Member Functions | |
static void * | get_derivative_helper (void *p) |
Protected Attributes | |
Minimizer * | m_minimizer |
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 |
default constructor
Definition at line 45 of file ExactInferenceMethod.cpp.
CExactInferenceMethod | ( | CKernel * | kernel, |
CFeatures * | features, | ||
CMeanFunction * | mean, | ||
CLabels * | labels, | ||
CLikelihoodModel * | model | ||
) |
constructor
kernel | covariance function |
features | features to use in inference |
mean | mean function to use |
labels | labels of the features |
model | likelihood model to use |
Definition at line 49 of file ExactInferenceMethod.cpp.
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virtual |
Definition at line 55 of file ExactInferenceMethod.cpp.
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Builds a dictionary of all parameters in SGObject as well of those of SGObjects that are parameters of this object. Dictionary maps parameters to the objects that own them.
dict | dictionary of parameters to be built. |
Definition at line 630 of file SGObject.cpp.
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check if members of object are valid for inference
Reimplemented from CInference.
Definition at line 91 of file ExactInferenceMethod.cpp.
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Creates a clone of the current object. This is done via recursively traversing all parameters, which corresponds to a deep copy. Calling equals on the cloned object always returns true although none of the memory of both objects overlaps.
Definition at line 747 of file SGObject.cpp.
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update gradients
Reimplemented from CInference.
Definition at line 64 of file ExactInferenceMethod.cpp.
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virtualinherited |
A deep copy. All the instance variables will also be copied.
Definition at line 231 of file SGObject.cpp.
Recursively compares the current SGObject to another one. Compares all registered numerical parameters, recursion upon complex (SGObject) parameters. Does not compare pointers!
May be overwritten but please do with care! Should not be necessary in most cases.
other | object to compare with |
accuracy | accuracy to use for comparison (optional) |
tolerant | allows linient check on float equality (within accuracy) |
Definition at line 651 of file SGObject.cpp.
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Getter for a class parameter, identified by a Tag. Throws an exception if the class does not have such a parameter.
_tag | name and type information of parameter |
Definition at line 367 of file SGObject.h.
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Getter for a class parameter, identified by a name. Throws an exception if the class does not have such a parameter.
name | name of the parameter |
Definition at line 388 of file SGObject.h.
get alpha vector
\[ \mu = K\alpha \]
where \(\mu\) is the mean and \(K\) is the prior covariance matrix.
Implements CInference.
Definition at line 147 of file ExactInferenceMethod.cpp.
get Cholesky decomposition 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.
Implements CInference.
Definition at line 155 of file ExactInferenceMethod.cpp.
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staticprotectedinherited |
pthread helper method to compute negative log marginal likelihood derivatives wrt hyperparameter
Definition at line 268 of file Inference.cpp.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt parameter of CInference class
param | parameter of CInference class |
Implements CInference.
Definition at line 288 of file ExactInferenceMethod.cpp.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt kernel's parameter
param | parameter of given kernel |
Implements CInference.
Definition at line 344 of file ExactInferenceMethod.cpp.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt parameter of likelihood model
param | parameter of given likelihood model |
Implements CInference.
Definition at line 320 of file ExactInferenceMethod.cpp.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt mean function's parameter
param | parameter of given mean function |
Implements CInference.
Definition at line 374 of file ExactInferenceMethod.cpp.
get diagonal vector
\[ Cov = (K^{-1}+sW^{2})^{-1} \]
where \(Cov\) is the posterior covariance matrix, \(K\) is the prior covariance matrix, and \(sW\) is the diagonal vector.
Implements CInference.
Definition at line 101 of file ExactInferenceMethod.cpp.
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inherited |
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inherited |
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inherited |
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get the gradient
parameters | parameter's dictionary |
Implements CDifferentiableFunction.
Definition at line 245 of file Inference.h.
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return what type of inference we are
Reimplemented from CInference.
Definition at line 89 of file ExactInferenceMethod.h.
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virtualinherited |
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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 CInference 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.
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. |
Definition at line 139 of file Inference.cpp.
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virtualinherited |
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inherited |
Definition at line 531 of file SGObject.cpp.
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Returns description of a given parameter string, if it exists. SG_ERROR otherwise
param_name | name of the parameter |
Definition at line 555 of file SGObject.cpp.
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Returns index of model selection parameter with provided index
param_name | name of model selection parameter |
Definition at line 568 of file SGObject.cpp.
get the E matrix used for multi classification
Definition at line 71 of file Inference.cpp.
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returns the name of the inference method
Implements CSGObject.
Definition at line 95 of file ExactInferenceMethod.h.
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get negative log marginal likelihood
\[ -log(p(y|X, \theta)) \]
where \(y\) are the labels, \(X\) are the features, and \(\theta\) represent hyperparameters.
Implements CInference.
Definition at line 118 of file ExactInferenceMethod.cpp.
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get log marginal likelihood gradient
\[ -\frac{\partial log(p(y|X, \theta))}{\partial \theta} \]
where \(y\) are the labels, \(X\) are the features, and \(\theta\) represent hyperparameters.
Definition at line 198 of file Inference.cpp.
returns covariance matrix \(\Sigma\) of the posterior Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\)
\[ p(f|y) = \mathcal{N}(\mu,\Sigma) \]
Implements CInference.
Definition at line 170 of file ExactInferenceMethod.cpp.
returns mean vector \(\mu\) of the posterior Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\)
\[ p(f|y) = \mathcal{N}(\mu,\Sigma) \]
Implements CInference.
Definition at line 163 of file ExactInferenceMethod.cpp.
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get the function value
Implements CDifferentiableFunction.
Definition at line 255 of file Inference.h.
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inherited |
Checks if object has a class parameter identified by a name.
name | name of the parameter |
Definition at line 289 of file SGObject.h.
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inherited |
Checks if object has a class parameter identified by a Tag.
tag | tag of the parameter containing name and type information |
Definition at line 301 of file SGObject.h.
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inherited |
Checks if a type exists for a class parameter identified by a name.
name | name of the parameter |
Definition at line 312 of file SGObject.h.
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virtualinherited |
If the SGSerializable is a class template then TRUE will be returned and GENERIC is set to the type of the generic.
generic | set to the type of the generic if returning TRUE |
Definition at line 329 of file SGObject.cpp.
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Load this object from file. If it will fail (returning FALSE) then this object will contain inconsistent data and should not be used!
file | where to load from |
prefix | prefix for members |
Definition at line 402 of file SGObject.cpp.
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protectedvirtualinherited |
Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_POST is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.
Definition at line 459 of file SGObject.cpp.
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Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_PRE is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 454 of file SGObject.cpp.
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static |
helper method used to specialize a base class instance
inference | inference method |
Definition at line 307 of file ExactInferenceMethod.cpp.
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virtualinherited |
Definition at line 295 of file SGObject.cpp.
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prints all parameter registered for model selection and their type
Definition at line 507 of file SGObject.cpp.
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prints registered parameters out
prefix | prefix for members |
Definition at line 341 of file SGObject.cpp.
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Set a minimizer
minimizer | minimizer used in inference method |
Reimplemented from CInference.
Definition at line 59 of file ExactInferenceMethod.cpp.
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Registers a class parameter which is identified by a tag. This enables the parameter to be modified by set() and retrieved by get(). Parameters can be registered in the constructor of the class.
_tag | name and type information of parameter |
value | value of the parameter |
Definition at line 439 of file SGObject.h.
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protectedinherited |
Registers a class parameter which is identified by a name. This enables the parameter to be modified by set() and retrieved by get(). Parameters can be registered in the constructor of the class.
name | name of the parameter |
value | value of the parameter along with type information |
Definition at line 452 of file SGObject.h.
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Save this object to file.
file | where to save the object; will be closed during returning if PREFIX is an empty string. |
prefix | prefix for members |
Definition at line 347 of file SGObject.cpp.
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Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_POST is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel.
Definition at line 469 of file SGObject.cpp.
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protectedvirtualinherited |
Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_PRE is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 464 of file SGObject.cpp.
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Setter for a class parameter, identified by a Tag. Throws an exception if the class does not have such a parameter.
_tag | name and type information of parameter |
value | value of the parameter |
Definition at line 328 of file SGObject.h.
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Setter for a class parameter, identified by a name. Throws an exception if the class does not have such a parameter.
name | name of the parameter |
value | value of the parameter along with type information |
Definition at line 354 of file SGObject.h.
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Definition at line 74 of file SGObject.cpp.
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Definition at line 79 of file SGObject.cpp.
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Definition at line 84 of file SGObject.cpp.
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Definition at line 89 of file SGObject.cpp.
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Definition at line 94 of file SGObject.cpp.
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Definition at line 99 of file SGObject.cpp.
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Definition at line 104 of file SGObject.cpp.
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Definition at line 109 of file SGObject.cpp.
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Definition at line 114 of file SGObject.cpp.
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Definition at line 119 of file SGObject.cpp.
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Definition at line 124 of file SGObject.cpp.
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Definition at line 129 of file SGObject.cpp.
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Definition at line 134 of file SGObject.cpp.
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Definition at line 139 of file SGObject.cpp.
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Definition at line 144 of file SGObject.cpp.
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set generic type to T
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set the parallel object
parallel | parallel object to use |
Definition at line 274 of file SGObject.cpp.
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set the version object
version | version object to use |
Definition at line 316 of file SGObject.cpp.
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set kernel
kern | kernel to set |
Reimplemented in CSingleSparseInference.
Definition at line 289 of file Inference.h.
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set likelihood model
mod | model to set |
Reimplemented in CKLDualInferenceMethod, and CKLInference.
Definition at line 340 of file Inference.h.
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A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.
Reimplemented in CGaussianKernel.
Definition at line 225 of file SGObject.cpp.
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whether combination of inference method and given likelihood function supports binary classification
Reimplemented in CEPInferenceMethod, CKLInference, CSingleFITCLaplaceInferenceMethod, and CSingleLaplaceInferenceMethod.
Definition at line 371 of file Inference.h.
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whether combination of inference method and given likelihood function supports multiclass classification
Reimplemented in CMultiLaplaceInferenceMethod.
Definition at line 378 of file Inference.h.
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virtual |
Reimplemented from CInference.
Definition at line 181 of file ExactInferenceMethod.h.
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unset generic type
this has to be called in classes specializing a template class
Definition at line 336 of file SGObject.cpp.
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update matrices except gradients
Reimplemented from CInference.
Definition at line 78 of file ExactInferenceMethod.cpp.
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update Cholesky matrix
Implements CInference.
Definition at line 177 of file ExactInferenceMethod.cpp.
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update covariance matrix of the posterior Gaussian
Definition at line 238 of file ExactInferenceMethod.cpp.
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update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter
Implements CInference.
Definition at line 262 of file ExactInferenceMethod.cpp.
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update mean vector of the posterior Gaussian
Definition at line 222 of file ExactInferenceMethod.cpp.
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virtualinherited |
Updates the hash of current parameter combination
Definition at line 281 of file SGObject.cpp.
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protectedvirtualinherited |
update train kernel matrix
Reimplemented in CSparseInference.
Definition at line 337 of file Inference.cpp.
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io
Definition at line 537 of file SGObject.h.
alpha vector used in process mean calculation
Definition at line 484 of file Inference.h.
the matrix used for multi classification
Definition at line 496 of file Inference.h.
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features to use
Definition at line 478 of file Inference.h.
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parameters wrt which we can compute gradients
Definition at line 552 of file SGObject.h.
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Whether gradients are updated
Definition at line 499 of file Inference.h.
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Hash of parameter values
Definition at line 555 of file SGObject.h.
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covariance function
Definition at line 469 of file Inference.h.
kernel matrix from features (non-scalled by inference scalling)
Definition at line 493 of file Inference.h.
upper triangular factor of Cholesky decomposition
Definition at line 487 of file Inference.h.
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labels of features
Definition at line 481 of file Inference.h.
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kernel scale
Definition at line 490 of file Inference.h.
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mean function
Definition at line 472 of file Inference.h.
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minimizer
Definition at line 466 of file Inference.h.
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likelihood function to use
Definition at line 475 of file Inference.h.
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model selection parameters
Definition at line 549 of file SGObject.h.
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parameters
Definition at line 546 of file SGObject.h.
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parallel
Definition at line 540 of file SGObject.h.
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version
Definition at line 543 of file SGObject.h.