SHOGUN
4.0.0
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The Laplace approximation inference method class for multi 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.
Code adapted from https://gist.github.com/yorkerlin/14ace49f2278f3859614 Gaussian Process Machine Learning Toolbox http://www.gaussianprocess.org/gpml/code/matlab/doc/ and GPstuff - Gaussian process models for Bayesian analysis http://becs.aalto.fi/en/research/bayes/gpstuff/
The reference pseudo code is the algorithm 3.3 of the GPML textbook
在文件 MultiLaplacianInferenceMethod.h 第 70 行定义.
Public 属性 | |
SGIO * | io |
Parallel * | parallel |
Version * | version |
Parameter * | m_parameters |
Parameter * | m_model_selection_parameters |
Parameter * | m_gradient_parameters |
ParameterMap * | m_parameter_map |
uint32_t | m_hash |
Protected 成员函数 | |
virtual void | update_approx_cov ()=0 |
virtual void | check_members () const |
virtual void | update_alpha ()=0 |
virtual void | update_chol ()=0 |
virtual void | update_deriv ()=0 |
virtual void | update_train_kernel () |
virtual SGVector< float64_t > | get_derivative_wrt_inference_method (const TParameter *param)=0 |
virtual SGVector< float64_t > | get_derivative_wrt_likelihood_model (const TParameter *param)=0 |
virtual SGVector< float64_t > | get_derivative_wrt_kernel (const TParameter *param)=0 |
virtual SGVector< float64_t > | get_derivative_wrt_mean (const TParameter *param)=0 |
virtual TParameter * | migrate (DynArray< TParameter * > *param_base, const SGParamInfo *target) |
virtual void | one_to_one_migration_prepare (DynArray< TParameter * > *param_base, const SGParamInfo *target, TParameter *&replacement, TParameter *&to_migrate, char *old_name=NULL) |
virtual void | load_serializable_pre () throw (ShogunException) |
virtual void | load_serializable_post () throw (ShogunException) |
virtual void | save_serializable_pre () throw (ShogunException) |
virtual void | save_serializable_post () throw (ShogunException) |
静态 Protected 成员函数 | |
static void * | get_derivative_helper (void *p) |
Protected 属性 | |
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_scale |
SGMatrix< float64_t > | m_ktrtr |
SGMatrix< float64_t > | m_E |
default constructor
在文件 MultiLaplacianInferenceMethod.cpp 第 102 行定义.
CMultiLaplacianInferenceMethod | ( | CKernel * | kernel, |
CFeatures * | features, | ||
CMeanFunction * | mean, | ||
CLabels * | labels, | ||
CLikelihoodModel * | model | ||
) |
constructor
kernel | covariance function |
features | features to use in inference |
mean | mean function |
labels | labels of the features |
model | Likelihood model to use |
在文件 MultiLaplacianInferenceMethod.cpp 第 107 行定义.
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virtual |
在文件 MultiLaplacianInferenceMethod.cpp 第 121 行定义.
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inherited |
Builds a dictionary of all parameters in SGObject as well of those of SGObjects that are parameters of this object. Dictionary maps parameters to the objects that own them.
dict | dictionary of parameters to be built. |
在文件 SGObject.cpp 第 1243 行定义.
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protectedvirtualinherited |
check if members of object are valid for inference
被 CFITCInferenceMethod , 以及 CExactInferenceMethod 重载.
在文件 InferenceMethod.cpp 第 275 行定义.
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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.
在文件 SGObject.cpp 第 1360 行定义.
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A deep copy. All the instance variables will also be copied.
在文件 SGObject.cpp 第 200 行定义.
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) |
在文件 SGObject.cpp 第 1264 行定义.
get alpha vector
\[ \mu = K\alpha+meanf \]
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}
在文件 LaplacianInferenceBase.cpp 第 104 行定义.
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staticprotectedinherited |
pthread helper method to compute negative log marginal likelihood derivatives wrt hyperparameter
在文件 InferenceMethod.cpp 第 221 行定义.
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protectedpure virtualinherited |
returns derivative of negative log marginal likelihood wrt parameter of CInferenceMethod class
param | parameter of CInferenceMethod class |
在 CKLInferenceMethod, CEPInferenceMethod, CFITCInferenceMethod, CExactInferenceMethod , 以及 CSingleLaplacianInferenceMethod 内被实现.
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protectedpure virtualinherited |
returns derivative of negative log marginal likelihood wrt kernel's parameter
param | parameter of given kernel |
在 CKLInferenceMethod, CEPInferenceMethod, CFITCInferenceMethod, CExactInferenceMethod , 以及 CSingleLaplacianInferenceMethod 内被实现.
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protectedpure virtualinherited |
returns derivative of negative log marginal likelihood wrt parameter of likelihood model
param | parameter of given likelihood model |
在 CKLInferenceMethod, CEPInferenceMethod, CFITCInferenceMethod, CExactInferenceMethod , 以及 CSingleLaplacianInferenceMethod 内被实现.
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protectedpure virtualinherited |
returns derivative of negative log marginal likelihood wrt mean function's parameter
param | parameter of given mean function |
在 CKLInferenceMethod, CEPInferenceMethod, CFITCInferenceMethod, CExactInferenceMethod , 以及 CSingleLaplacianInferenceMethod 内被实现.
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virtual |
get diagonal vector where the vector, \(\pi$\f, defined in the algorithm 3.3 of the GPML textbook @return the vector used for inference */ virtual SGVector<float64_t> get_diagonal_vector(); /** @return whether combination of Laplace approximation inference method and given likelihood function supports multi classification */ virtual bool supports_multiclass() const { check_members(); return m_model->supports_multiclass(); } protected: /** check if members of object are valid for inference */ virtual void check_members() const; /** update alpha matrix */ virtual void update_alpha(); /** update cholesky matrix */ virtual void update_chol(); /** update covariance matrix of the approximation to the posterior */ virtual void update_approx_cov(); /** update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter */ virtual void update_deriv(); /** returns derivative of negative log marginal likelihood wrt parameter of CInferenceMethod class @param param parameter of CInferenceMethod class @return derivative of negative log marginal likelihood */ virtual SGVector<float64_t> get_derivative_wrt_inference_method( const TParameter* param); /** returns derivative of negative log marginal likelihood wrt parameter of likelihood model @param param parameter of given likelihood model @return derivative of negative log marginal likelihood */ virtual SGVector<float64_t> get_derivative_wrt_likelihood_model( const TParameter* param); /** returns derivative of negative log marginal likelihood wrt kernel's parameter @param param parameter of given kernel @return derivative of negative log marginal likelihood */ virtual SGVector<float64_t> get_derivative_wrt_kernel( const TParameter* param); /** returns derivative of negative log marginal likelihood wrt mean function's parameter @param param parameter of given mean function @return derivative of negative log marginal likelihood */ virtual SGVector<float64_t> get_derivative_wrt_mean( const TParameter* param); private: void init(); protected: /** the matrix used to compute gradient wrt hyperparameters */ SGMatrix<float64_t> m_U; /** negative log marginal likelihood */ float64_t m_nlz; /** the helper method used to compute gradient of GP wrt hyperparameter @param raw gradient wrt hyperparameter @return the gradient of GP wrt hyperparameter */ virtual float64_t get_derivative_helper(SGMatrix<float64_t> dK); /** the helper used to compute gradient of GP for inference construct the \)$ vector defined in the algorithm 3.3 of the GPML textbook Noth that the vector is stored in m_W
在文件 MultiLaplacianInferenceMethod.cpp 第 188 行定义.
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inherited |
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virtualinherited |
get the gradient
parameters | parameter's dictionary |
在文件 InferenceMethod.h 第 215 行定义.
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return what type of inference we are
重载 CInferenceMethod .
在文件 LaplacianInferenceBase.h 第 75 行定义.
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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 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.
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. |
在文件 InferenceMethod.cpp 第 91 行定义.
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virtualinherited |
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virtualinherited |
get maximum for Brent's minimization method
在文件 LaplacianInferenceBase.h 第 191 行定义.
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virtualinherited |
get tolerance for Brent's minimization method
在文件 LaplacianInferenceBase.h 第 179 行定义.
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inherited |
在文件 SGObject.cpp 第 1135 行定义.
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Returns description of a given parameter string, if it exists. SG_ERROR otherwise
param_name | name of the parameter |
在文件 SGObject.cpp 第 1159 行定义.
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Returns index of model selection parameter with provided index
param_name | name of model selection parameter |
在文件 SGObject.cpp 第 1172 行定义.
get the E matrix used for multi classification
在文件 InferenceMethod.cpp 第 40 行定义.
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virtual |
returns the name of the inference method
在文件 MultiLaplacianInferenceMethod.h 第 94 行定义.
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virtual |
get negative log marginal likelihood
\[ -log(p(y|X, \theta)) \]
where \(y\) are the labels, \(X\) are the features, and \(\theta\) represent hyperparameters.
实现了 CInferenceMethod.
在文件 MultiLaplacianInferenceMethod.cpp 第 145 行定义.
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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.
在文件 InferenceMethod.cpp 第 150 行定义.
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get tolerance for newton iterations
在文件 LaplacianInferenceBase.h 第 155 行定义.
returns covariance matrix \(\Sigma=(K^{-1}+W)^{-1}\) of the Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\), which is an approximation to the posterior:
\[ p(f|y) \approx q(f|y) = \mathcal{N}(f|\mu,\Sigma) \]
实现了 CInferenceMethod.
在文件 LaplacianInferenceBase.cpp 第 122 行定义.
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.
实现了 CInferenceMethod.
在文件 LaplacianInferenceBase.cpp 第 113 行定义.
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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 |
在文件 SGObject.cpp 第 297 行定义.
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maps all parameters of this instance to the provided file version and loads all parameter data from the file into an array, which is sorted (basically calls load_file_parameter(...) for all parameters and puts all results into a sorted array)
file_version | parameter version of the file |
current_version | version from which mapping begins (you want to use Version::get_version_parameter() for this in most cases) |
file | file to load from |
prefix | prefix for members |
在文件 SGObject.cpp 第 704 行定义.
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loads some specified parameters from a file with a specified version The provided parameter info has a version which is recursively mapped until the file parameter version is reached. Note that there may be possibly multiple parameters in the mapping, therefore, a set of TParameter instances is returned
param_info | information of parameter |
file_version | parameter version of the file, must be <= provided parameter version |
file | file to load from |
prefix | prefix for members |
在文件 SGObject.cpp 第 545 行定义.
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virtualinherited |
Load this object from file. If it will fail (returning FALSE) then this object will contain inconsistent data and should not be used!
file | where to load from |
prefix | prefix for members |
param_version | (optional) a parameter version different to (this is mainly for testing, better do not use) |
在文件 SGObject.cpp 第 374 行定义.
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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. |
被 CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel , 以及 CExponentialKernel 重载.
在文件 SGObject.cpp 第 1062 行定义.
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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::LOAD_SERIALIZABLE_PRE is called.
ShogunException | will be thrown if an error occurs. |
被 CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool > , 以及 CDynamicObjectArray 重载.
在文件 SGObject.cpp 第 1057 行定义.
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Takes a set of TParameter instances (base) with a certain version and a set of target parameter infos and recursively maps the base level wise to the current version using CSGObject::migrate(...). The base is replaced. After this call, the base version containing parameters should be of same version/type as the initial target parameter infos. Note for this to work, the migrate methods and all the internal parameter mappings have to match
param_base | set of TParameter instances that are mapped to the provided target parameter infos |
base_version | version of the parameter base |
target_param_infos | set of SGParamInfo instances that specify the target parameter base |
在文件 SGObject.cpp 第 742 行定义.
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protectedvirtualinherited |
creates a new TParameter instance, which contains migrated data from the version that is provided. The provided parameter data base is used for migration, this base is a collection of all parameter data of the previous version. Migration is done FROM the data in param_base TO the provided param info Migration is always one version step. Method has to be implemented in subclasses, if no match is found, base method has to be called.
If there is an element in the param_base which equals the target, a copy of the element is returned. This represents the case when nothing has changed and therefore, the migrate method is not overloaded in a subclass
param_base | set of TParameter instances to use for migration |
target | parameter info for the resulting TParameter |
在文件 SGObject.cpp 第 949 行定义.
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protectedvirtualinherited |
This method prepares everything for a one-to-one parameter migration. One to one here means that only ONE element of the parameter base is needed for the migration (the one with the same name as the target). Data is allocated for the target (in the type as provided in the target SGParamInfo), and a corresponding new TParameter instance is written to replacement. The to_migrate pointer points to the single needed TParameter instance needed for migration. If a name change happened, the old name may be specified by old_name. In addition, the m_delete_data flag of to_migrate is set to true. So if you want to migrate data, the only thing to do after this call is converting the data in the m_parameter fields. If unsure how to use - have a look into an example for this. (base_migration_type_conversion.cpp for example)
param_base | set of TParameter instances to use for migration |
target | parameter info for the resulting TParameter |
replacement | (used as output) here the TParameter instance which is returned by migration is created into |
to_migrate | the only source that is used for migration |
old_name | with this parameter, a name change may be specified |
在文件 SGObject.cpp 第 889 行定义.
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在文件 SGObject.cpp 第 263 行定义.
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prints all parameter registered for model selection and their type
在文件 SGObject.cpp 第 1111 行定义.
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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 |
param_version | (optional) a parameter version different to (this is mainly for testing, better do not use) |
在文件 SGObject.cpp 第 315 行定义.
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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::SAVE_SERIALIZABLE_POST is called.
ShogunException | will be thrown if an error occurs. |
被 CKernel 重载.
在文件 SGObject.cpp 第 1072 行定义.
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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. |
被 CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool > , 以及 CDynamicObjectArray 重载.
在文件 SGObject.cpp 第 1067 行定义.
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在文件 SGObject.cpp 第 42 行定义.
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在文件 SGObject.cpp 第 47 行定义.
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在文件 SGObject.cpp 第 52 行定义.
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在文件 SGObject.cpp 第 57 行定义.
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在文件 SGObject.cpp 第 62 行定义.
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在文件 SGObject.cpp 第 67 行定义.
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在文件 SGObject.cpp 第 72 行定义.
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在文件 SGObject.cpp 第 77 行定义.
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在文件 SGObject.cpp 第 82 行定义.
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在文件 SGObject.cpp 第 87 行定义.
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在文件 SGObject.cpp 第 92 行定义.
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在文件 SGObject.cpp 第 97 行定义.
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在文件 SGObject.cpp 第 102 行定义.
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在文件 SGObject.cpp 第 107 行定义.
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在文件 SGObject.cpp 第 112 行定义.
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set generic type to T
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set maximum for Brent's minimization method
max | maximum for Brent's minimization method |
在文件 LaplacianInferenceBase.h 第 197 行定义.
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set tolerance for Brent's minimization method
tol | tolerance for Brent's minimization method |
在文件 LaplacianInferenceBase.h 第 185 行定义.
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set likelihood model
mod | model to set |
被 CKLInferenceMethod , 以及 CKLDualInferenceMethod 重载.
在文件 InferenceMethod.h 第 310 行定义.
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set tolerance for newton iterations
tol | tolerance for newton iterations to set |
在文件 LaplacianInferenceBase.h 第 161 行定义.
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A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.
被 CGaussianKernel 重载.
在文件 SGObject.cpp 第 194 行定义.
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whether combination of inference method and given likelihood function supports binary classification
被 CEPInferenceMethod, CKLInferenceMethod , 以及 CSingleLaplacianInferenceMethod 重载.
在文件 InferenceMethod.h 第 341 行定义.
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whether combination of inference method and given likelihood function supports multiclass classification
在文件 InferenceMethod.h 第 348 行定义.
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whether combination of inference method and given likelihood function supports regression
被 CFITCInferenceMethod, CKLInferenceMethod, CExactInferenceMethod , 以及 CSingleLaplacianInferenceMethod 重载.
在文件 InferenceMethod.h 第 334 行定义.
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unset generic type
this has to be called in classes specializing a template class
在文件 SGObject.cpp 第 304 行定义.
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protectedpure virtualinherited |
update covariance matrix of the approximation to the posterior
在 CSingleLaplacianInferenceMethod 内被实现.
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protectedpure virtualinherited |
update cholesky matrix
在 CEPInferenceMethod, CFITCInferenceMethod, CExactInferenceMethod, CKLDualInferenceMethod, CKLCovarianceInferenceMethod, CSingleLaplacianInferenceMethod , 以及 CKLLowerTriangularInferenceMethod 内被实现.
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protectedpure virtualinherited |
update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter
在 CEPInferenceMethod, CFITCInferenceMethod, CExactInferenceMethod, CKLDualInferenceMethod, CKLCovarianceInferenceMethod, CSingleLaplacianInferenceMethod , 以及 CKLLowerTriangularInferenceMethod 内被实现.
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Updates the hash of current parameter combination
在文件 SGObject.cpp 第 250 行定义.
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io
在文件 SGObject.h 第 496 行定义.
alpha vector used in process mean calculation
在文件 InferenceMethod.h 第 443 行定义.
derivative of log likelihood with respect to function location
在文件 LaplacianInferenceBase.h 第 209 行定义.
the matrix used for multi classification
在文件 InferenceMethod.h 第 455 行定义.
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features to use
在文件 InferenceMethod.h 第 437 行定义.
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parameters wrt which we can compute gradients
在文件 SGObject.h 第 511 行定义.
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Hash of parameter values
在文件 SGObject.h 第 517 行定义.
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max Newton's iterations
在文件 LaplacianInferenceBase.h 第 224 行定义.
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covariance function
在文件 InferenceMethod.h 第 428 行定义.
kernel matrix from features (non-scalled by inference scalling)
在文件 InferenceMethod.h 第 452 行定义.
upper triangular factor of Cholesky decomposition
在文件 InferenceMethod.h 第 446 行定义.
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labels of features
在文件 InferenceMethod.h 第 440 行定义.
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mean function
在文件 InferenceMethod.h 第 431 行定义.
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likelihood function to use
在文件 InferenceMethod.h 第 434 行定义.
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model selection parameters
在文件 SGObject.h 第 508 行定义.
mean vector of the approximation to the posterior
在文件 LaplacianInferenceBase.h 第 215 行定义.
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protectedinherited |
max iterations for Brent's minimization method
在文件 LaplacianInferenceBase.h 第 230 行定义.
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amount of tolerance for Brent's minimization method
在文件 LaplacianInferenceBase.h 第 227 行定义.
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map for different parameter versions
在文件 SGObject.h 第 514 行定义.
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parameters
在文件 SGObject.h 第 505 行定义.
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kernel scale
在文件 InferenceMethod.h 第 449 行定义.
covariance matrix of the approximation to the posterior
在文件 LaplacianInferenceBase.h 第 218 行定义.
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amount of tolerance for Newton's iterations
在文件 LaplacianInferenceBase.h 第 221 行定义.
noise matrix
在文件 LaplacianInferenceBase.h 第 212 行定义.
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parallel
在文件 SGObject.h 第 499 行定义.
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version
在文件 SGObject.h 第 502 行定义.