The Laplace approximation inference method class.
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.
For more details, see "Bayesian Classification with Gaussian Processes" by Christopher K.I Williams and David Barber, published 1998 in the IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 20, Number 12, Pages 1342-1351.
This specific implementation was adapted from the infLaplace.m file in the GPML toolbox.
在文件 LaplacianInferenceMethod.h 第 42 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_alpha () |
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 | check_members () const |
virtual void | update_train_kernel () |
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_mu |
SGMatrix< float64_t > | m_Sigma |
SGVector< float64_t > | W |
SGVector< float64_t > | sW |
SGVector< float64_t > | dlp |
SGVector< float64_t > | d2lp |
SGVector< float64_t > | d3lp |
SGVector< float64_t > | m_dfhat |
SGMatrix< float64_t > | m_Z |
SGVector< float64_t > | m_g |
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 |
default constructor
在文件 LaplacianInferenceMethod.cpp 第 74 行定义.
CLaplacianInferenceMethod | ( | 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 LaplacianInferenceMethod.cpp 第 79 行定义.
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virtual |
在文件 LaplacianInferenceMethod.cpp 第 94 行定义.
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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. |
在文件 SGObject.cpp 第 1185 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 263 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 1302 行定义.
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virtualinherited |
A deep copy. All the instance variables will also be copied.
在文件 SGObject.cpp 第 146 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 1206 行定义.
get alpha vector
\[ \mu = K\alpha \]
where \(\mu\) is the mean and \(K\) is the prior covariance matrix.
实现了 CInferenceMethod.
在文件 LaplacianInferenceMethod.cpp 第 161 行定义.
get Cholesky decomposition matrix
\[ L = Cholesky(W^{\frac{1}{2}}*K*W^{\frac{1}{2}}+I) \]
where \(K\) is the prior covariance matrix, \(sW\) is the vector returned by get_diagonal_vector(), and \(I\) is the identity matrix.
实现了 CInferenceMethod.
在文件 LaplacianInferenceMethod.cpp 第 170 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 209 行定义.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt parameter of CInferenceMethod class
param | parameter of CInferenceMethod class |
实现了 CInferenceMethod.
在文件 LaplacianInferenceMethod.cpp 第 453 行定义.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt kernel's parameter
param | parameter of given kernel |
实现了 CInferenceMethod.
在文件 LaplacianInferenceMethod.cpp 第 519 行定义.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt parameter of likelihood model
param | parameter of given likelihood model |
实现了 CInferenceMethod.
在文件 LaplacianInferenceMethod.cpp 第 485 行定义.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt mean function's parameter
param | parameter of given mean function |
实现了 CInferenceMethod.
在文件 LaplacianInferenceMethod.cpp 第 569 行定义.
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.
实现了 CInferenceMethod.
在文件 LaplacianInferenceMethod.cpp 第 112 行定义.
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virtualinherited |
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inherited |
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inherited |
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get the gradient
parameters | parameter's dictionary |
在文件 InferenceMethod.h 第 224 行定义.
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return what type of inference we are
重载 CInferenceMethod .
在文件 LaplacianInferenceMethod.h 第 65 行定义.
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virtualinherited |
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virtualinherited |
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inherited |
Computes an unbiased estimate of the marginal-likelihood,
\[ p(y|X,\theta), \]
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).
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 Cholesky factorization fails. |
在文件 InferenceMethod.cpp 第 79 行定义.
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virtualinherited |
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virtual |
get maximum for Brent's minimization method
在文件 LaplacianInferenceMethod.h 第 198 行定义.
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get tolerance for Brent's minimization method
在文件 LaplacianInferenceMethod.h 第 186 行定义.
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inherited |
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inherited |
在文件 SGObject.cpp 第 1077 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 1101 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 1114 行定义.
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returns the name of the inference method
实现了 CSGObject.
被 CLaplacianInferenceMethodWithLBFGS 重载.
在文件 LaplacianInferenceMethod.h 第 71 行定义.
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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.
实现了 CInferenceMethod.
在文件 LaplacianInferenceMethod.cpp 第 120 行定义.
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virtualinherited |
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 138 行定义.
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get tolerance for newton iterations
在文件 LaplacianInferenceMethod.h 第 162 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:
\[ p(f|y) \approx q(f|y) = \mathcal{N}(f|\mu,\Sigma) \]
Covariance matrix is evaluated using matrix inversion lemma:
\[ (K^{-1}+W)^{-1} = K - KW^{\frac{1}{2}}B^{-1}W^{\frac{1}{2}}K \]
where \(B=(W^{frac{1}{2}}*K*W^{frac{1}{2}}+I)\).
实现了 CInferenceMethod.
在文件 LaplacianInferenceMethod.cpp 第 186 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 LaplacianInferenceMethod.cpp 第 178 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 243 行定义.
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inherited |
maps all parameters of this instance to the provided file version and loads all parameter data from the file into an array, which is sorted (basically calls load_file_parameter(...) for all parameters and puts all results into a sorted array)
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 648 行定义.
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inherited |
loads some specified parameters from a file with a specified version The provided parameter info has a version which is recursively mapped until the file parameter version is reached. Note that there may be possibly multiple parameters in the mapping, therefore, a set of TParameter instances is returned
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 489 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 320 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 occurres. |
被 CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel , 以及 CExponentialKernel 重载.
在文件 SGObject.cpp 第 1004 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 occurres. |
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 999 行定义.
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inherited |
Takes a set of TParameter instances (base) with a certain version and a set of target parameter infos and recursively maps the base level wise to the current version using CSGObject::migrate(...). The base is replaced. After this call, the base version containing parameters should be of same version/type as the initial target parameter infos. Note for this to work, the migrate methods and all the internal parameter mappings have to match
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 686 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 893 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 833 行定义.
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virtualinherited |
在文件 SGObject.cpp 第 209 行定义.
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inherited |
prints all parameter registered for model selection and their type
在文件 SGObject.cpp 第 1053 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 261 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 occurres. |
被 CKernel 重载.
在文件 SGObject.cpp 第 1014 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 occurres. |
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 1009 行定义.
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inherited |
在文件 SGObject.cpp 第 38 行定义.
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inherited |
在文件 SGObject.cpp 第 43 行定义.
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inherited |
在文件 SGObject.cpp 第 48 行定义.
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inherited |
在文件 SGObject.cpp 第 53 行定义.
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inherited |
在文件 SGObject.cpp 第 58 行定义.
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inherited |
在文件 SGObject.cpp 第 63 行定义.
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inherited |
在文件 SGObject.cpp 第 68 行定义.
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inherited |
在文件 SGObject.cpp 第 73 行定义.
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inherited |
在文件 SGObject.cpp 第 78 行定义.
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inherited |
在文件 SGObject.cpp 第 83 行定义.
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inherited |
在文件 SGObject.cpp 第 88 行定义.
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inherited |
在文件 SGObject.cpp 第 93 行定义.
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inherited |
在文件 SGObject.cpp 第 98 行定义.
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inherited |
在文件 SGObject.cpp 第 103 行定义.
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在文件 SGObject.cpp 第 108 行定义.
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set generic type to T
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virtualinherited |
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virtualinherited |
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set maximum for Brent's minimization method
max | maximum for Brent's minimization method |
在文件 LaplacianInferenceMethod.h 第 204 行定义.
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set tolerance for Brent's minimization method
tol | tolerance for Brent's minimization method |
在文件 LaplacianInferenceMethod.h 第 192 行定义.
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virtualinherited |
set likelihood model
mod | model to set |
被 CKLInferenceMethod , 以及 CKLDualInferenceMethod 重载.
在文件 InferenceMethod.h 第 319 行定义.
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virtual |
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set tolerance for newton iterations
tol | tolerance for newton iterations to set |
在文件 LaplacianInferenceMethod.h 第 168 行定义.
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virtualinherited |
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virtualinherited |
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 140 行定义.
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virtual |
重载 CInferenceMethod .
在文件 LaplacianInferenceMethod.h 第 220 行定义.
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virtualinherited |
whether combination of inference method and given likelihood function supports multiclass classification
在文件 InferenceMethod.h 第 357 行定义.
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重载 CInferenceMethod .
在文件 LaplacianInferenceMethod.h 第 210 行定义.
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inherited |
unset generic type
this has to be called in classes specializing a template class
在文件 SGObject.cpp 第 250 行定义.
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protectedvirtual |
update alpha matrix
实现了 CInferenceMethod.
被 CLaplacianInferenceMethodWithLBFGS 重载.
在文件 LaplacianInferenceMethod.cpp 第 249 行定义.
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protectedvirtual |
update covariance matrix of the approximation to the posterior
在文件 LaplacianInferenceMethod.cpp 第 194 行定义.
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protectedvirtual |
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protectedvirtual |
update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter
实现了 CInferenceMethod.
在文件 LaplacianInferenceMethod.cpp 第 397 行定义.
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Updates the hash of current parameter combination
在文件 SGObject.cpp 第 196 行定义.
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protectedvirtualinherited |
second derivative of log likelihood with respect to function location
在文件 LaplacianInferenceMethod.h 第 315 行定义.
third derivative of log likelihood with respect to function location
在文件 LaplacianInferenceMethod.h 第 318 行定义.
derivative of log likelihood with respect to function location
在文件 LaplacianInferenceMethod.h 第 312 行定义.
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io
在文件 SGObject.h 第 461 行定义.
alpha vector used in process mean calculation
在文件 InferenceMethod.h 第 445 行定义.
在文件 LaplacianInferenceMethod.h 第 320 行定义.
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protectedinherited |
features to use
在文件 InferenceMethod.h 第 439 行定义.
在文件 LaplacianInferenceMethod.h 第 324 行定义.
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parameters wrt which we can compute gradients
在文件 SGObject.h 第 476 行定义.
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Hash of parameter values
在文件 SGObject.h 第 482 行定义.
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protectedinherited |
covariance function
在文件 InferenceMethod.h 第 430 行定义.
kernel matrix from features (non-scalled by inference scalling)
在文件 InferenceMethod.h 第 454 行定义.
upper triangular factor of Cholesky decomposition
在文件 InferenceMethod.h 第 448 行定义.
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labels of features
在文件 InferenceMethod.h 第 442 行定义.
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protectedinherited |
mean function
在文件 InferenceMethod.h 第 433 行定义.
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protectedinherited |
likelihood function to use
在文件 InferenceMethod.h 第 436 行定义.
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model selection parameters
在文件 SGObject.h 第 473 行定义.
mean vector of the approximation to the posterior
在文件 LaplacianInferenceMethod.h 第 300 行定义.
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map for different parameter versions
在文件 SGObject.h 第 479 行定义.
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parameters
在文件 SGObject.h 第 470 行定义.
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protectedinherited |
kernel scale
在文件 InferenceMethod.h 第 451 行定义.
covariance matrix of the approximation to the posterior
在文件 LaplacianInferenceMethod.h 第 303 行定义.
在文件 LaplacianInferenceMethod.h 第 322 行定义.
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parallel
在文件 SGObject.h 第 464 行定义.
square root of W
在文件 LaplacianInferenceMethod.h 第 309 行定义.
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version
在文件 SGObject.h 第 467 行定义.
noise matrix
在文件 LaplacianInferenceMethod.h 第 306 行定义.