SHOGUN
v3.0.0
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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.
Definition at line 42 of file LaplacianInferenceMethod.h.
Public Attributes | |
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 Member Functions | |
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) |
Static Protected Member Functions | |
static void * | get_derivative_helper (void *p) |
Protected Attributes | |
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
Definition at line 74 of file LaplacianInferenceMethod.cpp.
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 |
Definition at line 79 of file LaplacianInferenceMethod.cpp.
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virtual |
Definition at line 94 of file LaplacianInferenceMethod.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 1196 of file SGObject.cpp.
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protectedvirtualinherited |
check if members of object are valid for inference
Reimplemented in CFITCInferenceMethod, and CExactInferenceMethod.
Definition at line 253 of file InferenceMethod.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 1313 of file SGObject.cpp.
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virtualinherited |
A deep copy. All the instance variables will also be copied.
Definition at line 160 of file SGObject.h.
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) |
Definition at line 1217 of file SGObject.cpp.
get alpha vector
\[ \mu = K\alpha \]
where \(\mu\) is the mean and \(K\) is the prior covariance matrix.
Implements CInferenceMethod.
Definition at line 156 of file LaplacianInferenceMethod.cpp.
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.
Implements CInferenceMethod.
Definition at line 165 of file LaplacianInferenceMethod.cpp.
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staticprotectedinherited |
pthread helper method to compute negative log marginal likelihood derivatives wrt hyperparameter
Definition at line 206 of file InferenceMethod.cpp.
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returns derivative of negative log marginal likelihood wrt parameter of CInferenceMethod class
param | parameter of CInferenceMethod class |
Implements CInferenceMethod.
Definition at line 448 of file LaplacianInferenceMethod.cpp.
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returns derivative of negative log marginal likelihood wrt kernel's parameter
param | parameter of given kernel |
Implements CInferenceMethod.
Definition at line 514 of file LaplacianInferenceMethod.cpp.
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returns derivative of negative log marginal likelihood wrt parameter of likelihood model
param | parameter of given likelihood model |
Implements CInferenceMethod.
Definition at line 480 of file LaplacianInferenceMethod.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 CInferenceMethod.
Definition at line 564 of file LaplacianInferenceMethod.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 CInferenceMethod.
Definition at line 107 of file LaplacianInferenceMethod.cpp.
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get the gradient
parameters | parameter's dictionary |
Implements CDifferentiableFunction.
Definition at line 220 of file InferenceMethod.h.
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return what type of inference we are
Reimplemented from CInferenceMethod.
Definition at line 65 of file LaplacianInferenceMethod.h.
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Computes an unbiased estimate of the log-marginal-likelihood,
\[ log(p(y|X,\theta)), \]
where \(y\) are the labels, \(X\) are the features (omitted from in the following expressions), and \(\theta\) represent hyperparameters.
This is done via an 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. |
Definition at line 81 of file InferenceMethod.cpp.
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get maximum for Brent's minimization method
Definition at line 198 of file LaplacianInferenceMethod.h.
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get tolerance for Brent's minimization method
Definition at line 186 of file LaplacianInferenceMethod.h.
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Definition at line 1100 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 1124 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 1137 of file SGObject.cpp.
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returns the name of the inference method
Implements CSGObject.
Definition at line 71 of file LaplacianInferenceMethod.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 CInferenceMethod.
Definition at line 115 of file LaplacianInferenceMethod.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 140 of file InferenceMethod.cpp.
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get max Newton iterations
Definition at line 174 of file LaplacianInferenceMethod.h.
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get tolerance for newton iterations
Definition at line 162 of file LaplacianInferenceMethod.h.
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 \(B=(W^{frac{1}{2}}*K*W^{frac{1}{2}}+I)\).
Implements CInferenceMethod.
Definition at line 181 of file LaplacianInferenceMethod.cpp.
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.
Implements CInferenceMethod.
Definition at line 173 of file LaplacianInferenceMethod.cpp.
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get the function value
Implements CDifferentiableFunction.
Definition at line 230 of file InferenceMethod.h.
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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 |
Definition at line 268 of file SGObject.cpp.
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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 |
Definition at line 673 of file SGObject.cpp.
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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 |
Definition at line 514 of file SGObject.cpp.
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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) |
Definition at line 345 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 occurres. |
Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.
Definition at line 1029 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::LOAD_SERIALIZABLE_PRE is called.
ShogunException | Will be thrown if an error occurres. |
Reimplemented in CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, CDynamicArray< uint64_t >, and CDynamicObjectArray.
Definition at line 1024 of file SGObject.cpp.
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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 |
Definition at line 711 of file SGObject.cpp.
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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 |
Definition at line 918 of file SGObject.cpp.
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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 |
Definition at line 858 of file SGObject.cpp.
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prints all parameter registered for model selection and their type
Definition at line 1076 of file SGObject.cpp.
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prints registered parameters out
prefix | prefix for members |
Definition at line 280 of file SGObject.cpp.
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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) |
Definition at line 286 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::SAVE_SERIALIZABLE_POST is called.
ShogunException | Will be thrown if an error occurres. |
Reimplemented in CKernel.
Definition at line 1039 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 occurres. |
Reimplemented in CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, CDynamicArray< uint64_t >, and CDynamicObjectArray.
Definition at line 1034 of file SGObject.cpp.
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set generic type to T
Definition at line 41 of file SGObject.cpp.
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set the parallel object
parallel | parallel object to use |
Definition at line 220 of file SGObject.cpp.
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set the version object
version | version object to use |
Definition at line 255 of file SGObject.cpp.
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set maximum for Brent's minimization method
max | maximum for Brent's minimization method |
Definition at line 204 of file LaplacianInferenceMethod.h.
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set tolerance for Brent's minimization method
tol | tolerance for Brent's minimization method |
Definition at line 192 of file LaplacianInferenceMethod.h.
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set max Newton iterations
iter | max Newton iterations |
Definition at line 180 of file LaplacianInferenceMethod.h.
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set tolerance for newton iterations
tol | tolerance for newton iterations to set |
Definition at line 168 of file LaplacianInferenceMethod.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 151 of file SGObject.h.
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Reimplemented from CInferenceMethod.
Definition at line 220 of file LaplacianInferenceMethod.h.
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whether combination of inference method and given likelihood function supports multiclass classification
Definition at line 353 of file InferenceMethod.h.
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Reimplemented from CInferenceMethod.
Definition at line 210 of file LaplacianInferenceMethod.h.
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unset generic type
this has to be called in classes specializing a template class
Definition at line 275 of file SGObject.cpp.
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update data all matrices
Reimplemented from CInferenceMethod.
Definition at line 98 of file LaplacianInferenceMethod.cpp.
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update alpha matrix
Implements CInferenceMethod.
Definition at line 244 of file LaplacianInferenceMethod.cpp.
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update covariance matrix of the approximation to the posterior
Definition at line 189 of file LaplacianInferenceMethod.cpp.
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update cholesky matrix
Implements CInferenceMethod.
Definition at line 209 of file LaplacianInferenceMethod.cpp.
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update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter
Implements CInferenceMethod.
Definition at line 392 of file LaplacianInferenceMethod.cpp.
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Updates the hash of current parameter combination.
Definition at line 227 of file SGObject.cpp.
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update train kernel matrix
Reimplemented in CFITCInferenceMethod.
Definition at line 269 of file InferenceMethod.cpp.
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io
Definition at line 514 of file SGObject.h.
alpha vector used in process mean calculation
Definition at line 441 of file InferenceMethod.h.
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features to use
Definition at line 435 of file InferenceMethod.h.
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parameters wrt which we can compute gradients
Definition at line 529 of file SGObject.h.
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Hash of parameter values
Definition at line 535 of file SGObject.h.
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covariance function
Definition at line 426 of file InferenceMethod.h.
kernel matrix from features (non-scalled by inference scalling)
Definition at line 450 of file InferenceMethod.h.
upper triangular factor of Cholesky decomposition
Definition at line 444 of file InferenceMethod.h.
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labels of features
Definition at line 438 of file InferenceMethod.h.
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mean function
Definition at line 429 of file InferenceMethod.h.
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likelihood function to use
Definition at line 432 of file InferenceMethod.h.
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model selection parameters
Definition at line 526 of file SGObject.h.
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map for different parameter versions
Definition at line 532 of file SGObject.h.
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parameters
Definition at line 523 of file SGObject.h.
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kernel scale
Definition at line 447 of file InferenceMethod.h.
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parallel
Definition at line 517 of file SGObject.h.
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version
Definition at line 520 of file SGObject.h.