SHOGUN
4.1.0
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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 67 of file ExactInferenceMethod.h.
Static Public Member Functions | |
static CExactInferenceMethod * | obtain_from_generic (CInferenceMethod *inference) |
Public Attributes | |
SGIO * | io |
Parallel * | parallel |
Version * | version |
Parameter * | m_parameters |
Parameter * | m_model_selection_parameters |
Parameter * | m_gradient_parameters |
uint32_t | m_hash |
Protected Member Functions | |
virtual void | 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) |
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_log_scale |
SGMatrix< float64_t > | m_ktrtr |
SGMatrix< float64_t > | m_E |
bool | m_gradient_update |
default constructor
Definition at line 46 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 50 of file ExactInferenceMethod.cpp.
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virtual |
Definition at line 56 of file ExactInferenceMethod.cpp.
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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. |
Definition at line 597 of file SGObject.cpp.
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protectedvirtual |
check if members of object are valid for inference
Reimplemented from CInferenceMethod.
Definition at line 87 of file ExactInferenceMethod.cpp.
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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.
Definition at line 714 of file SGObject.cpp.
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update gradients
Reimplemented from CInferenceMethod.
Definition at line 60 of file ExactInferenceMethod.cpp.
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virtualinherited |
A deep copy. All the instance variables will also be copied.
Definition at line 198 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 618 of file SGObject.cpp.
get alpha vector
\[ \mu = K\alpha \]
where \(\mu\) is the mean and \(K\) is the prior covariance matrix.
Definition at line 143 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.
Definition at line 151 of file ExactInferenceMethod.cpp.
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staticprotectedinherited |
pthread helper method to compute negative log marginal likelihood derivatives wrt hyperparameter
Definition at line 255 of file InferenceMethod.cpp.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt parameter of CInferenceMethod class
param | parameter of CInferenceMethod class |
Implements CInferenceMethod.
Definition at line 284 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 CInferenceMethod.
Definition at line 340 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 CInferenceMethod.
Definition at line 316 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 CInferenceMethod.
Definition at line 370 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.
Definition at line 97 of file ExactInferenceMethod.cpp.
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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 |
Implements CDifferentiableFunction.
Definition at line 245 of file InferenceMethod.h.
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return what type of inference we are
Reimplemented from CInferenceMethod.
Definition at line 90 of file ExactInferenceMethod.h.
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virtualinherited |
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virtualinherited |
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inherited |
Computes an unbiased estimate of the marginal-likelihood (in log-domain),
\[ p(y|X,\theta), \]
where \(y\) are the labels, \(X\) are the features (omitted from in the following expressions), and \(\theta\) represent hyperparameters.
This is done via a Gaussian approximation to the posterior \(q(f|y, \theta)\approx p(f|y, \theta)\), which is computed by the underlying CInferenceMethod instance (if implemented, otherwise error), and then using an importance sample estimator
\[ p(y|\theta)=\int p(y|f)p(f|\theta)df =\int p(y|f)\frac{p(f|\theta)}{q(f|y, \theta)}q(f|y, \theta)df \approx\frac{1}{n}\sum_{i=1}^n p(y|f^{(i)})\frac{p(f^{(i)}|\theta)} {q(f^{(i)}|y, \theta)}, \]
where \( f^{(i)} \) are samples from the posterior approximation \( q(f|y, \theta) \). The resulting estimator has a low variance if \( q(f|y, \theta) \) is a good approximation. It has large variance otherwise (while still being consistent). Storing all number of log-domain ensures numerical stability.
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 126 of file InferenceMethod.cpp.
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virtualinherited |
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inherited |
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inherited |
Definition at line 498 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 522 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 535 of file SGObject.cpp.
get the E matrix used for multi classification
Definition at line 72 of file InferenceMethod.cpp.
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returns the name of the inference method
Implements CSGObject.
Definition at line 96 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 CInferenceMethod.
Definition at line 114 of file ExactInferenceMethod.cpp.
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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.
Definition at line 185 of file InferenceMethod.cpp.
returns covariance matrix \(\Sigma\) of the posterior Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\)
\[ p(f|y) = \mathcal{N}(\mu,\Sigma) \]
Implements CInferenceMethod.
Definition at line 166 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 CInferenceMethod.
Definition at line 159 of file ExactInferenceMethod.cpp.
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get the function value
Implements CDifferentiableFunction.
Definition at line 255 of file InferenceMethod.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 296 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 |
Definition at line 369 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 426 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 occurs. |
Reimplemented in CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 421 of file SGObject.cpp.
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static |
helper method used to specialize a base class instance
inference | inference method |
Definition at line 303 of file ExactInferenceMethod.cpp.
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virtualinherited |
Definition at line 262 of file SGObject.cpp.
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inherited |
prints all parameter registered for model selection and their type
Definition at line 474 of file SGObject.cpp.
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virtualinherited |
prints registered parameters out
prefix | prefix for members |
Definition at line 308 of file SGObject.cpp.
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virtualinherited |
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 314 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 occurs. |
Reimplemented in CKernel.
Definition at line 436 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 431 of file SGObject.cpp.
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Definition at line 41 of file SGObject.cpp.
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Definition at line 46 of file SGObject.cpp.
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Definition at line 51 of file SGObject.cpp.
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Definition at line 56 of file SGObject.cpp.
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Definition at line 61 of file SGObject.cpp.
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Definition at line 66 of file SGObject.cpp.
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Definition at line 71 of file SGObject.cpp.
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Definition at line 76 of file SGObject.cpp.
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Definition at line 81 of file SGObject.cpp.
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Definition at line 86 of file SGObject.cpp.
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Definition at line 91 of file SGObject.cpp.
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Definition at line 96 of file SGObject.cpp.
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Definition at line 101 of file SGObject.cpp.
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Definition at line 106 of file SGObject.cpp.
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Definition at line 111 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 241 of file SGObject.cpp.
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set the version object
version | version object to use |
Definition at line 283 of file SGObject.cpp.
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set kernel
kern | kernel to set |
Reimplemented in CSingleSparseInferenceBase.
Definition at line 289 of file InferenceMethod.h.
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virtualinherited |
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virtualinherited |
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virtualinherited |
set likelihood model
mod | model to set |
Reimplemented in CKLInferenceMethod, and CKLDualInferenceMethod.
Definition at line 340 of file InferenceMethod.h.
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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.
Reimplemented in CGaussianKernel.
Definition at line 192 of file SGObject.cpp.
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whether combination of inference method and given likelihood function supports binary classification
Reimplemented in CEPInferenceMethod, CKLInferenceMethod, CSingleFITCLaplacianInferenceMethod, and CSingleLaplacianInferenceMethod.
Definition at line 371 of file InferenceMethod.h.
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virtualinherited |
whether combination of inference method and given likelihood function supports multiclass classification
Definition at line 378 of file InferenceMethod.h.
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virtual |
Reimplemented from CInferenceMethod.
Definition at line 182 of file ExactInferenceMethod.h.
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inherited |
unset generic type
this has to be called in classes specializing a template class
Definition at line 303 of file SGObject.cpp.
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update matrices except gradients
Reimplemented from CInferenceMethod.
Definition at line 74 of file ExactInferenceMethod.cpp.
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update alpha matrix
Implements CInferenceMethod.
Definition at line 192 of file ExactInferenceMethod.cpp.
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update Cholesky matrix
Implements CInferenceMethod.
Definition at line 173 of file ExactInferenceMethod.cpp.
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update covariance matrix of the posterior Gaussian
Definition at line 234 of file ExactInferenceMethod.cpp.
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update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter
Implements CInferenceMethod.
Definition at line 258 of file ExactInferenceMethod.cpp.
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update mean vector of the posterior Gaussian
Definition at line 218 of file ExactInferenceMethod.cpp.
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Updates the hash of current parameter combination
Definition at line 248 of file SGObject.cpp.
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update train kernel matrix
Reimplemented in CSparseInferenceBase.
Definition at line 324 of file InferenceMethod.cpp.
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io
Definition at line 369 of file SGObject.h.
alpha vector used in process mean calculation
Definition at line 475 of file InferenceMethod.h.
the matrix used for multi classification
Definition at line 487 of file InferenceMethod.h.
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features to use
Definition at line 469 of file InferenceMethod.h.
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parameters wrt which we can compute gradients
Definition at line 384 of file SGObject.h.
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Whether gradients are updated
Definition at line 490 of file InferenceMethod.h.
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Hash of parameter values
Definition at line 387 of file SGObject.h.
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covariance function
Definition at line 460 of file InferenceMethod.h.
kernel matrix from features (non-scalled by inference scalling)
Definition at line 484 of file InferenceMethod.h.
upper triangular factor of Cholesky decomposition
Definition at line 478 of file InferenceMethod.h.
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labels of features
Definition at line 472 of file InferenceMethod.h.
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kernel scale
Definition at line 481 of file InferenceMethod.h.
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mean function
Definition at line 463 of file InferenceMethod.h.
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likelihood function to use
Definition at line 466 of file InferenceMethod.h.
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model selection parameters
Definition at line 381 of file SGObject.h.
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parameters
Definition at line 378 of file SGObject.h.
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parallel
Definition at line 372 of file SGObject.h.
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version
Definition at line 375 of file SGObject.h.