SHOGUN
3.2.1
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The Laplace approximation inference method with LBFGS class for regression and binary 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. We use the Limited-memory BFGS method to obtain the maximum of likelihood. Note that due to the Laplace approximation, the time complexity of the class still is O(n^3), where n is the number of training data points. However, in the optimization step we use L-BFGS method, which of the time complexity is O(n*m) to replace the Newton method, which of the time complexity is O(n^3). Here L-BFGS only uses the last m (m<<n) function/gradient pairs to find the optimal pointer
For more details, see Nocedal, Jorge, and Stephen J. Wright. "Numerical Optimization 2nd." (2006), Pages 177-180.
This specific implementation was based on the idea from Murphy, Kevin P. "Machine learning: a probabilistic perspective." (2012), Pages 251-252.
Definition at line 65 of file SingleLaplacianInferenceMethodWithLBFGS.h.
Public Member Functions | |
CSingleLaplacianInferenceMethodWithLBFGS () | |
CSingleLaplacianInferenceMethodWithLBFGS (CKernel *kernel, CFeatures *features, CMeanFunction *mean, CLabels *labels, CLikelihoodModel *model) | |
virtual | ~CSingleLaplacianInferenceMethodWithLBFGS () |
virtual const char * | get_name () const |
virtual void | set_lbfgs_parameters (int m=100, int max_linesearch=1000, int linesearch=LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE, int max_iterations=1000, float64_t delta=0.0, int past=0, float64_t epsilon=1e-5, float64_t min_step=1e-20, float64_t max_step=1e+20, float64_t ftol=1e-4, float64_t wolfe=0.9, float64_t gtol=0.9, float64_t xtol=1e-16, float64_t orthantwise_c=0.0, int orthantwise_start=0, int orthantwise_end=1) |
virtual void | set_newton_method (bool enable_newton_if_fail) |
virtual float64_t | get_negative_log_marginal_likelihood () |
virtual bool | supports_regression () const |
virtual bool | supports_binary () const |
virtual SGVector< float64_t > | get_diagonal_vector () |
virtual EInferenceType | get_inference_type () const |
virtual SGMatrix< float64_t > | get_cholesky () |
virtual SGVector< float64_t > | get_posterior_mean () |
virtual SGMatrix< float64_t > | get_posterior_covariance () |
virtual void | update () |
virtual float64_t | get_newton_tolerance () |
virtual void | set_newton_tolerance (float64_t tol) |
virtual int32_t | get_newton_iterations () |
virtual void | set_newton_iterations (int32_t iter) |
virtual float64_t | get_minimization_tolerance () |
virtual void | set_minimization_tolerance (float64_t tol) |
virtual float64_t | get_minimization_max () |
virtual void | set_minimization_max (float64_t max) |
float64_t | get_marginal_likelihood_estimate (int32_t num_importance_samples=1, float64_t ridge_size=1e-15) |
virtual CMap< TParameter *, SGVector< float64_t > > * | get_negative_log_marginal_likelihood_derivatives (CMap< TParameter *, CSGObject * > *parameters) |
virtual CMap< TParameter *, SGVector< float64_t > > * | get_gradient (CMap< TParameter *, CSGObject * > *parameters) |
virtual SGVector< float64_t > | get_value () |
virtual CFeatures * | get_features () |
virtual void | set_features (CFeatures *feat) |
virtual CKernel * | get_kernel () |
virtual void | set_kernel (CKernel *kern) |
virtual CMeanFunction * | get_mean () |
virtual void | set_mean (CMeanFunction *m) |
virtual CLabels * | get_labels () |
virtual void | set_labels (CLabels *lab) |
CLikelihoodModel * | get_model () |
virtual void | set_model (CLikelihoodModel *mod) |
virtual float64_t | get_scale () const |
virtual void | set_scale (float64_t scale) |
virtual bool | supports_multiclass () const |
virtual SGMatrix< float64_t > | get_multiclass_E () |
virtual CSGObject * | shallow_copy () const |
virtual CSGObject * | deep_copy () const |
virtual bool | is_generic (EPrimitiveType *generic) const |
template<class T > | |
void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
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void | set_generic () |
void | unset_generic () |
virtual void | print_serializable (const char *prefix="") |
virtual bool | save_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=Version::get_version_parameter()) |
virtual bool | load_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=Version::get_version_parameter()) |
DynArray< TParameter * > * | load_file_parameters (const SGParamInfo *param_info, int32_t file_version, CSerializableFile *file, const char *prefix="") |
DynArray< TParameter * > * | load_all_file_parameters (int32_t file_version, int32_t current_version, CSerializableFile *file, const char *prefix="") |
void | map_parameters (DynArray< TParameter * > *param_base, int32_t &base_version, DynArray< const SGParamInfo * > *target_param_infos) |
void | set_global_io (SGIO *io) |
SGIO * | get_global_io () |
void | set_global_parallel (Parallel *parallel) |
Parallel * | get_global_parallel () |
void | set_global_version (Version *version) |
Version * | get_global_version () |
SGStringList< char > | get_modelsel_names () |
void | print_modsel_params () |
char * | get_modsel_param_descr (const char *param_name) |
index_t | get_modsel_param_index (const char *param_name) |
void | build_gradient_parameter_dictionary (CMap< TParameter *, CSGObject * > *dict) |
virtual void | update_parameter_hash () |
virtual bool | parameter_hash_changed () |
virtual bool | equals (CSGObject *other, float64_t accuracy=0.0, bool tolerant=false) |
virtual CSGObject * | clone () |
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 | |
SGVector< float64_t > | m_sW |
SGVector< float64_t > | m_d2lp |
SGVector< float64_t > | m_d3lp |
SGVector< float64_t > | m_dfhat |
SGMatrix< float64_t > | m_Z |
SGVector< float64_t > | m_g |
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 |
Definition at line 43 of file SingleLaplacianInferenceMethodWithLBFGS.cpp.
CSingleLaplacianInferenceMethodWithLBFGS | ( | CKernel * | kernel, |
CFeatures * | features, | ||
CMeanFunction * | mean, | ||
CLabels * | labels, | ||
CLikelihoodModel * | model | ||
) |
Definition at line 49 of file SingleLaplacianInferenceMethodWithLBFGS.cpp.
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Definition at line 160 of file SingleLaplacianInferenceMethodWithLBFGS.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 1243 of file SGObject.cpp.
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check if members of object are valid for inference
Reimplemented in CFITCInferenceMethod, and CExactInferenceMethod.
Definition at line 275 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 1360 of file SGObject.cpp.
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virtualinherited |
A deep copy. All the instance variables will also be copied.
Definition at line 200 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 1264 of file SGObject.cpp.
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}
Definition at line 104 of file LaplacianInferenceBase.cpp.
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pthread helper method to compute negative log marginal likelihood derivatives wrt hyperparameter
Definition at line 221 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 406 of file SingleLaplacianInferenceMethod.cpp.
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protectedvirtualinherited |
returns derivative of negative log marginal likelihood wrt kernel's parameter
param | parameter of given kernel |
Implements CInferenceMethod.
Definition at line 472 of file SingleLaplacianInferenceMethod.cpp.
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protectedvirtualinherited |
returns derivative of negative log marginal likelihood wrt parameter of likelihood model
param | parameter of given likelihood model |
Implements CInferenceMethod.
Definition at line 438 of file SingleLaplacianInferenceMethod.cpp.
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protectedvirtualinherited |
returns derivative of negative log marginal likelihood wrt mean function's parameter
param | parameter of given mean function |
Implements CInferenceMethod.
Definition at line 522 of file SingleLaplacianInferenceMethod.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 93 of file SingleLaplacianInferenceMethod.cpp.
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get the gradient
parameters | parameter's dictionary |
Implements CDifferentiableFunction.
Definition at line 215 of file InferenceMethod.h.
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return what type of inference we are
Reimplemented from CInferenceMethod.
Definition at line 75 of file LaplacianInferenceBase.h.
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virtualinherited |
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virtualinherited |
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Computes an unbiased estimate of the marginal-likelihood (in log-domain),
\[ p(y|X,\theta), \]
where \(y\) are the labels, \(X\) are the features (omitted from in the following expressions), and \(\theta\) represent hyperparameters.
This is done via a Gaussian approximation to the posterior \(q(f|y, \theta)\approx p(f|y, \theta)\), which is computed by the underlying 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 91 of file InferenceMethod.cpp.
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get maximum for Brent's minimization method
Definition at line 191 of file LaplacianInferenceBase.h.
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get tolerance for Brent's minimization method
Definition at line 179 of file LaplacianInferenceBase.h.
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Definition at line 1135 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 1159 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 1172 of file SGObject.cpp.
get the E matrix used for multi classification
Definition at line 40 of file InferenceMethod.cpp.
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virtual |
returns the name of the inference method
Reimplemented from CSingleLaplacianInferenceMethod.
Definition at line 91 of file SingleLaplacianInferenceMethodWithLBFGS.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 106 of file SingleLaplacianInferenceMethod.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 150 of file InferenceMethod.cpp.
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get max Newton iterations
Definition at line 167 of file LaplacianInferenceBase.h.
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get tolerance for newton iterations
Definition at line 155 of file LaplacianInferenceBase.h.
returns covariance matrix \(\Sigma=(K^{-1}+W)^{-1}\) of the Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\), which is an approximation to the posterior:
\[ p(f|y) \approx q(f|y) = \mathcal{N}(f|\mu,\Sigma) \]
Implements CInferenceMethod.
Definition at line 122 of file LaplacianInferenceBase.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 113 of file LaplacianInferenceBase.cpp.
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get the function value
Implements CDifferentiableFunction.
Definition at line 225 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 297 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 704 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 545 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 374 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 1062 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 1057 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 742 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 949 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 889 of file SGObject.cpp.
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Definition at line 263 of file SGObject.cpp.
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prints all parameter registered for model selection and their type
Definition at line 1111 of file SGObject.cpp.
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virtualinherited |
prints registered parameters out
prefix | prefix for members |
Definition at line 309 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 315 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 1072 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 1067 of file SGObject.cpp.
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Definition at line 42 of file SGObject.cpp.
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Definition at line 47 of file SGObject.cpp.
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Definition at line 52 of file SGObject.cpp.
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Definition at line 57 of file SGObject.cpp.
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Definition at line 62 of file SGObject.cpp.
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Definition at line 67 of file SGObject.cpp.
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Definition at line 72 of file SGObject.cpp.
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Definition at line 77 of file SGObject.cpp.
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Definition at line 82 of file SGObject.cpp.
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Definition at line 87 of file SGObject.cpp.
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Definition at line 92 of file SGObject.cpp.
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Definition at line 97 of file SGObject.cpp.
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Definition at line 102 of file SGObject.cpp.
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Definition at line 107 of file SGObject.cpp.
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Definition at line 112 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 243 of file SGObject.cpp.
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set the version object
version | version object to use |
Definition at line 284 of file SGObject.cpp.
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virtual |
Definition at line 66 of file SingleLaplacianInferenceMethodWithLBFGS.cpp.
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set maximum for Brent's minimization method
max | maximum for Brent's minimization method |
Definition at line 197 of file LaplacianInferenceBase.h.
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set tolerance for Brent's minimization method
tol | tolerance for Brent's minimization method |
Definition at line 185 of file LaplacianInferenceBase.h.
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set likelihood model
mod | model to set |
Reimplemented in CKLInferenceMethod, and CKLDualInferenceMethod.
Definition at line 310 of file InferenceMethod.h.
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set max Newton iterations
iter | max Newton iterations |
Definition at line 173 of file LaplacianInferenceBase.h.
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virtual |
Definition at line 60 of file SingleLaplacianInferenceMethodWithLBFGS.cpp.
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set tolerance for newton iterations
tol | tolerance for newton iterations to set |
Definition at line 161 of file LaplacianInferenceBase.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 194 of file SGObject.cpp.
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Reimplemented from CInferenceMethod.
Definition at line 95 of file SingleLaplacianInferenceMethod.h.
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whether combination of inference method and given likelihood function supports multiclass classification
Definition at line 348 of file InferenceMethod.h.
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virtualinherited |
Reimplemented from CInferenceMethod.
Definition at line 85 of file SingleLaplacianInferenceMethod.h.
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unset generic type
this has to be called in classes specializing a template class
Definition at line 304 of file SGObject.cpp.
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update data all matrices
Reimplemented from CInferenceMethod.
Definition at line 80 of file LaplacianInferenceBase.cpp.
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update alpha matrix
Reimplemented from CSingleLaplacianInferenceMethod.
Definition at line 185 of file SingleLaplacianInferenceMethodWithLBFGS.cpp.
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protectedvirtualinherited |
update covariance matrix of the approximation to the posterior
Implements CLaplacianInferenceBase.
Definition at line 147 of file SingleLaplacianInferenceMethod.cpp.
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update cholesky matrix
Implements CInferenceMethod.
Definition at line 167 of file SingleLaplacianInferenceMethod.cpp.
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protectedvirtualinherited |
update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter
Implements CInferenceMethod.
Definition at line 350 of file SingleLaplacianInferenceMethod.cpp.
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Updates the hash of current parameter combination
Definition at line 250 of file SGObject.cpp.
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update train kernel matrix
Reimplemented in CFITCInferenceMethod.
Definition at line 291 of file InferenceMethod.cpp.
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io
Definition at line 496 of file SGObject.h.
alpha vector used in process mean calculation
Definition at line 443 of file InferenceMethod.h.
second derivative of log likelihood with respect to function location
Definition at line 177 of file SingleLaplacianInferenceMethod.h.
third derivative of log likelihood with respect to function location
Definition at line 180 of file SingleLaplacianInferenceMethod.h.
Definition at line 182 of file SingleLaplacianInferenceMethod.h.
derivative of log likelihood with respect to function location
Definition at line 209 of file LaplacianInferenceBase.h.
the matrix used for multi classification
Definition at line 455 of file InferenceMethod.h.
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protectedinherited |
features to use
Definition at line 437 of file InferenceMethod.h.
Definition at line 186 of file SingleLaplacianInferenceMethod.h.
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parameters wrt which we can compute gradients
Definition at line 511 of file SGObject.h.
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inherited |
Hash of parameter values
Definition at line 517 of file SGObject.h.
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protectedinherited |
max Newton's iterations
Definition at line 224 of file LaplacianInferenceBase.h.
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covariance function
Definition at line 428 of file InferenceMethod.h.
kernel matrix from features (non-scalled by inference scalling)
Definition at line 452 of file InferenceMethod.h.
upper triangular factor of Cholesky decomposition
Definition at line 446 of file InferenceMethod.h.
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protectedinherited |
labels of features
Definition at line 440 of file InferenceMethod.h.
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protectedinherited |
mean function
Definition at line 431 of file InferenceMethod.h.
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protectedinherited |
likelihood function to use
Definition at line 434 of file InferenceMethod.h.
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inherited |
model selection parameters
Definition at line 508 of file SGObject.h.
mean vector of the approximation to the posterior
Definition at line 215 of file LaplacianInferenceBase.h.
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protectedinherited |
max iterations for Brent's minimization method
Definition at line 230 of file LaplacianInferenceBase.h.
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protectedinherited |
amount of tolerance for Brent's minimization method
Definition at line 227 of file LaplacianInferenceBase.h.
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map for different parameter versions
Definition at line 514 of file SGObject.h.
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parameters
Definition at line 505 of file SGObject.h.
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kernel scale
Definition at line 449 of file InferenceMethod.h.
covariance matrix of the approximation to the posterior
Definition at line 218 of file LaplacianInferenceBase.h.
square root of W
Definition at line 174 of file SingleLaplacianInferenceMethod.h.
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amount of tolerance for Newton's iterations
Definition at line 221 of file LaplacianInferenceBase.h.
noise matrix
Definition at line 212 of file LaplacianInferenceBase.h.
Definition at line 184 of file SingleLaplacianInferenceMethod.h.
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parallel
Definition at line 499 of file SGObject.h.
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version
Definition at line 502 of file SGObject.h.