SHOGUN
3.2.1
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The KL approximation inference method class.
The class is implemented based on the KL method in the Challis's paper which uses 1-band (diagonal) represention. Note that in order to do variational inference, each diagonal element should be positive. This implementation updates the diagonal elements in log domain.
Code adapted from http://hannes.nickisch.org/code/approxXX.tar.gz and Gaussian Process Machine Learning Toolbox http://www.gaussianprocess.org/gpml/code/matlab/doc/ and the reference paper is Challis, Edward, and David Barber. "Concave Gaussian variational approximations for inference in large-scale Bayesian linear models." International conference on Artificial Intelligence and Statistics. 2011.
The adapted Matlab code can be found at https://gist.github.com/yorkerlin/d8acb388d03c6976728e
Note that "ApproxDiagonal" means a variational diagonal co-variance matrix is used in inference.
Definition at line 74 of file KLApproxDiagonalInferenceMethod.h.
Public Member Functions | |
CKLApproxDiagonalInferenceMethod () | |
CKLApproxDiagonalInferenceMethod (CKernel *kernel, CFeatures *features, CMeanFunction *mean, CLabels *labels, CLikelihoodModel *model) | |
virtual | ~CKLApproxDiagonalInferenceMethod () |
virtual const char * | get_name () const |
virtual SGVector< float64_t > | get_alpha () |
virtual SGVector< float64_t > | get_diagonal_vector () |
virtual EInferenceType | get_inference_type () const |
virtual float64_t | get_negative_log_marginal_likelihood () |
virtual SGVector< float64_t > | get_posterior_mean () |
virtual SGMatrix< float64_t > | get_posterior_covariance () |
virtual bool | supports_regression () const |
virtual bool | supports_binary () const |
virtual void | set_model (CLikelihoodModel *mod) |
virtual void | update () |
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 SGMatrix< float64_t > | get_cholesky () |
virtual void | set_noise_factor (float64_t noise_factor) |
virtual void | set_max_attempt (index_t max_attempt) |
virtual void | set_exp_factor (float64_t exp_factor) |
virtual void | set_min_coeff_kernel (float64_t min_coeff_kernel) |
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 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 () |
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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 |
Static Protected Member Functions | |
static void * | get_derivative_helper (void *p) |
default constructor
Definition at line 55 of file KLApproxDiagonalInferenceMethod.cpp.
CKLApproxDiagonalInferenceMethod | ( | CKernel * | kernel, |
CFeatures * | features, | ||
CMeanFunction * | mean, | ||
CLabels * | labels, | ||
CLikelihoodModel * | model | ||
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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 60 of file KLApproxDiagonalInferenceMethod.cpp.
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virtual |
Definition at line 96 of file KLApproxDiagonalInferenceMethod.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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check the provided likelihood model supports variational inference
mod | the provided likelihood model |
Definition at line 57 of file KLInferenceMethod.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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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
Note that m_alpha contains not only the alpha vector defined in the reference but also a vector corresponding to the lower triangular of C
Note that alpha=K^{-1}(mu-mean), where mean is generated from mean function, K is generated from cov function and mu is not only the posterior mean but also the variational mean
Definition at line 74 of file KLApproxDiagonalInferenceMethod.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.
Note that in some sub class L is not the Cholesky decomposition In this case, L will still be used to compute required matrix for prediction see CGaussianProcessMachine::get_posterior_variances()
Definition at line 461 of file KLInferenceMethod.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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compute matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter in cov function Note that get_derivative_wrt_inference_method(const TParameter* param) and get_derivative_wrt_kernel(const TParameter* param) will call this function
the | gradient wrt hyperparameter related to cov |
Implements CKLInferenceMethod.
Definition at line 153 of file KLLowerTriangularInferenceMethod.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 410 of file KLInferenceMethod.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 427 of file KLInferenceMethod.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 326 of file KLInferenceMethod.cpp.
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returns derivative of negative log marginal likelihood wrt mean function's parameter
param | parameter of given mean function |
Implements CInferenceMethod.
Definition at line 342 of file KLInferenceMethod.cpp.
get diagonal vector
Note that this vector is not avaliable for the KL method
The diagonal vector W is NOT used in this KL method Therefore, return empty vector
Definition at line 91 of file KLLowerTriangularInferenceMethod.cpp.
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get the gradient
parameters | parameter's dictionary |
Implements CDifferentiableFunction.
Definition at line 215 of file InferenceMethod.h.
compute the gradient wrt variational parameters given the current variational parameters (mu and s2)
Implements CKLInferenceMethod.
Definition at line 121 of file KLApproxDiagonalInferenceMethod.cpp.
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return what type of inference we are
Reimplemented from CInferenceMethod.
Definition at line 99 of file KLInferenceMethod.h.
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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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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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returns the name of the inference method
Reimplemented from CKLLowerTriangularInferenceMethod.
Definition at line 97 of file KLApproxDiagonalInferenceMethod.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 318 of file KLInferenceMethod.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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the helper function to compute the negative log marginal likelihood
Implements CKLInferenceMethod.
Definition at line 156 of file KLApproxDiagonalInferenceMethod.cpp.
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compute the negative log marginal likelihood given the current variational parameters (mu and s2)
Definition at line 275 of file KLInferenceMethod.cpp.
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 239 of file KLInferenceMethod.cpp.
returns mean vector \(\mu\) of the Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\), which is an approximation to the posterior:
\[ p(f|y) \approx q(f|y) = \mathcal{N}(f|\mu,\Sigma) \]
Implements CInferenceMethod.
Definition at line 231 of file KLInferenceMethod.cpp.
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get the function value
Implements CDifferentiableFunction.
Definition at line 225 of file InferenceMethod.h.
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this method is used to dynamic-cast the likelihood model, m_model, to variational likelihood model.
Definition at line 268 of file KLInferenceMethod.cpp.
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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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Using L-BFGS to estimate posterior parameters
Reimplemented in CKLDualInferenceMethod.
Definition at line 381 of file KLInferenceMethod.cpp.
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pre-compute the information for lbfgs optimization. This function needs to be called before calling get_negative_log_marginal_likelihood_wrt_parameters() and/or get_gradient_of_nlml_wrt_parameters(SGVector<float64_t> gradient)
Implements CKLInferenceMethod.
Definition at line 100 of file KLApproxDiagonalInferenceMethod.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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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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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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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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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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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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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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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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set exp factor to exponentially increase noise factor
exp_factor | should be greater than 1.0 default value is 2 |
Definition at line 189 of file KLInferenceMethod.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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Definition at line 282 of file KLInferenceMethod.cpp.
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set max attempt to ensure Kernel matrix to be positive definite
max_attempt | should be non-negative. 0 means infinity attempts default value is 0 |
Definition at line 183 of file KLInferenceMethod.cpp.
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set minimum coeefficient of kernel matrix used in LDLT factorization
min_coeff_kernel | should be non-negative default value is 1e-5 |
Definition at line 177 of file KLInferenceMethod.cpp.
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set variational likelihood model
mod | model to set |
Reimplemented from CInferenceMethod.
Reimplemented in CKLDualInferenceMethod.
Definition at line 67 of file KLInferenceMethod.cpp.
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set noise factor to ensure Kernel matrix to be positive definite by adding non-negative noise to diagonal elements of Kernel matrix
noise_factor | should be non-negative default value is 1e-10 |
Definition at line 171 of file KLInferenceMethod.cpp.
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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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compute the inv(corrected_Kernel*sq(m_scale))*A
A | input matrix |
Definition at line 126 of file KLLowerTriangularInferenceMethod.cpp.
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Reimplemented from CInferenceMethod.
Definition at line 167 of file KLInferenceMethod.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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Reimplemented from CInferenceMethod.
Definition at line 157 of file KLInferenceMethod.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 156 of file KLInferenceMethod.cpp.
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update alpha vector
Implements CInferenceMethod.
Definition at line 178 of file KLApproxDiagonalInferenceMethod.cpp.
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update covariance matrix of the approximation to the posterior
update_Sigma() does the similar job Therefore, this function body is empty
Implements CKLInferenceMethod.
Definition at line 166 of file KLLowerTriangularInferenceMethod.cpp.
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update cholesky matrix
Implements CInferenceMethod.
Definition at line 173 of file KLLowerTriangularInferenceMethod.cpp.
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update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter
get_derivative_related_cov(MatrixXd eigen_dK) does the similar job Therefore, this function body is empty
Implements CInferenceMethod.
Definition at line 99 of file KLLowerTriangularInferenceMethod.cpp.
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correct the kernel matrix and factorizated the corrected Kernel matrix for update
Reimplemented from CKLInferenceMethod.
Definition at line 106 of file KLLowerTriangularInferenceMethod.cpp.
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a helper function used to correct the kernel matrix using LDLT factorization
Definition at line 200 of file KLInferenceMethod.cpp.
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compute inv(corrected_Kernel)*Sigma matrix
Implements CKLLowerTriangularInferenceMethod.
Definition at line 229 of file KLApproxDiagonalInferenceMethod.cpp.
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Updates the hash of current parameter combination
Definition at line 250 of file SGObject.cpp.
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compute posterior Sigma matrix
Implements CKLLowerTriangularInferenceMethod.
Definition at line 221 of file KLApproxDiagonalInferenceMethod.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.
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Definition at line 437 of file KLInferenceMethod.h.
the matrix used for multi classification
Definition at line 455 of file InferenceMethod.h.
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Definition at line 443 of file KLInferenceMethod.h.
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The factor used to exponentially increase noise_factor
Definition at line 294 of file KLInferenceMethod.h.
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features to use
Definition at line 437 of file InferenceMethod.h.
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Definition at line 452 of file KLInferenceMethod.h.
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parameters wrt which we can compute gradients
Definition at line 511 of file SGObject.h.
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Definition at line 458 of file KLInferenceMethod.h.
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Hash of parameter values
Definition at line 517 of file SGObject.h.
The K^{-1}Sigma matrix
Definition at line 127 of file KLLowerTriangularInferenceMethod.h.
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covariance function
Definition at line 428 of file InferenceMethod.h.
The L*sqrt(D) matrix, where L and D are defined in LDLT factorization on Kernel*sq(m_scale)
Definition at line 136 of file KLLowerTriangularInferenceMethod.h.
The permutation sequence of P, where P are defined in LDLT factorization on Kernel*sq(m_scale)
Definition at line 139 of file KLLowerTriangularInferenceMethod.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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labels of features
Definition at line 440 of file InferenceMethod.h.
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Definition at line 431 of file KLInferenceMethod.h.
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The Log-determinant of Kernel
Definition at line 133 of file KLLowerTriangularInferenceMethod.h.
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Definition at line 425 of file KLInferenceMethod.h.
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Max number of attempt to correct kernel matrix to be positive definite
Definition at line 297 of file KLInferenceMethod.h.
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Definition at line 434 of file KLInferenceMethod.h.
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Definition at line 428 of file KLInferenceMethod.h.
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Definition at line 449 of file KLInferenceMethod.h.
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mean function
Definition at line 431 of file InferenceMethod.h.
The mean vector generated from mean function
Definition at line 130 of file KLLowerTriangularInferenceMethod.h.
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The minimum coeefficient of kernel matrix in LDLT factorization used to check whether the kernel matrix is positive definite or not
Definition at line 288 of file KLInferenceMethod.h.
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Definition at line 446 of file KLInferenceMethod.h.
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likelihood function to use
Definition at line 434 of file InferenceMethod.h.
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model selection parameters
Definition at line 508 of file SGObject.h.
mean vector of the approximation to the posterior Note that m_mu is also a variational parameter
Definition at line 414 of file KLInferenceMethod.h.
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The factor used to ensure kernel matrix to be positive definite
Definition at line 291 of file KLInferenceMethod.h.
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Definition at line 464 of file KLInferenceMethod.h.
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Definition at line 470 of file KLInferenceMethod.h.
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Definition at line 467 of file KLInferenceMethod.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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Definition at line 440 of file KLInferenceMethod.h.
variational parameter sigma2 Note that sigma2 = diag(m_Sigma)
Definition at line 422 of file KLInferenceMethod.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 417 of file KLInferenceMethod.h.
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Definition at line 455 of file KLInferenceMethod.h.
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Definition at line 461 of file KLInferenceMethod.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.