SHOGUN
4.1.0
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The dual KL approximation inference method class.
This inference process is described in the reference paper Mohammad Emtiyaz Khan, Aleksandr Y. Aravkin, Michael P. Friedlander, Matthias Seeger Fast Dual Variational Inference for Non-Conjugate Latent Gaussian Models. ICML2013
The idea is to optimize the log marginal likelihood with equality constaints (primal problem) by solving the Lagrangian dual problem. The equality constaints are:
\[ h = \mu, \rho = \sigma^2 = diag(\Sigma) \]
, where h and \(\rho\) are auxiliary variables, \(\mu\) and \(\sigma^2\) are variational variables, and \(\Sigma\) is an approximated posterior covariance matrix. The equality constaints are variational mean constaint ( \(\mu\)) and variational variance constaint ( \(\sigma^2\)).
For detailed information, please refer to the paper.
Definition at line 65 of file KLDualInferenceMethod.h.
Public Member Functions | |
CKLDualInferenceMethod () | |
CKLDualInferenceMethod (CKernel *kernel, CFeatures *features, CMeanFunction *mean, CLabels *labels, CLikelihoodModel *model) | |
virtual | ~CKLDualInferenceMethod () |
virtual const char * | get_name () const |
virtual EInferenceType | get_inference_type () const |
virtual SGVector< float64_t > | get_alpha () |
virtual SGVector< float64_t > | get_diagonal_vector () |
void | set_model (CLikelihoodModel *mod) |
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 | 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="") |
virtual bool | load_serializable (CSerializableFile *file, const char *prefix="") |
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 () |
Static Public Member Functions | |
static CKLDualInferenceMethod * | 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 |
Static Protected Member Functions | |
static void * | get_derivative_helper (void *p) |
default constructor
Definition at line 55 of file KLDualInferenceMethod.cpp.
CKLDualInferenceMethod | ( | 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 KLDualInferenceMethod.cpp.
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Definition at line 89 of file KLDualInferenceMethod.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 597 of file SGObject.cpp.
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check the provided likelihood model supports dual variational inference or not
mod | the provided likelihood model |
Definition at line 93 of file KLDualInferenceMethod.cpp.
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check if members of object are valid for inference
Reimplemented in CSparseInferenceBase, CExactInferenceMethod, CFITCInferenceMethod, CSparseVGInferenceMethod, and CMultiLaplacianInferenceMethod.
Definition at line 309 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 714 of file SGObject.cpp.
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update gradients
Reimplemented from CInferenceMethod.
Definition at line 156 of file KLInferenceMethod.cpp.
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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
\[ \mu = K\alpha+mean_f \]
where \(\mu\) is the mean and \(K\) is the prior covariance matrix.
Definition at line 80 of file KLDualInferenceMethod.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 451 of file KLInferenceMethod.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.
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 related to cov |
Implements CKLInferenceMethod.
Definition at line 258 of file KLDualInferenceMethod.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 411 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 337 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 353 of file KLInferenceMethod.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 440 of file KLDualInferenceMethod.cpp.
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compute the objective value for LBFGS optimizer
The mathematical equation (equation 24 in the paper) is defined as below
\[ min_{\lambda \in S}{0.5*[(\lambda-y)^TK(\lambda-y)-log(det(A_{\lambda}))]-mean_{f}^T(\lambda-y)+\sum_{i=1}^{n}{Fenchel_i{(\lambda)}}} \]
where S is the feasible set defined for \(\lambda\), K comes from covariance function, \(mean_f\) comes from mean function, \(\lambda\) is the dual parameter, y are data labels, n is the number point, \(A_{\lambda}=K^{-1}+diag(\lambda)\), and \(Fenchel_i{(\lambda)}=Fenchel_i{(\alpha,\lambda)}\) since \(\alpha\) is implicitly defined by \(\lambda\)
Note that S and \(Fenchel_i{(\lambda)}\) are specified by the data modeling distribution, which are implemented in dual variational likelihood class.
Definition at line 173 of file KLDualInferenceMethod.cpp.
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this method is used to dynamic-cast the likelihood model, m_model, to dual variational likelihood model.
Definition at line 106 of file KLDualInferenceMethod.cpp.
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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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compute the gradient of the objective function for LBFGS optimizer The mathematical equation (equation 25 in the paper) is defined as below
\[ 0.5*[2*K(\lambda-y)-diag(A_{\lambda}^{-1})]-mean_{f}+\sum_{i=1}^{n}{\nabla Fenchel_i{(\lambda)}} \]
where \(A_{\lambda}=K^{-1}+diag(\lambda)\), K comes from covariance function, \(mean_f\) comes from mean function, \(\lambda\) is the dual parameter, y are data labels, n is the number point, and \(\nabla Fenchel_i{(\lambda)}\) is the gradient of \(Fenchel_i{(\lambda)}\) wrt to \(\lambda\)
Note that \(\nabla Fenchel_i{(\lambda)}\) are specified by the data modeling distribution, which are implemented in dual variational likelihood class.
Definition at line 194 of file KLDualInferenceMethod.cpp.
compute the gradient wrt variational parameters given the current variational parameters (mu and s2)
Implements CKLInferenceMethod.
Definition at line 140 of file KLDualInferenceMethod.h.
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return what type of inference we are
Reimplemented from CKLInferenceMethod.
Definition at line 94 of file KLDualInferenceMethod.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 126 of file InferenceMethod.cpp.
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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
Reimplemented from CKLInferenceMethod.
Definition at line 88 of file KLDualInferenceMethod.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 329 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 185 of file InferenceMethod.cpp.
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the helper function to compute the negative log marginal likelihood
Implements CKLInferenceMethod.
Definition at line 249 of file KLDualInferenceMethod.cpp.
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compute the negative log marginal likelihood given the current variational parameters (mu and s2)
Definition at line 286 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 251 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 244 of file KLInferenceMethod.cpp.
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get the function value
Implements CDifferentiableFunction.
Definition at line 255 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 279 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 296 of file SGObject.cpp.
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Using L-BFGS to estimate posterior parameters
Reimplemented from CKLInferenceMethod.
Definition at line 410 of file KLDualInferenceMethod.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 133 of file KLDualInferenceMethod.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 |
Definition at line 369 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 426 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 421 of file SGObject.cpp.
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helper method used to specialize a base class instance
inference | inference method |
Definition at line 67 of file KLDualInferenceMethod.cpp.
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Definition at line 262 of file SGObject.cpp.
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prints all parameter registered for model selection and their type
Definition at line 474 of file SGObject.cpp.
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prints registered parameters out
prefix | prefix for members |
Definition at line 308 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 |
Definition at line 314 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 436 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 431 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 201 of file KLInferenceMethod.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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Definition at line 293 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 195 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 189 of file KLInferenceMethod.cpp.
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set variational likelihood model
mod | model to set |
Reimplemented from CKLInferenceMethod.
Definition at line 100 of file KLDualInferenceMethod.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 183 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 192 of file SGObject.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 378 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 303 of file SGObject.cpp.
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update all matrices except gradients
Reimplemented from CInferenceMethod.
Definition at line 169 of file KLInferenceMethod.cpp.
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update alpha matrix
Implements CInferenceMethod.
Definition at line 290 of file KLDualInferenceMethod.cpp.
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update covariance matrix of the approximation to the posterior
Implements CKLInferenceMethod.
Definition at line 462 of file KLDualInferenceMethod.cpp.
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update cholesky matrix
Implements CInferenceMethod.
Definition at line 455 of file KLDualInferenceMethod.cpp.
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update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter
Implements CInferenceMethod.
Definition at line 448 of file KLDualInferenceMethod.cpp.
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correct the kernel matrix and factorizated the corrected Kernel matrix for update
Reimplemented in CKLLowerTriangularInferenceMethod.
Definition at line 207 of file KLInferenceMethod.cpp.
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a helper function used to correct the kernel matrix using LDLT factorization
Definition at line 212 of file KLInferenceMethod.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.
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Definition at line 440 of file KLInferenceMethod.h.
the matrix used for multi classification
Definition at line 487 of file InferenceMethod.h.
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Definition at line 446 of file KLInferenceMethod.h.
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The factor used to exponentially increase noise_factor
Definition at line 297 of file KLInferenceMethod.h.
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features to use
Definition at line 469 of file InferenceMethod.h.
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Definition at line 455 of file KLInferenceMethod.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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Definition at line 461 of file KLInferenceMethod.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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Definition at line 434 of file KLInferenceMethod.h.
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kernel scale
Definition at line 481 of file InferenceMethod.h.
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Definition at line 428 of file KLInferenceMethod.h.
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Max number of attempt to correct kernel matrix to be positive definite
Definition at line 300 of file KLInferenceMethod.h.
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Definition at line 437 of file KLInferenceMethod.h.
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Definition at line 431 of file KLInferenceMethod.h.
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Definition at line 452 of file KLInferenceMethod.h.
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mean function
Definition at line 463 of file InferenceMethod.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 291 of file KLInferenceMethod.h.
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Definition at line 449 of file KLInferenceMethod.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.
mean vector of the approximation to the posterior Note that m_mu is also a variational parameter
Definition at line 417 of file KLInferenceMethod.h.
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The factor used to ensure kernel matrix to be positive definite
Definition at line 294 of file KLInferenceMethod.h.
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Definition at line 467 of file KLInferenceMethod.h.
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Definition at line 473 of file KLInferenceMethod.h.
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Definition at line 470 of file KLInferenceMethod.h.
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parameters
Definition at line 378 of file SGObject.h.
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Definition at line 443 of file KLInferenceMethod.h.
variational parameter sigma2 Note that sigma2 = diag(m_Sigma)
Definition at line 425 of file KLInferenceMethod.h.
covariance matrix of the approximation to the posterior
Definition at line 420 of file KLInferenceMethod.h.
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Definition at line 458 of file KLInferenceMethod.h.
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Definition at line 464 of file KLInferenceMethod.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.