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SHOGUN
4.1.0
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Class of the Expectation Propagation (EP) posterior approximation inference method.
For more details, see: Minka, T. P. (2001). A Family of Algorithms for Approximate Bayesian Inference. PhD thesis, Massachusetts Institute of Technology
在文件 EPInferenceMethod.h 第 53 行定义.
静态 Public 成员函数 | |
| static CEPInferenceMethod * | obtain_from_generic (CInferenceMethod *inference) |
Public 属性 | |
| SGIO * | io |
| Parallel * | parallel |
| Version * | version |
| Parameter * | m_parameters |
| Parameter * | m_model_selection_parameters |
| Parameter * | m_gradient_parameters |
| uint32_t | m_hash |
Protected 成员函数 | |
| virtual void | compute_gradient () |
| virtual void | update_alpha () |
| virtual void | update_chol () |
| virtual void | update_approx_cov () |
| virtual void | update_approx_mean () |
| virtual void | update_negative_ml () |
| 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 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) |
静态 Protected 成员函数 | |
| static void * | get_derivative_helper (void *p) |
Protected 属性 | |
| CKernel * | m_kernel |
| CMeanFunction * | m_mean |
| CLikelihoodModel * | m_model |
| CFeatures * | m_features |
| CLabels * | m_labels |
| SGVector< float64_t > | m_alpha |
| SGMatrix< float64_t > | m_L |
| float64_t | m_log_scale |
| SGMatrix< float64_t > | m_ktrtr |
| SGMatrix< float64_t > | m_E |
| bool | m_gradient_update |
default constructor
在文件 EPInferenceMethod.cpp 第 63 行定义.
| CEPInferenceMethod | ( | CKernel * | kernel, |
| CFeatures * | features, | ||
| CMeanFunction * | mean, | ||
| CLabels * | labels, | ||
| CLikelihoodModel * | model | ||
| ) |
constructor
| kernel | covariance function |
| features | features to use in inference |
| mean | mean function |
| labels | labels of the features |
| model | likelihood model to use |
在文件 EPInferenceMethod.cpp 第 68 行定义.
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virtual |
在文件 EPInferenceMethod.cpp 第 75 行定义.
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inherited |
Builds a dictionary of all parameters in SGObject as well of those of SGObjects that are parameters of this object. Dictionary maps parameters to the objects that own them.
| dict | dictionary of parameters to be built. |
在文件 SGObject.cpp 第 597 行定义.
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protectedvirtualinherited |
check if members of object are valid for inference
被 CSparseInferenceBase, CExactInferenceMethod, CFITCInferenceMethod, CSparseVGInferenceMethod , 以及 CMultiLaplacianInferenceMethod 重载.
在文件 InferenceMethod.cpp 第 309 行定义.
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virtualinherited |
Creates a clone of the current object. This is done via recursively traversing all parameters, which corresponds to a deep copy. Calling equals on the cloned object always returns true although none of the memory of both objects overlaps.
在文件 SGObject.cpp 第 714 行定义.
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protectedvirtual |
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virtualinherited |
A deep copy. All the instance variables will also be copied.
在文件 SGObject.cpp 第 198 行定义.
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) |
在文件 SGObject.cpp 第 618 行定义.
returns vector to compute posterior mean of Gaussian Process under EP approximation:
\[ \mathbb{E}_q[f_*|X,y,x_*] = k^T_*\alpha \]
where \(k^T_*\) - covariance between training points \(X\) and test point \(x_*\), and for EP approximation:
\[ \alpha = (K + \tilde{S}^{-1})^{-1}\tilde{S}^{-1}\tilde{\nu} = (I-\tilde{S}^{\frac{1}{2}}B^{-1}\tilde{S}^{\frac{1}{2}}K)\tilde{\nu} \]
where \(K\) is the prior covariance matrix, \(\tilde{S}^{\frac{1}{2}}\) is the diagonal matrix (see description of get_diagonal_vector() method) and \(\tilde{\nu}\) - natural parameter ( \(\tilde{\nu} = \tilde{S}\tilde{\mu}\)).
在文件 EPInferenceMethod.cpp 第 107 行定义.
returns upper triangular factor \(L^T\) of the Cholesky decomposition ( \(LL^T\)) of the matrix:
\[ B = (\tilde{S}^{\frac{1}{2}}K\tilde{S}^{\frac{1}{2}}+I) \]
where \(\tilde{S}^{\frac{1}{2}}\) is the diagonal matrix (see description of get_diagonal_vector() method) and \(K\) is the prior covariance matrix.
在文件 EPInferenceMethod.cpp 第 115 行定义.
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staticprotectedinherited |
pthread helper method to compute negative log marginal likelihood derivatives wrt hyperparameter
在文件 InferenceMethod.cpp 第 255 行定义.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt parameter of CInferenceMethod class
| param | parameter of CInferenceMethod class |
实现了 CInferenceMethod.
在文件 EPInferenceMethod.cpp 第 466 行定义.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt kernel's parameter
| param | parameter of given kernel |
实现了 CInferenceMethod.
在文件 EPInferenceMethod.cpp 第 492 行定义.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt parameter of likelihood model
| param | parameter of given likelihood model |
实现了 CInferenceMethod.
在文件 EPInferenceMethod.cpp 第 485 行定义.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt mean function's parameter
| param | parameter of given mean function |
实现了 CInferenceMethod.
在文件 EPInferenceMethod.cpp 第 522 行定义.
returns diagonal vector of the diagonal matrix:
\[ \tilde{S}^{\frac{1}{2}} = \sqrt{\tilde{S}} \]
where \(\tilde{S} = \text{diag}(\tilde{\tau})\), and \(\tilde{\tau}\)
在文件 EPInferenceMethod.cpp 第 123 行定义.
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virtualinherited |
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inherited |
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inherited |
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inherited |
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virtualinherited |
get the gradient
| parameters | parameter's dictionary |
在文件 InferenceMethod.h 第 245 行定义.
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virtual |
return what type of inference we are
重载 CInferenceMethod .
在文件 EPInferenceMethod.h 第 76 行定义.
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virtualinherited |
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virtualinherited |
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inherited |
Computes an unbiased estimate of the marginal-likelihood (in log-domain),
\[ p(y|X,\theta), \]
where \(y\) are the labels, \(X\) are the features (omitted from in the following expressions), and \(\theta\) represent hyperparameters.
This is done via a Gaussian approximation to the posterior \(q(f|y, \theta)\approx p(f|y, \theta)\), which is computed by the underlying CInferenceMethod instance (if implemented, otherwise error), and then using an importance sample estimator
\[ p(y|\theta)=\int p(y|f)p(f|\theta)df =\int p(y|f)\frac{p(f|\theta)}{q(f|y, \theta)}q(f|y, \theta)df \approx\frac{1}{n}\sum_{i=1}^n p(y|f^{(i)})\frac{p(f^{(i)}|\theta)} {q(f^{(i)}|y, \theta)}, \]
where \( f^{(i)} \) are samples from the posterior approximation \( q(f|y, \theta) \). The resulting estimator has a low variance if \( q(f|y, \theta) \) is a good approximation. It has large variance otherwise (while still being consistent). Storing all number of log-domain ensures numerical stability.
| num_importance_samples | the number of importance samples \(n\) from \( q(f|y, \theta) \). |
| ridge_size | scalar that is added to the diagonal of the involved Gaussian distribution's covariance of GP prior and posterior approximation to stabilise things. Increase if covariance matrix is not numerically positive semi-definite. |
在文件 InferenceMethod.cpp 第 126 行定义.
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virtual |
returns maximum number of sweeps over all variables
在文件 EPInferenceMethod.h 第 228 行定义.
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virtualinherited |
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returns minimum number of sweeps over all variables
在文件 EPInferenceMethod.h 第 216 行定义.
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inherited |
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inherited |
在文件 SGObject.cpp 第 498 行定义.
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Returns description of a given parameter string, if it exists. SG_ERROR otherwise
| param_name | name of the parameter |
在文件 SGObject.cpp 第 522 行定义.
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inherited |
Returns index of model selection parameter with provided index
| param_name | name of model selection parameter |
在文件 SGObject.cpp 第 535 行定义.
get the E matrix used for multi classification
在文件 InferenceMethod.cpp 第 72 行定义.
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virtual |
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virtual |
returns the negative logarithm of the marginal likelihood function:
\[ -log(p(y|X, \theta)) \]
where \(y\) are the labels, \(X\) are the features, and \(\theta\) represent hyperparameters.
实现了 CInferenceMethod.
在文件 EPInferenceMethod.cpp 第 99 行定义.
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virtualinherited |
get log marginal likelihood gradient
\[ -\frac{\partial log(p(y|X, \theta))}{\partial \theta} \]
where \(y\) are the labels, \(X\) are the features, and \(\theta\) represent hyperparameters.
在文件 InferenceMethod.cpp 第 185 行定义.
returns covariance matrix \(\Sigma=(K^{-1}+\tilde{S})^{-1}\) of the Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\), which is an approximation to the posterior:
\[ p(f|X,y) \approx q(f|X,y) = \mathcal{N}(f|\mu,\Sigma) \]
Covariance matrix \(\Sigma\) is evaluated using matrix inversion lemma:
\[ \Sigma = (K^{-1}+\tilde{S})^{-1} = K - K\tilde{S}^{\frac{1}{2}}B^{-1}\tilde{S}^{\frac{1}{2}}K \]
where \(B=(\tilde{S}^{\frac{1}{2}}K\tilde{S}^{\frac{1}{2}}+I)\).
实现了 CInferenceMethod.
在文件 EPInferenceMethod.cpp 第 138 行定义.
returns mean vector \(\mu\) of the Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\), which is an approximation to the posterior:
\[ p(f|X,y) \approx q(f|X,y) = \mathcal{N}(f|\mu,\Sigma) \]
Mean vector \(\mu\) is evaluated like:
\[ \mu = \Sigma\tilde{\nu} \]
where \(\Sigma\) - covariance matrix of the posterior approximation and \(\tilde{\nu}\) - natural parameter ( \(\tilde{\nu} = \tilde{S}\tilde{\mu}\)).
实现了 CInferenceMethod.
在文件 EPInferenceMethod.cpp 第 131 行定义.
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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 |
在文件 SGObject.cpp 第 296 行定义.
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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 |
在文件 SGObject.cpp 第 369 行定义.
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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. |
被 CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel , 以及 CExponentialKernel 重载.
在文件 SGObject.cpp 第 426 行定义.
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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. |
被 CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool > , 以及 CDynamicObjectArray 重载.
在文件 SGObject.cpp 第 421 行定义.
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static |
helper method used to specialize a base class instance
| inference | inference method |
在文件 EPInferenceMethod.cpp 第 86 行定义.
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virtualinherited |
在文件 SGObject.cpp 第 262 行定义.
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inherited |
prints all parameter registered for model selection and their type
在文件 SGObject.cpp 第 474 行定义.
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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 |
在文件 SGObject.cpp 第 314 行定义.
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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. |
被 CKernel 重载.
在文件 SGObject.cpp 第 436 行定义.
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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. |
被 CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool > , 以及 CDynamicObjectArray 重载.
在文件 SGObject.cpp 第 431 行定义.
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inherited |
在文件 SGObject.cpp 第 41 行定义.
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inherited |
在文件 SGObject.cpp 第 46 行定义.
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在文件 SGObject.cpp 第 51 行定义.
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在文件 SGObject.cpp 第 56 行定义.
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inherited |
在文件 SGObject.cpp 第 61 行定义.
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在文件 SGObject.cpp 第 66 行定义.
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在文件 SGObject.cpp 第 71 行定义.
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在文件 SGObject.cpp 第 76 行定义.
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inherited |
在文件 SGObject.cpp 第 81 行定义.
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在文件 SGObject.cpp 第 86 行定义.
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在文件 SGObject.cpp 第 91 行定义.
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在文件 SGObject.cpp 第 96 行定义.
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inherited |
在文件 SGObject.cpp 第 101 行定义.
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在文件 SGObject.cpp 第 106 行定义.
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inherited |
在文件 SGObject.cpp 第 111 行定义.
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inherited |
set generic type to T
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inherited |
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inherited |
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virtualinherited |
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sets maximum number of sweeps over all variables
| max_sweep | maximum number of sweeps to set |
在文件 EPInferenceMethod.h 第 234 行定义.
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virtualinherited |
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sets minimum number of sweeps over all variables
| min_sweep | minimum number of sweeps to set |
在文件 EPInferenceMethod.h 第 222 行定义.
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set likelihood model
| mod | model to set |
被 CKLInferenceMethod , 以及 CKLDualInferenceMethod 重载.
在文件 InferenceMethod.h 第 340 行定义.
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virtual |
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virtualinherited |
A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.
被 CGaussianKernel 重载.
在文件 SGObject.cpp 第 192 行定义.
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virtual |
重载 CInferenceMethod .
在文件 EPInferenceMethod.h 第 240 行定义.
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virtualinherited |
whether combination of inference method and given likelihood function supports multiclass classification
在文件 InferenceMethod.h 第 378 行定义.
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whether combination of inference method and given likelihood function supports regression
被 CExactInferenceMethod, CKLInferenceMethod, CFITCInferenceMethod, CSparseVGInferenceMethod, CSingleFITCLaplacianInferenceMethod , 以及 CSingleLaplacianInferenceMethod 重载.
在文件 InferenceMethod.h 第 364 行定义.
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inherited |
unset generic type
this has to be called in classes specializing a template class
在文件 SGObject.cpp 第 303 行定义.
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protectedvirtual |
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protectedvirtual |
update covariance matrix of the approximation to the posterior
在文件 EPInferenceMethod.cpp 第 353 行定义.
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protectedvirtual |
update mean vector of the approximation to the posterior
在文件 EPInferenceMethod.cpp 第 376 行定义.
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protectedvirtual |
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protectedvirtual |
update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter
实现了 CInferenceMethod.
在文件 EPInferenceMethod.cpp 第 446 行定义.
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protectedvirtual |
update negative marginal likelihood
在文件 EPInferenceMethod.cpp 第 390 行定义.
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virtualinherited |
Updates the hash of current parameter combination
在文件 SGObject.cpp 第 248 行定义.
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protectedvirtualinherited |
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inherited |
io
在文件 SGObject.h 第 369 行定义.
alpha vector used in process mean calculation
在文件 InferenceMethod.h 第 475 行定义.
the matrix used for multi classification
在文件 InferenceMethod.h 第 487 行定义.
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protectedinherited |
features to use
在文件 InferenceMethod.h 第 469 行定义.
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parameters wrt which we can compute gradients
在文件 SGObject.h 第 384 行定义.
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Whether gradients are updated
在文件 InferenceMethod.h 第 490 行定义.
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Hash of parameter values
在文件 SGObject.h 第 387 行定义.
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protectedinherited |
covariance function
在文件 InferenceMethod.h 第 460 行定义.
kernel matrix from features (non-scalled by inference scalling)
在文件 InferenceMethod.h 第 484 行定义.
upper triangular factor of Cholesky decomposition
在文件 InferenceMethod.h 第 478 行定义.
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protectedinherited |
labels of features
在文件 InferenceMethod.h 第 472 行定义.
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protectedinherited |
kernel scale
在文件 InferenceMethod.h 第 481 行定义.
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protectedinherited |
mean function
在文件 InferenceMethod.h 第 463 行定义.
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protectedinherited |
likelihood function to use
在文件 InferenceMethod.h 第 466 行定义.
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model selection parameters
在文件 SGObject.h 第 381 行定义.
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parameters
在文件 SGObject.h 第 378 行定义.
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parallel
在文件 SGObject.h 第 372 行定义.
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version
在文件 SGObject.h 第 375 行定义.
