SHOGUN
4.1.0
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The SingleFITCLaplace approximation inference method class for regression and binary Classification. Note that the number of inducing points (m) is usually far less than the number of input points (n). (the time complexity is computed based on the assumption m < n)
Warning: the time complexity of method, CSingleFITCLaplacianBase::get_derivative_wrt_kernel(const TParameter* param), depends on the implementation of virtual kernel method, CKernel::get_parameter_gradient_diagonal(param, i). The default time complexity of the kernel method can be O(n^2)
Warning: the the time complexity increases from O(m^2*n) to O(n^2*m) if method CSingleFITCLaplacianInferenceMethod::get_posterior_covariance() is called
This specific implementation was adapted from the infFITC_Laplace.m file in the GPML toolbox.
Definition at line 61 of file SingleFITCLaplacianInferenceMethod.h.
Static Public Member Functions | |
static CSingleFITCLaplacianInferenceMethod * | 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) |
Friends | |
class | CFITCPsiLine |
default constructor
Definition at line 95 of file SingleFITCLaplacianInferenceMethod.cpp.
CSingleFITCLaplacianInferenceMethod | ( | CKernel * | kernel, |
CFeatures * | features, | ||
CMeanFunction * | mean, | ||
CLabels * | labels, | ||
CLikelihoodModel * | model, | ||
CFeatures * | inducing_features | ||
) |
constructor
kernel | covariance function |
features | features to use in inference |
mean | mean function |
labels | labels of the features |
model | Likelihood model to use |
inducing_features | features to use |
Definition at line 100 of file SingleFITCLaplacianInferenceMethod.cpp.
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virtual |
Definition at line 168 of file SingleFITCLaplacianInferenceMethod.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.
check the bound constraint is vailid or not
bound | bound constrains of inducing features |
name | the name of the bound |
Definition at line 202 of file SingleSparseInferenceBase.cpp.
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check whether features and inducing features are set
Definition at line 49 of file SparseInferenceBase.cpp.
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check whether the provided kernel can compute the gradient wrt inducing features
Note that currently we check the name of the provided kernel to determine whether the kernel can compute the derivatives wrt inducing_features
The name of a supported Kernel must end with "SparseKernel"
Definition at line 96 of file SingleSparseInferenceBase.cpp.
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check if members of object are valid for inference
Reimplemented from CInferenceMethod.
Reimplemented in CFITCInferenceMethod, and CSparseVGInferenceMethod.
Definition at line 128 of file SparseInferenceBase.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 133 of file SingleFITCLaplacianInferenceMethod.cpp.
efficiently compute the matrix-vector product \(\Sigma \times al$\f, where \)$ is the FITC equivalent covariance n-by-n matrix (prior) of f_n
al | input vector |
Definition at line 187 of file SingleFITCLaplacianInferenceMethod.cpp.
efficiently compute the matrix-vector product \( \inv{\inv{W}+\Sigma} \times x$\f, where \)$ is the FITC equivalent covariance n-by-n matrix (prior) of f_n
x | input vector |
Definition at line 172 of file SingleFITCLaplacianInferenceMethod.cpp.
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convert inducing features and features to the same represention
Note that these two kinds of features can be different types. The reasons are listed below.
Definition at line 54 of file SparseInferenceBase.cpp.
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A deep copy. All the instance variables will also be copied.
Definition at line 198 of file SGObject.cpp.
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returns derivative of negative log marginal likelihood wrt param when W has at least one negative element
res | raw derivative |
param | parameter |
Definition at line 817 of file SingleFITCLaplacianInferenceMethod.cpp.
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whether enable to opitmize inducing features
is_optmization | enable optimization |
Definition at line 257 of file SingleSparseInferenceBase.cpp.
Recursively compares the current SGObject to another one. Compares all registered numerical parameters, recursion upon complex (SGObject) parameters. Does not compare pointers!
May be overwritten but please do with care! Should not be necessary in most cases.
other | object to compare with |
accuracy | accuracy to use for comparison (optional) |
tolerant | allows linient check on float equality (within accuracy) |
Definition at line 618 of file SGObject.cpp.
get alpha vector
\[ \mu = K\alpha \]
where \(\mu\) is the mean and \(K\) is the prior covariance matrix.
Definition at line 136 of file SparseInferenceBase.cpp.
efficiently compute the Cholesky decomposition of inverse of the input matrix chol(inv(mtx))
mtx | symmetric positive definite matrix |
Definition at line 214 of file SingleFITCLaplacianInferenceMethod.cpp.
get Cholesky decomposition matrix
\[ L = Cholesky(sW*K*sW+I) \]
where \(K\) is the prior covariance matrix, \(sW\) is the vector returned by get_diagonal_vector(), and \(I\) is the identity matrix.
Definition at line 145 of file SparseInferenceBase.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.
helper function to compute variables which are required to compute negative log marginal likelihood implicit derivatives
d | raw derivative |
Definition at line 785 of file SingleFITCLaplacianInferenceMethod.cpp.
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compute variables which are required to compute negative log marginal likelihood derivatives wrt cov-like hyperparameter \(\theta\)
Note that scale, which is a hyperparameter in inference_method, is a cov-like hyperparameter hyperparameters in cov function are cov-like hyperparameters
ddiagKi | \(\textbf{diag}(\frac{\partial {\Sigma_{n}}}{\partial {\theta}})\) |
dKuui | \(\frac{\partial {\Sigma_{m}}}{\partial {\theta}}\) |
dKui | \(\frac{\partial {\Sigma_{m,n}}}{\partial {\theta}}\) |
v | auxiliary variable related to explicit derivative |
R | auxiliary variable related to explicit derivative |
Definition at line 132 of file SingleFITCLaplacianBase.cpp.
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compute variables which are required to compute negative log marginal likelihood full derivatives wrt cov-like hyperparameter \(\theta\)
Note that scale, which is a hyperparameter in inference_method, is a cov-like hyperparameter hyperparameters in cov function are cov-like hyperparameters
ddiagKi | \(\textbf{diag}(\frac{\partial {\Sigma_{n}}}{\partial {\theta}})\) |
dKuui | \(\frac{\partial {\Sigma_{m}}}{\partial {\theta}}\) |
dKui | \(\frac{\partial {\Sigma_{m,n}}}{\partial {\theta}}\) |
Reimplemented from CSingleFITCLaplacianBase.
Definition at line 587 of file SingleFITCLaplacianInferenceMethod.cpp.
helper function to compute variables which are required to compute negative log marginal likelihood derivatives wrt the diagonal part of cov-like hyperparameter \(\theta\)
Definition at line 74 of file SingleFITCLaplacianBase.cpp.
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protectedvirtualinherited |
helper function to compute variables which are required to compute negative log marginal likelihood derivatives wrt cov-like hyperparameter \(\theta\)
Note that scale, which is a hyperparameter in inference_method, is a cov-like hyperparameter hyperparameters in cov function are cov-like hyperparameters what is more, derivative wrt inducing_noise will also use this function
dKuui | \(\frac{\partial {\Sigma_{m}}}{\partial {\theta}}\) |
v | auxiliary variable related to explicit derivative |
R | auxiliary variable related to explicit derivative |
Definition at line 87 of file SingleFITCLaplacianBase.cpp.
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protectedvirtualinherited |
helper function to compute variables which are required to compute negative log marginal likelihood derivatives wrt inducing features
Note that the kernel must support to compute the derivatives wrt inducing features
BdK | auxiliary variable related to explicit derivative or implicit derivative |
param | parameter of given kernel |
Definition at line 216 of file SingleFITCLaplacianBase.cpp.
helper function to compute variables which are required to compute negative log marginal likelihood derivatives wrt mean \(\lambda\)
dmu | \(\frac{\partial {\mu_{n}}}{\partial {\lambda}}\) |
Reimplemented from CSingleFITCLaplacianBase.
Definition at line 770 of file SingleFITCLaplacianInferenceMethod.cpp.
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returns derivative of negative log marginal likelihood wrt inducing features (input) Note that in order to call this method, kernel must support FITC inference, which means derivatives wrt inducing features can be computed
Note that the kernel must support to compute the derivatives wrt inducing features
param | parameter of given kernel |
Reimplemented from CSingleFITCLaplacianBase.
Definition at line 827 of file SingleFITCLaplacianInferenceMethod.cpp.
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returns derivative of negative log marginal likelihood wrt inducing noise
param | parameter of given inference class |
Reimplemented from CSingleFITCLaplacianBase.
Definition at line 874 of file SingleFITCLaplacianInferenceMethod.cpp.
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returns derivative of negative log marginal likelihood wrt parameter of CInferenceMethod class
param | parameter of CInferenceMethod class |
Reimplemented from CSingleSparseInferenceBase.
Definition at line 631 of file SingleFITCLaplacianInferenceMethod.cpp.
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returns derivative of negative log marginal likelihood wrt kernel's parameter
param | parameter of given kernel |
Reimplemented from CSingleSparseInferenceBase.
Definition at line 725 of file SingleFITCLaplacianInferenceMethod.cpp.
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returns derivative of negative log marginal likelihood wrt parameter of likelihood model
param | parameter of given likelihood model |
Implements CSingleFITCLaplacianBase.
Definition at line 690 of file SingleFITCLaplacianInferenceMethod.cpp.
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returns derivative of negative log marginal likelihood wrt mean function's parameter
param | parameter of given mean function |
Reimplemented from CSingleFITCLaplacianBase.
Definition at line 795 of file SingleFITCLaplacianInferenceMethod.cpp.
get diagonal vector
Definition at line 160 of file SingleFITCLaplacianInferenceMethod.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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get the noise for inducing points
Definition at line 119 of file SparseInferenceBase.cpp.
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return what type of inference we are
Reimplemented from CSparseInferenceBase.
Definition at line 94 of file SingleFITCLaplacianInferenceMethod.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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get maximum for Brent's minimization method
Definition at line 199 of file SingleFITCLaplacianInferenceMethod.h.
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get tolerance for Brent's minimization method
Definition at line 187 of file SingleFITCLaplacianInferenceMethod.h.
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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 CSingleFITCLaplacianBase.
Reimplemented in CSingleFITCLaplacianInferenceMethodWithLBFGS.
Definition at line 87 of file SingleFITCLaplacianInferenceMethod.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 231 of file SingleFITCLaplacianInferenceMethod.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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get max Newton iterations
Definition at line 175 of file SingleFITCLaplacianInferenceMethod.h.
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get tolerance for newton iterations
Definition at line 163 of file SingleFITCLaplacianInferenceMethod.h.
returns covariance matrix \(\Sigma=(K^{-1}+W)^{-1}\) of the Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\), which is an approximation to the posterior:
Note that the time complexity of this method is O(n^3), where n is the number of samples
\[ p(f_n|y) \approx q(f|y) = \mathcal{N}(f|\mu,\Sigma) \]
Implements CSparseInferenceBase.
Definition at line 928 of file SingleFITCLaplacianInferenceMethod.cpp.
returns mean vector \(\mu\) of the Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\), which is an approximation to the posterior:
\[ p(f_n|y) \approx q(f|y) = \mathcal{N}(f|\mu,\Sigma) \]
Mean vector \(\mu\) is evaluated using FITC inference and Newton's method.
Implements CSparseInferenceBase.
Definition at line 903 of file SingleFITCLaplacianInferenceMethod.cpp.
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get the function value
Implements CDifferentiableFunction.
Definition at line 255 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 296 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 |
Definition at line 369 of file SGObject.cpp.
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protectedvirtualinherited |
Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_POST is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.
Definition at line 426 of file SGObject.cpp.
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protectedvirtualinherited |
Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_PRE is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 421 of file SGObject.cpp.
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static |
helper method used to specialize a base class instance
inference | inference method |
Definition at line 202 of file SingleFITCLaplacianInferenceMethod.cpp.
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opitmize inducing features
Definition at line 262 of file SingleSparseInferenceBase.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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protectedvirtualinherited |
Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_POST is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel.
Definition at line 436 of file SGObject.cpp.
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protectedvirtualinherited |
Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_PRE is called.
ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 431 of file SGObject.cpp.
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Definition at line 41 of file SGObject.cpp.
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Definition at line 46 of file SGObject.cpp.
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Definition at line 51 of file SGObject.cpp.
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Definition at line 56 of file SGObject.cpp.
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Definition at line 61 of file SGObject.cpp.
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Definition at line 66 of file SGObject.cpp.
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Definition at line 71 of file SGObject.cpp.
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Definition at line 76 of file SGObject.cpp.
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Definition at line 81 of file SGObject.cpp.
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Definition at line 86 of file SGObject.cpp.
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Definition at line 91 of file SGObject.cpp.
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Definition at line 96 of file SGObject.cpp.
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Definition at line 101 of file SGObject.cpp.
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Definition at line 106 of file SGObject.cpp.
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Definition at line 111 of file SGObject.cpp.
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set generic type to T
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set the parallel object
parallel | parallel object to use |
Definition at line 241 of file SGObject.cpp.
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set the version object
version | version object to use |
Definition at line 283 of file SGObject.cpp.
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set inducing features
feat | features to set |
Definition at line 109 of file SparseInferenceBase.h.
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set the noise for inducing points
noise | noise for inducing points |
The noise is used to enfore the kernel matrix about the inducing points are positive definite
Definition at line 113 of file SparseInferenceBase.cpp.
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set kernel
kern | kernel to set |
Reimplemented from CInferenceMethod.
Definition at line 85 of file SingleSparseInferenceBase.cpp.
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set the lower bound of inducing features
bound | lower bound constrains of inducing features |
Note that if the length of the bound is 1, it means the bound constraint applies to each dimension of all inducing features
Note that if the length of the bound is greater than 1, it means each dimension of the bound constraint applies to the corresponding dimension of inducing features
Definition at line 219 of file SingleSparseInferenceBase.cpp.
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set the max number of iterations used in optimization of inducing features
it | max number of iterations |
Definition at line 230 of file SingleSparseInferenceBase.cpp.
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set maximum for Brent's minimization method
max | maximum for Brent's minimization method |
Definition at line 205 of file SingleFITCLaplacianInferenceMethod.h.
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set tolerance for Brent's minimization method
tol | tolerance for Brent's minimization method |
Definition at line 193 of file SingleFITCLaplacianInferenceMethod.h.
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set likelihood model
mod | model to set |
Reimplemented in CKLInferenceMethod, and CKLDualInferenceMethod.
Definition at line 340 of file InferenceMethod.h.
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set max Newton iterations
iter | max Newton iterations |
Definition at line 181 of file SingleFITCLaplacianInferenceMethod.h.
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set tolerance for newton iterations
tol | tolerance for newton iterations to set |
Definition at line 169 of file SingleFITCLaplacianInferenceMethod.h.
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set the tolearance used in optimization of inducing features
tol | tolearance |
Definition at line 235 of file SingleSparseInferenceBase.cpp.
set the upper bound of inducing features
bound | upper bound constrains of inducing features |
Note that if the length of the bound is 1, it means the bound constraint applies to each dimension of all inducing features
Note that if the length of the bound is greater than 1, it means each dimension of the bound constraint applies to the corresponding dimension of inducing features
Definition at line 224 of file SingleSparseInferenceBase.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 117 of file SingleFITCLaplacianInferenceMethod.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 107 of file SingleFITCLaplacianInferenceMethod.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 matrices except gradients
Implements CSparseInferenceBase.
Definition at line 146 of file SingleFITCLaplacianInferenceMethod.cpp.
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update alpha matrix
Implements CSingleFITCLaplacianBase.
Reimplemented in CSingleFITCLaplacianInferenceMethodWithLBFGS.
Definition at line 346 of file SingleFITCLaplacianInferenceMethod.cpp.
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update covariance matrix of the approximation to the posterior
Definition at line 267 of file SingleFITCLaplacianInferenceMethod.cpp.
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update cholesky matrix
Implements CSingleFITCLaplacianBase.
Definition at line 458 of file SingleFITCLaplacianInferenceMethod.cpp.
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update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter
Implements CSingleFITCLaplacianBase.
Definition at line 555 of file SingleFITCLaplacianInferenceMethod.cpp.
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pre-compution for Newton's method
Definition at line 271 of file SingleFITCLaplacianInferenceMethod.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 from CInferenceMethod.
Definition at line 154 of file SparseInferenceBase.cpp.
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friend |
Definition at line 63 of file SingleFITCLaplacianInferenceMethod.h.
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io
Definition at line 369 of file SGObject.h.
Note that alpha is NOT post.alpha alpha and post.alpha are defined in infFITC.m and infFITC_Laplace.m
Definition at line 232 of file SingleFITCLaplacianBase.h.
alpha vector used in process mean calculation
Definition at line 475 of file InferenceMethod.h.
Definition at line 241 of file SingleFITCLaplacianBase.h.
Cholesky of inverse covariance of inducing features
Definition at line 405 of file SingleFITCLaplacianInferenceMethod.h.
second derivative of log likelihood with respect to function location
Definition at line 381 of file SingleFITCLaplacianInferenceMethod.h.
third derivative of log likelihood with respect to function location
Definition at line 384 of file SingleFITCLaplacianInferenceMethod.h.
derivative of negative log (approximated) marginal likelihood wrt f
Definition at line 408 of file SingleFITCLaplacianInferenceMethod.h.
d0 defined in infFITC_Laplace.m
Definition at line 422 of file SingleFITCLaplacianInferenceMethod.h.
derivative of log likelihood with respect to function location
Definition at line 387 of file SingleFITCLaplacianInferenceMethod.h.
the matrix used for multi classification
Definition at line 487 of file InferenceMethod.h.
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features to use
Definition at line 469 of file InferenceMethod.h.
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Definition at line 219 of file SingleSparseInferenceBase.h.
g defined in infFITC_Laplace.m
Definition at line 411 of file SingleFITCLaplacianInferenceMethod.h.
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parameters wrt which we can compute gradients
Definition at line 384 of file SGObject.h.
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Whether gradients are updated
Definition at line 490 of file InferenceMethod.h.
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Hash of parameter values
Definition at line 387 of file SGObject.h.
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tolearance used in optimizing inducing_features
Definition at line 193 of file SingleSparseInferenceBase.h.
inducing features for approximation
Definition at line 305 of file SparseInferenceBase.h.
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max Newton's iterations
Definition at line 396 of file SingleFITCLaplacianInferenceMethod.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.
diagonal elements of kernel matrix m_ktrtr
Definition at line 323 of file SparseInferenceBase.h.
covariance matrix of inducing features and training features
Definition at line 314 of file SparseInferenceBase.h.
covariance matrix of inducing features
Definition at line 311 of file SparseInferenceBase.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 222 of file SingleSparseInferenceBase.h.
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noise of the inducing variables
Definition at line 308 of file SparseInferenceBase.h.
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kernel scale
Definition at line 481 of file InferenceMethod.h.
lower bound of inducing features
Definition at line 184 of file SingleSparseInferenceBase.h.
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max number of iterations
Definition at line 190 of file SingleSparseInferenceBase.h.
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mean function
Definition at line 463 of file InferenceMethod.h.
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likelihood function to use
Definition at line 466 of file InferenceMethod.h.
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model selection parameters
Definition at line 381 of file SGObject.h.
mean vector of the the posterior Gaussian distribution
Definition at line 320 of file SparseInferenceBase.h.
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whether optimize inducing features
Definition at line 196 of file SingleSparseInferenceBase.h.
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max iterations for Brent's minimization method
Definition at line 402 of file SingleFITCLaplacianInferenceMethod.h.
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amount of tolerance for Brent's minimization method
Definition at line 399 of file SingleFITCLaplacianInferenceMethod.h.
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parameters
Definition at line 378 of file SGObject.h.
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the negative log likelihood without constant terms of
\[ -log(p(f_n|y)) \]
used in Newton's method
Definition at line 419 of file SingleFITCLaplacianInferenceMethod.h.
Rvdd=W where W is defined in infFITC.m and Rvdd is defined in infFITC_Laplace.m Note that W is NOT the diagonal matrix
Definition at line 250 of file SingleFITCLaplacianBase.h.
covariance matrix of the the posterior Gaussian distribution
Definition at line 317 of file SparseInferenceBase.h.
square root of W
Definition at line 378 of file SingleFITCLaplacianInferenceMethod.h.
t=1/g_sn2 in regression, where g_sn2 is defined in infFITC.m t=W.*dd in Laplace for binary classification, where W and dd are defined in infFITC_Laplace.m
Definition at line 238 of file SingleFITCLaplacianBase.h.
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amount of tolerance for Newton's iterations
Definition at line 393 of file SingleFITCLaplacianInferenceMethod.h.
upper bound of inducing features
Definition at line 187 of file SingleSparseInferenceBase.h.
Definition at line 253 of file SingleFITCLaplacianBase.h.
Definition at line 244 of file SingleFITCLaplacianBase.h.
noise matrix
Definition at line 390 of file SingleFITCLaplacianInferenceMethod.h.
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whether W contains negative elements
Definition at line 425 of file SingleFITCLaplacianInferenceMethod.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.