SHOGUN
4.1.0
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The SingleLaplace approximation inference method class for regression and binary Classification.
This inference method approximates the posterior likelihood function by using Laplace's method. Here, we compute a Gaussian approximation to the posterior via a Taylor expansion around the maximum of the posterior likelihood function.
For more details, see "Bayesian Classification with Gaussian Processes" by Christopher K.I Williams and David Barber, published 1998 in the IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 20, Number 12, Pages 1342-1351.
This specific implementation was adapted from the infLaplace.m file in the GPML toolbox.
Definition at line 43 of file SingleLaplacianInferenceMethod.h.
Static Public Member Functions | |
static CSingleLaplacianInferenceMethod * | 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 |
Protected Member Functions | |
virtual void | update_init () |
virtual void | update_alpha () |
virtual void | update_chol () |
virtual void | update_approx_cov () |
virtual void | update_deriv () |
virtual SGVector< float64_t > | get_derivative_wrt_inference_method (const TParameter *param) |
virtual SGVector< float64_t > | get_derivative_wrt_likelihood_model (const TParameter *param) |
virtual SGVector< float64_t > | get_derivative_wrt_kernel (const TParameter *param) |
virtual SGVector< float64_t > | get_derivative_wrt_mean (const TParameter *param) |
virtual void | compute_gradient () |
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) |
Static Protected Member Functions | |
static void * | get_derivative_helper (void *p) |
Protected Attributes | |
SGVector< float64_t > | m_sW |
SGVector< float64_t > | m_d2lp |
SGVector< float64_t > | m_d3lp |
SGVector< float64_t > | m_dfhat |
SGMatrix< float64_t > | m_Z |
SGVector< float64_t > | m_g |
float64_t | m_Psi |
SGVector< float64_t > | m_dlp |
SGVector< float64_t > | m_W |
SGVector< float64_t > | m_mu |
SGMatrix< float64_t > | m_Sigma |
float64_t | m_tolerance |
index_t | m_iter |
float64_t | m_opt_tolerance |
float64_t | m_opt_max |
CKernel * | m_kernel |
CMeanFunction * | m_mean |
CLikelihoodModel * | m_model |
CFeatures * | m_features |
CLabels * | m_labels |
SGVector< float64_t > | m_alpha |
SGMatrix< float64_t > | m_L |
float64_t | m_log_scale |
SGMatrix< float64_t > | m_ktrtr |
SGMatrix< float64_t > | m_E |
bool | m_gradient_update |
default constructor
Definition at line 74 of file SingleLaplacianInferenceMethod.cpp.
CSingleLaplacianInferenceMethod | ( | 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 |
Definition at line 79 of file SingleLaplacianInferenceMethod.cpp.
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virtual |
Definition at line 117 of file SingleLaplacianInferenceMethod.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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protectedvirtualinherited |
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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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.
Definition at line 714 of file SGObject.cpp.
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protectedvirtualinherited |
update gradients
Reimplemented from CInferenceMethod.
Definition at line 80 of file LaplacianInferenceBase.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
\[ \mu = K\alpha+meanf \]
where \(\mu\) is the mean, \(K\) is the prior covariance matrix, and \(meanf$\f is the mean prior fomr MeanFunction */ virtual SGVector<float64_t> get_alpha(); /** get Cholesky decomposition matrix @return Cholesky decomposition of matrix: for binary and regression case \f[ L = Cholesky(W^{\frac{1}{2}}*K*W^{\frac{1}{2}}+I) \f] where \) \( is the prior covariance matrix, \)sW \( is the vector returned by get_diagonal_vector(), and \) \( is the identity matrix. for multiclass case \f[ M = Cholesky(\sum_\text{c}{E_\text{c}) \f] where \){c}
Definition at line 115 of file LaplacianInferenceBase.cpp.
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pthread helper method to compute negative log marginal likelihood derivatives wrt hyperparameter
Definition at line 255 of file InferenceMethod.cpp.
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returns derivative of negative log marginal likelihood wrt parameter of CInferenceMethod class
param | parameter of CInferenceMethod class |
Implements CInferenceMethod.
Definition at line 450 of file SingleLaplacianInferenceMethod.cpp.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt kernel's parameter
param | parameter of given kernel |
Implements CInferenceMethod.
Definition at line 515 of file SingleLaplacianInferenceMethod.cpp.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt parameter of likelihood model
param | parameter of given likelihood model |
Implements CInferenceMethod.
Definition at line 481 of file SingleLaplacianInferenceMethod.cpp.
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protectedvirtual |
returns derivative of negative log marginal likelihood wrt mean function's parameter
param | parameter of given mean function |
Implements CInferenceMethod.
Definition at line 557 of file SingleLaplacianInferenceMethod.cpp.
get diagonal vector
\[ Cov = (K^{-1}+sW^{2})^{-1} \]
where \(Cov\) is the posterior covariance matrix, \(K\) is the prior covariance matrix, and \(sW\) is the diagonal vector.
Definition at line 95 of file SingleLaplacianInferenceMethod.cpp.
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inherited |
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inherited |
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inherited |
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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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return what type of inference we are
Reimplemented from CLaplacianInferenceBase.
Definition at line 72 of file SingleLaplacianInferenceMethod.h.
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virtualinherited |
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Computes an unbiased estimate of the marginal-likelihood (in log-domain),
\[ p(y|X,\theta), \]
where \(y\) are the labels, \(X\) are the features (omitted from in the following expressions), and \(\theta\) represent hyperparameters.
This is done via a Gaussian approximation to the posterior \(q(f|y, \theta)\approx p(f|y, \theta)\), which is computed by the underlying CInferenceMethod instance (if implemented, otherwise error), and then using an importance sample estimator
\[ p(y|\theta)=\int p(y|f)p(f|\theta)df =\int p(y|f)\frac{p(f|\theta)}{q(f|y, \theta)}q(f|y, \theta)df \approx\frac{1}{n}\sum_{i=1}^n p(y|f^{(i)})\frac{p(f^{(i)}|\theta)} {q(f^{(i)}|y, \theta)}, \]
where \( f^{(i)} \) are samples from the posterior approximation \( q(f|y, \theta) \). The resulting estimator has a low variance if \( q(f|y, \theta) \) is a good approximation. It has large variance otherwise (while still being consistent). Storing all number of log-domain ensures numerical stability.
num_importance_samples | the number of importance samples \(n\) from \( q(f|y, \theta) \). |
ridge_size | scalar that is added to the diagonal of the involved Gaussian distribution's covariance of GP prior and posterior approximation to stabilise things. Increase if covariance matrix is not numerically positive semi-definite. |
Definition at line 126 of file InferenceMethod.cpp.
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virtualinherited |
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get maximum for Brent's minimization method
Definition at line 177 of file LaplacianInferenceBase.h.
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get tolerance for Brent's minimization method
Definition at line 165 of file LaplacianInferenceBase.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 CLaplacianInferenceBase.
Reimplemented in CSingleLaplacianInferenceMethodWithLBFGS.
Definition at line 66 of file SingleLaplacianInferenceMethod.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 121 of file SingleLaplacianInferenceMethod.cpp.
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get log marginal likelihood gradient
\[ -\frac{\partial log(p(y|X, \theta))}{\partial \theta} \]
where \(y\) are the labels, \(X\) are the features, and \(\theta\) represent hyperparameters.
Definition at line 185 of file InferenceMethod.cpp.
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get max Newton iterations
Definition at line 153 of file LaplacianInferenceBase.h.
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get tolerance for newton iterations
Definition at line 141 of file LaplacianInferenceBase.h.
returns covariance matrix \(\Sigma=(K^{-1}+W)^{-1}\) of the Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\), which is an approximation to the posterior:
\[ p(f|y) \approx q(f|y) = \mathcal{N}(f|\mu,\Sigma) \]
Implements CInferenceMethod.
Definition at line 124 of file LaplacianInferenceBase.cpp.
returns mean vector \(\mu\) of the Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\), which is an approximation to the posterior:
\[ p(f|y) \approx q(f|y) = \mathcal{N}(f|\mu,\Sigma) \]
Mean vector \(\mu\) is evaluated using Newton's method.
Implements CInferenceMethod.
Definition at line 590 of file SingleLaplacianInferenceMethod.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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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 |
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 104 of file SingleLaplacianInferenceMethod.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 kernel
kern | kernel to set |
Reimplemented in CSingleSparseInferenceBase.
Definition at line 289 of file InferenceMethod.h.
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set maximum for Brent's minimization method
max | maximum for Brent's minimization method |
Definition at line 183 of file LaplacianInferenceBase.h.
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set tolerance for Brent's minimization method
tol | tolerance for Brent's minimization method |
Definition at line 171 of file LaplacianInferenceBase.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 159 of file LaplacianInferenceBase.h.
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set tolerance for newton iterations
tol | tolerance for newton iterations to set |
Definition at line 147 of file LaplacianInferenceBase.h.
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A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.
Reimplemented in CGaussianKernel.
Definition at line 192 of file SGObject.cpp.
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virtual |
Reimplemented from CInferenceMethod.
Definition at line 108 of file SingleLaplacianInferenceMethod.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 98 of file SingleLaplacianInferenceMethod.h.
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unset generic type
this has to be called in classes specializing a template class
Definition at line 303 of file SGObject.cpp.
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update all matrices except gradients
Reimplemented from CLaplacianInferenceBase.
Definition at line 234 of file SingleLaplacianInferenceMethod.cpp.
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update alpha matrix
Implements CInferenceMethod.
Reimplemented in CSingleLaplacianInferenceMethodWithLBFGS.
Definition at line 299 of file SingleLaplacianInferenceMethod.cpp.
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update covariance matrix of the approximation to the posterior
Implements CLaplacianInferenceBase.
Definition at line 162 of file SingleLaplacianInferenceMethod.cpp.
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update cholesky matrix
Implements CInferenceMethod.
Definition at line 182 of file SingleLaplacianInferenceMethod.cpp.
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update matrices which are required to compute negative log marginal likelihood derivatives wrt hyperparameter
Implements CInferenceMethod.
Definition at line 394 of file SingleLaplacianInferenceMethod.cpp.
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Definition at line 249 of file SingleLaplacianInferenceMethod.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.
second derivative of log likelihood with respect to function location
Definition at line 208 of file SingleLaplacianInferenceMethod.h.
third derivative of log likelihood with respect to function location
Definition at line 211 of file SingleLaplacianInferenceMethod.h.
Definition at line 213 of file SingleLaplacianInferenceMethod.h.
derivative of log likelihood with respect to function location
Definition at line 197 of file LaplacianInferenceBase.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.
Definition at line 217 of file SingleLaplacianInferenceMethod.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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max Newton's iterations
Definition at line 212 of file LaplacianInferenceBase.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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kernel scale
Definition at line 481 of file InferenceMethod.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 approximation to the posterior
Definition at line 203 of file LaplacianInferenceBase.h.
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max iterations for Brent's minimization method
Definition at line 218 of file LaplacianInferenceBase.h.
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amount of tolerance for Brent's minimization method
Definition at line 215 of file LaplacianInferenceBase.h.
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parameters
Definition at line 378 of file SGObject.h.
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protected |
Definition at line 219 of file SingleLaplacianInferenceMethod.h.
covariance matrix of the approximation to the posterior
Definition at line 206 of file LaplacianInferenceBase.h.
square root of W
Definition at line 205 of file SingleLaplacianInferenceMethod.h.
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amount of tolerance for Newton's iterations
Definition at line 209 of file LaplacianInferenceBase.h.
noise matrix
Definition at line 200 of file LaplacianInferenceBase.h.
Definition at line 215 of file SingleLaplacianInferenceMethod.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.