SHOGUN
4.1.0
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Class that models dual variational likelihood.
This likelihood model 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 mathematical definition (equation 19 in the paper) is as below
\[ Fenchel_i(\alpha_i,\lambda_i) = max_{h_i,\rho_i}{\alpha_i h_i+\lambda_i \rho_i /2 - E_{q(f_i|h_i,\rho_i)}(-log(p(y_i|f_i)))} \]
where \(\alpha_i\), \(\lambda_i\) are Lagrange multipliers with respective to constraints \(h_i=\mu_i\) and \(\rho_i=\sigma_i^2\) respectively, \(\mu\) and \(\sigma_i\) are variational Gaussian parameters, y_i is data label, \(q(f_i)\) is the variational Gaussian distribution, and p(y_i) is the data distribution to be specified. In this setting, \(\alpha\) and \(\lambda\) are called dual parameters for \(\mu\) and \(\sigma^2\) respectively.
Definition at line 63 of file DualVariationalGaussianLikelihood.h.
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 | precompute () |
virtual CVariationalGaussianLikelihood * | get_variational_likelihood () const |
virtual void | init_likelihood ()=0 |
virtual void | set_likelihood (CLikelihoodModel *lik) |
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) |
Protected Attributes | |
SGVector< float64_t > | m_lambda |
float64_t | m_strict_scale |
bool | m_is_valid |
SGVector< float64_t > | m_mu |
SGVector< float64_t > | m_s2 |
SGVector< float64_t > | m_lab |
CLikelihoodModel * | m_likelihood |
default constructor
Definition at line 45 of file DualVariationalGaussianLikelihood.cpp.
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Definition at line 51 of file DualVariationalGaussianLikelihood.cpp.
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this method is used for adjusting step size to ensure the updated value satisfied lower/upper bound constrain
The updated value is defined as below. lambda_new = m_lambda + direction * step
direction | direction for m_lambda update |
step | original step size (non-negative) |
Definition at line 111 of file DualVariationalGaussianLikelihood.cpp.
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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. |
Definition at line 597 of file SGObject.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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A deep copy. All the instance variables will also be copied.
Definition at line 198 of file SGObject.cpp.
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whether the lower bound is strict
Implemented in CLogitDVGLikelihood.
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check whether the dual parameters are valid or not.
Definition at line 182 of file DualVariationalGaussianLikelihood.cpp.
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whether the upper bound is strict
Implemented in CLogitDVGLikelihood.
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.
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pure virtual |
get the derivative of the dual objective function with respect to param
param | parameter |
Implemented in CLogitDVGLikelihood.
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pure virtual |
get the lower bound for dual parameter (lambda)
Implemented in CLogitDVGLikelihood.
evaluate the dual objective function
Implemented in CLogitDVGLikelihood.
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pure virtual |
get the upper bound for dual parameter (lambda)
Implemented in CLogitDVGLikelihood.
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virtualinherited |
get derivative of log likelihood \(log(p(y|f))\) with respect to given parameter
lab | labels used |
func | function location |
param | parameter |
Reimplemented from CLikelihoodModel.
Definition at line 88 of file VariationalLikelihood.cpp.
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virtual |
get derivative of log likelihood \(log(p(y|f))\) with respect to given hyperparameter Note that variational parameters are NOT considered as hyperparameters
param | parameter |
Implements CVariationalLikelihood.
Definition at line 90 of file DualVariationalGaussianLikelihood.cpp.
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virtualinherited |
returns the first moment of a given (unnormalized) probability distribution \(q(f_i) = Z_i^-1 p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2)\), where \( Z_i=\int p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2) df_i\).
This method is useful for EP local likelihood approximation.
mu | mean of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
s2 | variance of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
lab | labels \(y_i\) |
i | index i |
Implements CLikelihoodModel.
Definition at line 140 of file VariationalLikelihood.cpp.
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virtualinherited |
returns the first moment of a given (unnormalized) probability distribution \(q(f_i) = Z_i^-1 p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2)\) for each \(f_i\), where \( Z_i=\int p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2) df_i\).
Wrapper method which calls get_first_moment multiple times.
mu | mean of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
s2 | variance of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
lab | labels \(y_i\) |
Definition at line 72 of file LikelihoodModel.cpp.
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virtualinherited |
get derivative of log likelihood \(log(p(y|f))\) with respect to location function \(f\)
lab | labels used |
func | function location |
i | index, choices are 1, 2, and 3 for first, second, and third derivatives respectively |
Implements CLikelihoodModel.
Definition at line 125 of file VariationalLikelihood.cpp.
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virtualinherited |
Returns the logarithm of the point-wise likelihood \(log(p(y_i|f_i))\) for each label \(y_i\).
One can evaluate log-likelihood like: \( log(p(y|f)) = \sum_{i=1}^{n} log(p(y_i|f_i))\)
lab | labels \(y_i\) |
func | values of the function \(f_i\) |
Implements CLikelihoodModel.
Definition at line 118 of file VariationalLikelihood.cpp.
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Returns the log-likelihood \(log(p(y|f)) = \sum_{i=1}^{n} log(p(y_i|f_i))\) for each of the provided functions \( f \) in the given matrix.
Wrapper method which calls get_log_probability_f multiple times.
lab | labels \(y_i\) |
F | values of the function \(f_i\) where each column of the matrix is one function \( f \). |
Definition at line 51 of file LikelihoodModel.cpp.
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virtualinherited |
returns the zeroth moment of a given (unnormalized) probability distribution:
\[ log(Z_i) = log\left(\int p(y_i|f_i) \mathcal{N}(f_i|\mu,\sigma^2) df_i\right) \]
for each \(f_i\).
mu | mean of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
s2 | variance of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
lab | labels \(y_i\) |
Implements CLikelihoodModel.
Definition at line 132 of file VariationalLikelihood.cpp.
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get model type
Reimplemented from CLikelihoodModel.
Definition at line 112 of file VariationalLikelihood.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 dual parameter (alpha) for variational mu
Implemented in CLogitDVGLikelihood.
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returns the name of the likelihood model
Implements CSGObject.
Reimplemented in CLogitDVGLikelihood.
Definition at line 75 of file DualVariationalGaussianLikelihood.h.
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returns the logarithm of the predictive density of \(y_*\):
\[ log(p(y_*|X,y,x_*)) = log\left(\int p(y_*|f_*) p(f_*|X,y,x_*) df_*\right) \]
which approximately equals to
\[ log\left(\int p(y_*|f_*) \mathcal{N}(f_*|\mu,\sigma^2) df_*\right) \]
where normal distribution \(\mathcal{N}(\mu,\sigma^2)\) is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\).
NOTE: if lab equals to NULL, then each \(y_*\) equals to one.
mu | posterior mean of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
s2 | posterior variance of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
lab | labels \(y_*\) |
Reimplemented in CSoftMaxLikelihood.
Definition at line 45 of file LikelihoodModel.cpp.
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returns mean of the predictive marginal \(p(y_*|X,y,x_*)\)
NOTE: if lab equals to NULL, then each \(y_*\) equals to one.
mu | posterior mean of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
s2 | posterior variance of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
lab | labels \(y_*\) |
Implements CLikelihoodModel.
Definition at line 72 of file VariationalLikelihood.cpp.
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returns variance of the predictive marginal \(p(y_*|X,y,x_*)\)
NOTE: if lab equals to NULL, then each \(y_*\) equals to one.
mu | posterior mean of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
s2 | posterior variance of a Gaussian distribution \(\mathcal{N}(\mu,\sigma^2)\), which is an approximation to the posterior marginal \(p(f_*|X,y,x_*)\) |
lab | labels \(y_*\) |
Implements CLikelihoodModel.
Definition at line 80 of file VariationalLikelihood.cpp.
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virtualinherited |
get derivative of the first derivative of log likelihood with respect to function location, i.e. \(\frac{\partial log(p(y|f))}{\partial f}\) with respect to given parameter
lab | labels used |
func | function location |
param | parameter |
Reimplemented from CLikelihoodModel.
Definition at line 96 of file VariationalLikelihood.cpp.
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returns the second moment of a given (unnormalized) probability distribution \(q(f_i) = Z_i^-1 p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2)\), where \( Z_i=\int p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2) df_i\).
This method is useful for EP local likelihood approximation.
mu | mean of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
s2 | variance of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
lab | labels \(y_i\) |
i | index i |
Implements CLikelihoodModel.
Definition at line 148 of file VariationalLikelihood.cpp.
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virtualinherited |
returns the second moment of a given (unnormalized) probability distribution \(q(f_i) = Z_i^-1 p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2)\) for each \(f_i\), where \( Z_i=\int p(y_i|f_i)\mathcal{N}(f_i|\mu,\sigma^2) df_i\).
Wrapper method which calls get_second_moment multiple times.
mu | mean of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
s2 | variance of the \(\mathcal{N}(f_i|\mu,\sigma^2)\) |
lab | labels \(y_i\) |
Definition at line 89 of file LikelihoodModel.cpp.
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virtualinherited |
get derivative of the second derivative of log likelihood with respect to function location, i.e. \(\frac{\partial^{2} log(p(y|f))}{\partial f^{2}}\) with respect to given parameter
lab | labels used |
func | function location |
param | parameter |
Reimplemented from CLikelihoodModel.
Definition at line 104 of file VariationalLikelihood.cpp.
get the dual parameter (lambda) for variational s2
Implemented in CLogitDVGLikelihood.
returns the expection of the logarithm of a given probability distribution wrt the variational distribution given m_mu and m_s2
Implements CVariationalLikelihood.
Definition at line 66 of file DualVariationalGaussianLikelihood.cpp.
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get derivative of the variational expection of log likelihood with respect to given parameter
param | parameter |
Implements CVariationalLikelihood.
Definition at line 78 of file DualVariationalGaussianLikelihood.cpp.
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this method is used to dynamic-cast the likelihood model, m_likelihood, to variational likelihood model.
Definition at line 55 of file DualVariationalGaussianLikelihood.cpp.
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this method is called to initialize m_likelihood in init()
Implements CVariationalLikelihood.
Implemented in CLogitDVGLikelihood, CLogitVGPiecewiseBoundLikelihood, CNumericalVGLikelihood, CLogitVGLikelihood, CProbitVGLikelihood, and CStudentsTVGLikelihood.
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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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Definition at line 262 of file SGObject.cpp.
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compute common variables later used in get_variational_expection and get_variational_first_derivative. Note that this method will automatically be called when set_variational_distribution is called
Definition at line 213 of file DualVariationalGaussianLikelihood.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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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.
set dual parameters for variational parameters
the_lambda | dual parameter for variational mean |
lab | labels/data used |
Note that dual parameter (alpha) for the variational variance is implicitly set based on lambda
Definition at line 157 of file DualVariationalGaussianLikelihood.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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this method used to set m_likelihood
Definition at line 49 of file VariationalLikelihood.cpp.
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set a non-negative noise factor in order to correct the variance if variance is close to zero or negative setting 0 means correction is not applied
noise_factor | noise factor |
The default value is 1e-6.
Reimplemented from CVariationalGaussianLikelihood.
Definition at line 72 of file DualVariationalGaussianLikelihood.cpp.
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set the m_strict_scale
strict_scale | must be between 0 and 1 exclusively |
Definition at line 103 of file DualVariationalGaussianLikelihood.cpp.
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set the variational distribution given data and parameters
mu | mean of the variational distribution |
s2 | variance of the variational distribution |
lab | labels/data used |
Note that the variational distribution is Gaussian
Reimplemented from CVariationalGaussianLikelihood.
Definition at line 96 of file DualVariationalGaussianLikelihood.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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return whether likelihood function supports binary classification
Reimplemented from CLikelihoodModel.
Definition at line 162 of file VariationalLikelihood.cpp.
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return whether likelihood function supports computing the derivative wrt hyperparameter Note that variational parameters are NOT considered as hyperparameters
Implements CVariationalLikelihood.
Definition at line 84 of file DualVariationalGaussianLikelihood.cpp.
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return whether likelihood function supports multiclass classification
Reimplemented from CLikelihoodModel.
Definition at line 168 of file VariationalLikelihood.cpp.
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return whether likelihood function supports regression
Reimplemented from CLikelihoodModel.
Definition at line 156 of file VariationalLikelihood.cpp.
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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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Updates the hash of current parameter combination
Definition at line 248 of file SGObject.cpp.
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io
Definition at line 369 of file SGObject.h.
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parameters wrt which we can compute gradients
Definition at line 384 of file SGObject.h.
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Hash of parameter values
Definition at line 387 of file SGObject.h.
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whether m_lambda is satisfied lower bound and/or upper bound condition.
Definition at line 238 of file DualVariationalGaussianLikelihood.h.
the label of data
Definition at line 277 of file VariationalLikelihood.h.
The dual variables (lambda) for the variational parameter s2.
Note that in variational Gaussian inference, there is a relationship between lambda and alpha, where alpha is the dual parameter for variational parameter mu
Therefore, the dual variables (alpha) for variational parameter mu is not explicitly saved.
Definition at line 227 of file DualVariationalGaussianLikelihood.h.
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the distribution used to model data
Definition at line 280 of file VariationalLikelihood.h.
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model selection parameters
Definition at line 381 of file SGObject.h.
The mean of variational Gaussian distribution
Definition at line 79 of file VariationalGaussianLikelihood.h.
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parameters
Definition at line 378 of file SGObject.h.
The variance of variational Gaussian distribution
Definition at line 82 of file VariationalGaussianLikelihood.h.
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The value used to ensure strict bound(s) for m_lambda in adjust_step_wrt_dual_parameter()
Note that the value should be between 0 and 1 exclusively.
The default value is 1e-5.
Definition at line 235 of file DualVariationalGaussianLikelihood.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.