SHOGUN
v3.0.0

This class implements the Hilbert Schmidtd Independence Criterion based independence test as described in [1].
Given samples \(Z=\{(x_i,y_i)\}_{i=1}^m\) from the joint distribution \(\textbf{P}_x\textbf{P}_y\), does the joint distribution factorize as \(\textbf{P}_{xy}=\textbf{P}_x\textbf{P}_y\)?
The HSIC is a kernel based independence criterion, which is based on the largest singular value of a CrossCovariance Operator in a reproducing kernel Hilbert space (RKHS). Its population expression is zero if and only if the two underlying distributions are independent.
This class can compute empirical biased estimates:
\[ m\text{HSIC}(Z)[,p,q]^2)=\frac{1}{m^2}\text{trace}\textbf{KHLH} \]
where \(\textbf{H}=\textbf{I}\frac{1}{m}\textbf{11}^T\) is a centering matrix and \(\textbf{K}, \textbf{L}\) are kernel matrices of both sets of samples.
Note that computing the statistic returns m*MMD; same holds for the null distribution samples.
Along with the statistic comes a method to compute a pvalue based on different methods. Bootstrapping, is also possible. If unsure which one to use, bootstrapping with 250 iterations always is correct (but slow).
To choose, use set_null_approximation_method() and choose from
HSIC_GAMMA: for a very fast, but not consistent test based on moment matching of a Gamma distribution, as described in [1].
BOOTSTRAPPING: For permuting available samples to sample nulldistribution. Bootstrapping is done on precomputed kernel matrices, since they have to be stored anyway when the statistic is computed.
A very basic method for kernel selection when using CGaussianKernel is to use the median distance of the underlying data. See examples how to do that. More advanced methods will follow in the near future. However, the median heuristic works in quite some cases. See [1].
[1]: Gretton, A., Fukumizu, K., Teo, C., & Song, L. (2008). A kernel statistical test of independence. Advances in Neural Information Processing Systems, 18.
Public Attributes  
SGIO *  io 
Parallel *  parallel 
Version *  version 
Parameter *  m_parameters 
Parameter *  m_model_selection_parameters 
Parameter *  m_gradient_parameters 
ParameterMap *  m_parameter_map 
uint32_t  m_hash 
Protected Member Functions  
SGMatrix< float64_t >  get_kernel_matrix_K () 
SGMatrix< float64_t >  get_kernel_matrix_L () 
virtual TParameter *  migrate (DynArray< TParameter * > *param_base, const SGParamInfo *target) 
virtual void  one_to_one_migration_prepare (DynArray< TParameter * > *param_base, const SGParamInfo *target, TParameter *&replacement, TParameter *&to_migrate, char *old_name=NULL) 
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  
CKernel *  m_kernel_p 
CKernel *  m_kernel_q 
CFeatures *  m_p_and_q 
index_t  m_m 
index_t  m_bootstrap_iterations 
ENullApproximationMethod  m_null_approximation_method 
Constructor
p_and_q  feature data. Is assumed to contain samples from both p and q. First all samples from p, then from index m all samples from q 
kernel_p  kernel to use on samples from p 
kernel_q  kernel to use on samples from q 
p_and_q  samples from p and q, appended 
m  index of first sample of q 
Constructor. This is a convienience constructor which copies both features to one element and then calls the other constructor. Needs twice the memory for a short time
kernel_p  kernel to use on samples from p 
kernel_q  kernel to use on samples from q 
p  samples from distribution p, will be copied and NOT SG_REF'ed 
q  samples from distribution q, will be copied and NOT SG_REF'ed 
merges both sets of samples and computes the test statistic m_bootstrap_iteration times. This version precomputes the kenrel matrix once by hand, then performs bootstrapping on this one. The matrix has to be stored anyway when statistic is computed.
Reimplemented from CKernelIndependenceTestStatistic.

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 1196 of file SGObject.cpp.

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 1313 of file SGObject.cpp.
computes a pvalue based on current method for approximating the nulldistribution. The pvalue is the 1p quantile of the null distribution where the given statistic lies in.
statistic  statistic value to compute the pvalue for 
Reimplemented from CTwoDistributionsTestStatistic.

virtual 
Computes the HSIC statistic (see class description) for underlying kernels and data. Note that it is multiplied by the number of used samples. It is a biased estimator. Note that it is m*HSIC_b.
Note that since kernel matrices have to be stored, it has quadratic space costs.
Implements CTestStatistic.
computes a threshold based on current method for approximating the nulldistribution. The threshold is the value that a statistic has to have in ordner to reject the nullhypothesis.
alpha  test level to reject nullhypothesis 
Reimplemented from CTwoDistributionsTestStatistic.

virtualinherited 
A deep copy. All the instance variables will also be copied.
Definition at line 160 of file SGObject.h.
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) 
Definition at line 1217 of file SGObject.cpp.
Approximates the nulldistribution by a two parameter gamma distribution. Returns parameters.
NOTE: the gamma distribution is fitted to m*HSIC_b. But since compute_statistic() returnes the biased estimate, you can safely call this with values from compute_statistic(). However, the attached features have to be the SAME size, as these, the statistic was computed on. If compute_threshold() or compute_p_value() are used, this is ensured automatically. Note that m*Nulldistribution is fitted, which is fine since the statistic is also m*HSIC.
Has quadratic computational costs in terms of samples.
Called by compute_p_value() if null approximation method is set to MMD2_GAMMA.

inherited 

inherited 

inherited 

inherited 
Definition at line 98 of file TwoDistributionsTestStatistic.h.

inherited 
Definition at line 1100 of file SGObject.cpp.

inherited 
Returns description of a given parameter string, if it exists. SG_ERROR otherwise
param_name  name of the parameter 
Definition at line 1124 of file SGObject.cpp.

inherited 
Returns index of model selection parameter with provided index
param_name  name of model selection parameter 
Definition at line 1137 of file SGObject.cpp.

virtual 
Returns the name of the SGSerializable instance. It MUST BE the CLASS NAME without the prefixed `C'.
Implements CKernelIndependenceTestStatistic.

virtualinherited 
Getter for joint features, SG_REF's
Reimplemented in CLinearTimeMMD.
Definition at line 151 of file TwoDistributionsTestStatistic.cpp.

virtual 
returns the statistic type of this test statistic
Implements CTestStatistic.

virtualinherited 
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 268 of file SGObject.cpp.

inherited 
maps all parameters of this instance to the provided file version and loads all parameter data from the file into an array, which is sorted (basically calls load_file_parameter(...) for all parameters and puts all results into a sorted array)
file_version  parameter version of the file 
current_version  version from which mapping begins (you want to use Version::get_version_parameter() for this in most cases) 
file  file to load from 
prefix  prefix for members 
Definition at line 673 of file SGObject.cpp.

inherited 
loads some specified parameters from a file with a specified version The provided parameter info has a version which is recursively mapped until the file parameter version is reached. Note that there may be possibly multiple parameters in the mapping, therefore, a set of TParameter instances is returned
param_info  information of parameter 
file_version  parameter version of the file, must be <= provided parameter version 
file  file to load from 
prefix  prefix for members 
Definition at line 514 of file SGObject.cpp.

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 
param_version  (optional) a parameter version different to (this is mainly for testing, better do not use) 
Definition at line 345 of file SGObject.cpp.

protectedvirtualinherited 
Can (optionally) be overridden to postinitialize 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 occurres. 
Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.
Definition at line 1029 of file SGObject.cpp.

protectedvirtualinherited 
Can (optionally) be overridden to preinitialize 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 occurres. 
Reimplemented in CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, CDynamicArray< uint64_t >, and CDynamicObjectArray.
Definition at line 1024 of file SGObject.cpp.

inherited 
Takes a set of TParameter instances (base) with a certain version and a set of target parameter infos and recursively maps the base level wise to the current version using CSGObject::migrate(...). The base is replaced. After this call, the base version containing parameters should be of same version/type as the initial target parameter infos. Note for this to work, the migrate methods and all the internal parameter mappings have to match
param_base  set of TParameter instances that are mapped to the provided target parameter infos 
base_version  version of the parameter base 
target_param_infos  set of SGParamInfo instances that specify the target parameter base 
Definition at line 711 of file SGObject.cpp.

protectedvirtualinherited 
creates a new TParameter instance, which contains migrated data from the version that is provided. The provided parameter data base is used for migration, this base is a collection of all parameter data of the previous version. Migration is done FROM the data in param_base TO the provided param info Migration is always one version step. Method has to be implemented in subclasses, if no match is found, base method has to be called.
If there is an element in the param_base which equals the target, a copy of the element is returned. This represents the case when nothing has changed and therefore, the migrate method is not overloaded in a subclass
param_base  set of TParameter instances to use for migration 
target  parameter info for the resulting TParameter 
Definition at line 918 of file SGObject.cpp.

protectedvirtualinherited 
This method prepares everything for a onetoone parameter migration. One to one here means that only ONE element of the parameter base is needed for the migration (the one with the same name as the target). Data is allocated for the target (in the type as provided in the target SGParamInfo), and a corresponding new TParameter instance is written to replacement. The to_migrate pointer points to the single needed TParameter instance needed for migration. If a name change happened, the old name may be specified by old_name. In addition, the m_delete_data flag of to_migrate is set to true. So if you want to migrate data, the only thing to do after this call is converting the data in the m_parameter fields. If unsure how to use  have a look into an example for this. (base_migration_type_conversion.cpp for example)
param_base  set of TParameter instances to use for migration 
target  parameter info for the resulting TParameter 
replacement  (used as output) here the TParameter instance which is returned by migration is created into 
to_migrate  the only source that is used for migration 
old_name  with this parameter, a name change may be specified 
Definition at line 858 of file SGObject.cpp.

virtualinherited 
Performs the complete twosample test on current data and returns a pvalue.
This is a wrapper that calls compute_statistic first and then calls compute_p_value using the obtained statistic. In some statistic classes, it might be possible to compute statistic and pvalue in one single run which is more efficient. Therefore, this method might be overwritten in subclasses.
The method for computing the pvalue can be set via set_null_approximation_method().
Reimplemented in CLinearTimeMMD.
Definition at line 50 of file TestStatistic.cpp.

inherited 
Performs the complete twosample test on current data and returns a binary answer wheter null hypothesis is rejected or not.
This is just a wrapper for the above perform_test() method that returns a pvalue. If this pvalue lies below the test level alpha, the null hypothesis is rejected.
Should not be overwritten in subclasses. (Therefore not virtual)
alpha  test level alpha. 
Definition at line 58 of file TestStatistic.cpp.

inherited 
prints all parameter registered for model selection and their type
Definition at line 1076 of file SGObject.cpp.

virtualinherited 
prints registered parameters out
prefix  prefix for members 
Definition at line 280 of file SGObject.cpp.

virtualinherited 
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 
param_version  (optional) a parameter version different to (this is mainly for testing, better do not use) 
Definition at line 286 of file SGObject.cpp.

protectedvirtualinherited 
Can (optionally) be overridden to postinitialize 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 occurres. 
Reimplemented in CKernel.
Definition at line 1039 of file SGObject.cpp.

protectedvirtualinherited 
Can (optionally) be overridden to preinitialize 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 occurres. 
Reimplemented in CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, CDynamicArray< uint64_t >, and CDynamicObjectArray.
Definition at line 1034 of file SGObject.cpp.

virtualinherited 
sets the number of bootstrap iterations for bootstrap_null()
bootstrap_iterations  how often bootstrapping shall be done 
Definition at line 44 of file TestStatistic.cpp.

inherited 
set generic type to T
Definition at line 41 of file SGObject.cpp.

inherited 

inherited 
set the parallel object
parallel  parallel object to use 
Definition at line 220 of file SGObject.cpp.

inherited 
set the version object
version  version object to use 
Definition at line 255 of file SGObject.cpp.

virtualinherited 
sets the method how to approximate the nulldistribution
null_approximation_method  method to use 
Definition at line 38 of file TestStatistic.cpp.

virtualinherited 
Setter for joint features
p_and_q  joint features from p and q to set 
Reimplemented in CLinearTimeMMD.
Definition at line 143 of file TwoDistributionsTestStatistic.cpp.

virtualinherited 
A shallow copy. All the SGObject instance variables will be simply assigned and SG_REFed.
Reimplemented in CGaussianKernel.
Definition at line 151 of file SGObject.h.

inherited 
unset generic type
this has to be called in classes specializing a template class
Definition at line 275 of file SGObject.cpp.

virtualinherited 
Updates the hash of current parameter combination.
Definition at line 227 of file SGObject.cpp.

inherited 
io
Definition at line 514 of file SGObject.h.

protectedinherited 
number of iterations for bootstrapping nulldistributions
Definition at line 138 of file TestStatistic.h.

inherited 
parameters wrt which we can compute gradients
Definition at line 529 of file SGObject.h.

inherited 
Hash of parameter values
Definition at line 535 of file SGObject.h.

protectedinherited 
underlying kernel for p
Definition at line 88 of file KernelIndependenceTestStatistic.h.

protectedinherited 
underlying kernel for q
Definition at line 91 of file KernelIndependenceTestStatistic.h.

protectedinherited 
defines the first index of samples of q
Definition at line 110 of file TwoDistributionsTestStatistic.h.

inherited 
model selection parameters
Definition at line 526 of file SGObject.h.

protectedinherited 
Defines how the the null distribution is approximated
Definition at line 141 of file TestStatistic.h.

protectedinherited 
concatenated samples of the two distributions (two blocks)
Definition at line 107 of file TwoDistributionsTestStatistic.h.

inherited 
map for different parameter versions
Definition at line 532 of file SGObject.h.

inherited 
parameters
Definition at line 523 of file SGObject.h.

inherited 
parallel
Definition at line 517 of file SGObject.h.

inherited 
version
Definition at line 520 of file SGObject.h.