SHOGUN
4.2.0

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 \(\textbf{P}_{xy}\), 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. Sampling from null is also possible. If unsure which one to use, sampling 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].
PERMUTATION: For permuting available samples to sample nulldistribution. This 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 Member Functions  
CHSIC ()  
CHSIC (CKernel *kernel_p, CKernel *kernel_q, CFeatures *p, CFeatures *q)  
virtual  ~CHSIC () 
virtual float64_t  compute_statistic () 
virtual float64_t  compute_p_value (float64_t statistic) 
virtual float64_t  compute_threshold (float64_t alpha) 
virtual const char *  get_name () const 
virtual EStatisticType  get_statistic_type () const 
virtual void  set_p (CFeatures *p) 
virtual void  set_q (CFeatures *q) 
SGVector< float64_t >  fit_null_gamma () 
virtual SGVector< float64_t >  sample_null () 
virtual void  set_kernel_p (CKernel *kernel_p) 
virtual void  set_kernel_q (CKernel *kernel_q) 
virtual CKernel *  get_kernel_p () 
virtual CKernel *  get_kernel_q () 
virtual CFeatures *  get_p () 
virtual CFeatures *  get_q () 
virtual float64_t  perform_test () 
bool  perform_test (float64_t alpha) 
virtual void  set_num_null_samples (index_t num_null_samples) 
virtual void  set_null_approximation_method (ENullApproximationMethod null_approximation_method) 
virtual CSGObject *  shallow_copy () const 
virtual CSGObject *  deep_copy () const 
virtual bool  is_generic (EPrimitiveType *generic) const 
template<class T >  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
template<>  
void  set_generic () 
void  unset_generic () 
virtual void  print_serializable (const char *prefix="") 
virtual bool  save_serializable (CSerializableFile *file, const char *prefix="") 
virtual bool  load_serializable (CSerializableFile *file, const char *prefix="") 
void  set_global_io (SGIO *io) 
SGIO *  get_global_io () 
void  set_global_parallel (Parallel *parallel) 
Parallel *  get_global_parallel () 
void  set_global_version (Version *version) 
Version *  get_global_version () 
SGStringList< char >  get_modelsel_names () 
void  print_modsel_params () 
char *  get_modsel_param_descr (const char *param_name) 
index_t  get_modsel_param_index (const char *param_name) 
void  build_gradient_parameter_dictionary (CMap< TParameter *, CSGObject * > *dict) 
virtual void  update_parameter_hash () 
virtual bool  parameter_hash_changed () 
virtual bool  equals (CSGObject *other, float64_t accuracy=0.0, bool tolerant=false) 
virtual CSGObject *  clone () 
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  
SGMatrix< float64_t >  get_kernel_matrix_K () 
SGMatrix< float64_t >  get_kernel_matrix_L () 
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 
CFeatures *  m_q 
index_t  m_num_null_samples 
ENullApproximationMethod  m_null_approximation_method 

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.

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.
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 CHypothesisTest.

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 CHypothesisTest.
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 CHypothesisTest.

virtualinherited 
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.
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 
Definition at line 158 of file KernelIndependenceTest.cpp.
Definition at line 184 of file KernelIndependenceTest.cpp.

virtualinherited 
Getter for kernel for features from p, SG_REF'ed
Definition at line 146 of file KernelIndependenceTest.cpp.

virtualinherited 
Getter for kernel for features from q, SG_REF'ed
Definition at line 152 of file KernelIndependenceTest.cpp.

inherited 
Definition at line 498 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 522 of file SGObject.cpp.

inherited 
Returns index of model selection parameter with provided index
param_name  name of model selection parameter 
Definition at line 535 of file SGObject.cpp.

virtual 

virtualinherited 
Getter for features from p, SG_REF'ed
Definition at line 121 of file IndependenceTest.cpp.

virtualinherited 
Getter for features from q, SG_REF'ed
Definition at line 127 of file IndependenceTest.cpp.

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

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 296 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 
Definition at line 369 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 occurs. 
Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.
Definition at line 426 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 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.

virtualinherited 
Definition at line 262 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 CStreamingMMD.
Definition at line 113 of file HypothesisTest.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 121 of file HypothesisTest.cpp.

inherited 
prints all parameter registered for model selection and their type
Definition at line 474 of file SGObject.cpp.

virtualinherited 
prints registered parameters out
prefix  prefix for members 
Definition at line 308 of file SGObject.cpp.
merges both sets of samples and computes the test statistic m_num_null_sample times. This version precomputes the kenrel matrix once by hand, then samples using this one. The matrix has to be stored anyway when statistic is computed.
Reimplemented from CKernelIndependenceTest.

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 
Definition at line 314 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 occurs. 
Reimplemented in CKernel.
Definition at line 436 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 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.

inherited 
Definition at line 41 of file SGObject.cpp.

inherited 
Definition at line 46 of file SGObject.cpp.

inherited 
Definition at line 51 of file SGObject.cpp.

inherited 
Definition at line 56 of file SGObject.cpp.

inherited 
Definition at line 61 of file SGObject.cpp.

inherited 
Definition at line 66 of file SGObject.cpp.

inherited 
Definition at line 71 of file SGObject.cpp.

inherited 
Definition at line 76 of file SGObject.cpp.

inherited 
Definition at line 81 of file SGObject.cpp.

inherited 
Definition at line 86 of file SGObject.cpp.

inherited 
Definition at line 91 of file SGObject.cpp.

inherited 
Definition at line 96 of file SGObject.cpp.

inherited 
Definition at line 101 of file SGObject.cpp.

inherited 
Definition at line 106 of file SGObject.cpp.

inherited 
Definition at line 111 of file SGObject.cpp.

inherited 
set generic type to T

inherited 

inherited 
set the parallel object
parallel  parallel object to use 
Definition at line 241 of file SGObject.cpp.

inherited 
set the version object
version  version object to use 
Definition at line 283 of file SGObject.cpp.

virtualinherited 
Setter for kernel for features from distribution p, SG_REFs it
kernel_p  kernel for features from p 
Definition at line 130 of file KernelIndependenceTest.cpp.

virtualinherited 
Setter for kernel for features from distribution q, SG_REFs it
kernel_q  kernel for features from q 
Definition at line 138 of file KernelIndependenceTest.cpp.

virtualinherited 
sets the method how to approximate the nulldistribution
null_approximation_method  method to use 
Definition at line 61 of file HypothesisTest.cpp.

virtualinherited 
sets the number of permutation iterations for sample_null()
num_null_samples  how often permutation shall be done 
Definition at line 67 of file HypothesisTest.cpp.

virtual 
Setter for features from distribution p, SG_REFs it
p  features from p 
Reimplemented from CIndependenceTest.

virtual 
Setter for features from distribution q, SG_REFs it
q  features from q 
Reimplemented from CIndependenceTest.

virtualinherited 
A shallow copy. All the SGObject instance variables will be simply assigned and SG_REFed.
Reimplemented in CGaussianKernel.
Definition at line 192 of file SGObject.cpp.

inherited 
unset generic type
this has to be called in classes specializing a template class
Definition at line 303 of file SGObject.cpp.

virtualinherited 
Updates the hash of current parameter combination
Definition at line 248 of file SGObject.cpp.

inherited 
io
Definition at line 369 of file SGObject.h.

inherited 
parameters wrt which we can compute gradients
Definition at line 384 of file SGObject.h.

inherited 
Hash of parameter values
Definition at line 387 of file SGObject.h.

protectedinherited 
underlying kernel for p
Definition at line 137 of file KernelIndependenceTest.h.

protectedinherited 
underlying kernel for q
Definition at line 140 of file KernelIndependenceTest.h.

inherited 
model selection parameters
Definition at line 381 of file SGObject.h.

protectedinherited 
Defines how the the null distribution is approximated
Definition at line 177 of file HypothesisTest.h.

protectedinherited 
number of iterations for sampling from nulldistributions
Definition at line 174 of file HypothesisTest.h.

protectedinherited 
samples of the distribution p
Definition at line 116 of file IndependenceTest.h.

inherited 
parameters
Definition at line 378 of file SGObject.h.

protectedinherited 
samples of the distribution q
Definition at line 119 of file IndependenceTest.h.

inherited 
parallel
Definition at line 372 of file SGObject.h.

inherited 
version
Definition at line 375 of file SGObject.h.