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CHSIC Class Reference

Detailed Description

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 Cross-Covariance 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 p-value 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 null-distribution. 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, 1-8.

Definition at line 91 of file HSIC.h.

Inheritance diagram for CHSIC:
Inheritance graph
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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
 

Constructor & Destructor Documentation

CHSIC ( )

Constructor

Definition at line 40 of file HSIC.cpp.

CHSIC ( CKernel *  kernel_p,
CKernel *  kernel_q,
CFeatures *  p,
CFeatures *  q 
)

Constructor.

Initializes the kernels and features from the two distributions and SG_REFs them

Parameters
kernel_pkernel to use on samples from p
kernel_qkernel to use on samples from q
psamples from distribution p
qsamples from distribution q

Definition at line 45 of file HSIC.cpp.

~CHSIC ( )
virtual

destructor

Definition at line 60 of file HSIC.cpp.

Member Function Documentation

void build_gradient_parameter_dictionary ( CMap< TParameter *, CSGObject * > *  dict)
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.

Parameters
dictdictionary of parameters to be built.

Definition at line 597 of file SGObject.cpp.

CSGObject * clone ( )
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.

Returns
an identical copy of the given object, which is disjoint in memory. NULL if the clone fails. Note that the returned object is SG_REF'ed

Definition at line 714 of file SGObject.cpp.

float64_t compute_p_value ( float64_t  statistic)
virtual

computes a p-value based on current method for approximating the null-distribution. The p-value is the 1-p quantile of the null- distribution where the given statistic lies in.

Parameters
statisticstatistic value to compute the p-value for
Returns
p-value parameter statistic is the (1-p) percentile of the null distribution

Reimplemented from CHypothesisTest.

Definition at line 107 of file HSIC.cpp.

float64_t compute_statistic ( )
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.

Returns
m*HSIC (unbiased estimate)

Implements CHypothesisTest.

Definition at line 73 of file HSIC.cpp.

float64_t compute_threshold ( float64_t  alpha)
virtual

computes a threshold based on current method for approximating the null-distribution. The threshold is the value that a statistic has to have in ordner to reject the null-hypothesis.

Parameters
alphatest level to reject null-hypothesis
Returns
threshold for statistics to reject null-hypothesis

Reimplemented from CHypothesisTest.

Definition at line 129 of file HSIC.cpp.

CSGObject * deep_copy ( ) const
virtualinherited

A deep copy. All the instance variables will also be copied.

Definition at line 198 of file SGObject.cpp.

bool equals ( CSGObject *  other,
float64_t  accuracy = 0.0,
bool  tolerant = false 
)
virtualinherited

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.

Parameters
otherobject to compare with
accuracyaccuracy to use for comparison (optional)
tolerantallows linient check on float equality (within accuracy)
Returns
true if all parameters were equal, false if not

Definition at line 618 of file SGObject.cpp.

SGVector< float64_t > fit_null_gamma ( )

Approximates the null-distribution 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*Null-distribution 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.

Returns
vector with two parameters for gamma distribution. To use: call gamma_cdf(statistic, a, b).

Definition at line 151 of file HSIC.cpp.

SGIO * get_global_io ( )
inherited

get the io object

Returns
io object

Definition at line 235 of file SGObject.cpp.

Parallel * get_global_parallel ( )
inherited

get the parallel object

Returns
parallel object

Definition at line 277 of file SGObject.cpp.

Version * get_global_version ( )
inherited

get the version object

Returns
version object

Definition at line 290 of file SGObject.cpp.

SGMatrix< float64_t > get_kernel_matrix_K ( )
protectedinherited
Returns
kernel matrix on samples from p. Distinguishes CustomKernels

Definition at line 158 of file KernelIndependenceTest.cpp.

SGMatrix< float64_t > get_kernel_matrix_L ( )
protectedinherited
Returns
kernel matrix on samples from q. Distinguishes CustomKernels

Definition at line 184 of file KernelIndependenceTest.cpp.

CKernel * get_kernel_p ( )
virtualinherited

Getter for kernel for features from p, SG_REF'ed

Returns
kernel for features from p

Definition at line 146 of file KernelIndependenceTest.cpp.

CKernel * get_kernel_q ( )
virtualinherited

Getter for kernel for features from q, SG_REF'ed

Returns
kernel for features from q

Definition at line 152 of file KernelIndependenceTest.cpp.

SGStringList< char > get_modelsel_names ( )
inherited
Returns
vector of names of all parameters which are registered for model selection

Definition at line 498 of file SGObject.cpp.

char * get_modsel_param_descr ( const char *  param_name)
inherited

Returns description of a given parameter string, if it exists. SG_ERROR otherwise

Parameters
param_namename of the parameter
Returns
description of the parameter

Definition at line 522 of file SGObject.cpp.

index_t get_modsel_param_index ( const char *  param_name)
inherited

Returns index of model selection parameter with provided index

Parameters
param_namename of model selection parameter
Returns
index of model selection parameter with provided name, -1 if there is no such

Definition at line 535 of file SGObject.cpp.

virtual const char* get_name ( ) const
virtual
Returns
the class name

Implements CKernelIndependenceTest.

Definition at line 143 of file HSIC.h.

CFeatures * get_p ( )
virtualinherited

Getter for features from p, SG_REF'ed

Returns
feature object from p

Definition at line 121 of file IndependenceTest.cpp.

CFeatures * get_q ( )
virtualinherited

Getter for features from q, SG_REF'ed

Returns
feature object from q

Definition at line 127 of file IndependenceTest.cpp.

virtual EStatisticType get_statistic_type ( ) const
virtual

returns the statistic type of this test statistic

Implements CHypothesisTest.

Definition at line 149 of file HSIC.h.

bool is_generic ( EPrimitiveType *  generic) const
virtualinherited

If the SGSerializable is a class template then TRUE will be returned and GENERIC is set to the type of the generic.

Parameters
genericset to the type of the generic if returning TRUE
Returns
TRUE if a class template.

Definition at line 296 of file SGObject.cpp.

bool load_serializable ( CSerializableFile *  file,
const char *  prefix = "" 
)
virtualinherited

Load this object from file. If it will fail (returning FALSE) then this object will contain inconsistent data and should not be used!

Parameters
filewhere to load from
prefixprefix for members
Returns
TRUE if done, otherwise FALSE

Definition at line 369 of file SGObject.cpp.

void load_serializable_post ( )
throw (ShogunException
)
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.

Exceptions
ShogunExceptionwill 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.

void load_serializable_pre ( )
throw (ShogunException
)
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.

Exceptions
ShogunExceptionwill 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.

bool parameter_hash_changed ( )
virtualinherited
Returns
whether parameter combination has changed since last update

Definition at line 262 of file SGObject.cpp.

float64_t perform_test ( )
virtualinherited

Performs the complete two-sample test on current data and returns a p-value.

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 p-value in one single run which is more efficient. Therefore, this method might be overwritten in subclasses.

The method for computing the p-value can be set via set_null_approximation_method().

Returns
p-value such that computed statistic is the (1-p) quantile of the estimated null distribution

Reimplemented in CStreamingMMD.

Definition at line 113 of file HypothesisTest.cpp.

bool perform_test ( float64_t  alpha)
inherited

Performs the complete two-sample 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 p-value. If this p-value lies below the test level alpha, the null hypothesis is rejected.

Should not be overwritten in subclasses. (Therefore not virtual)

Parameters
alphatest level alpha.
Returns
true if null hypothesis is rejected and false otherwise

Definition at line 121 of file HypothesisTest.cpp.

void print_modsel_params ( )
inherited

prints all parameter registered for model selection and their type

Definition at line 474 of file SGObject.cpp.

void print_serializable ( const char *  prefix = "")
virtualinherited

prints registered parameters out

Parameters
prefixprefix for members

Definition at line 308 of file SGObject.cpp.

SGVector< float64_t > sample_null ( )
virtual

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.

Returns
vector of all statistics

Reimplemented from CKernelIndependenceTest.

Definition at line 236 of file HSIC.cpp.

bool save_serializable ( CSerializableFile *  file,
const char *  prefix = "" 
)
virtualinherited

Save this object to file.

Parameters
filewhere to save the object; will be closed during returning if PREFIX is an empty string.
prefixprefix for members
Returns
TRUE if done, otherwise FALSE

Definition at line 314 of file SGObject.cpp.

void save_serializable_post ( )
throw (ShogunException
)
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.

Exceptions
ShogunExceptionwill be thrown if an error occurs.

Reimplemented in CKernel.

Definition at line 436 of file SGObject.cpp.

void save_serializable_pre ( )
throw (ShogunException
)
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.

Exceptions
ShogunExceptionwill 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.

void set_generic ( )
inherited

Definition at line 41 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 46 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 51 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 56 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 61 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 66 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 71 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 76 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 81 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 86 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 91 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 96 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 101 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 106 of file SGObject.cpp.

void set_generic ( )
inherited

Definition at line 111 of file SGObject.cpp.

void set_generic ( )
inherited

set generic type to T

void set_global_io ( SGIO *  io)
inherited

set the io object

Parameters
ioio object to use

Definition at line 228 of file SGObject.cpp.

void set_global_parallel ( Parallel *  parallel)
inherited

set the parallel object

Parameters
parallelparallel object to use

Definition at line 241 of file SGObject.cpp.

void set_global_version ( Version *  version)
inherited

set the version object

Parameters
versionversion object to use

Definition at line 283 of file SGObject.cpp.

void set_kernel_p ( CKernel *  kernel_p)
virtualinherited

Setter for kernel for features from distribution p, SG_REFs it

Parameters
kernel_pkernel for features from p

Definition at line 130 of file KernelIndependenceTest.cpp.

void set_kernel_q ( CKernel *  kernel_q)
virtualinherited

Setter for kernel for features from distribution q, SG_REFs it

Parameters
kernel_qkernel for features from q

Definition at line 138 of file KernelIndependenceTest.cpp.

void set_null_approximation_method ( ENullApproximationMethod  null_approximation_method)
virtualinherited

sets the method how to approximate the null-distribution

Parameters
null_approximation_methodmethod to use

Definition at line 61 of file HypothesisTest.cpp.

void set_num_null_samples ( index_t  num_null_samples)
virtualinherited

sets the number of permutation iterations for sample_null()

Parameters
num_null_sampleshow often permutation shall be done

Definition at line 67 of file HypothesisTest.cpp.

void set_p ( CFeatures *  p)
virtual

Setter for features from distribution p, SG_REFs it

Parameters
pfeatures from p

Reimplemented from CIndependenceTest.

Definition at line 280 of file HSIC.cpp.

void set_q ( CFeatures *  q)
virtual

Setter for features from distribution q, SG_REFs it

Parameters
qfeatures from q

Reimplemented from CIndependenceTest.

Definition at line 286 of file HSIC.cpp.

CSGObject * shallow_copy ( ) const
virtualinherited

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.

void unset_generic ( )
inherited

unset generic type

this has to be called in classes specializing a template class

Definition at line 303 of file SGObject.cpp.

void update_parameter_hash ( )
virtualinherited

Updates the hash of current parameter combination

Definition at line 248 of file SGObject.cpp.

Member Data Documentation

SGIO* io
inherited

io

Definition at line 369 of file SGObject.h.

Parameter* m_gradient_parameters
inherited

parameters wrt which we can compute gradients

Definition at line 384 of file SGObject.h.

uint32_t m_hash
inherited

Hash of parameter values

Definition at line 387 of file SGObject.h.

CKernel* m_kernel_p
protectedinherited

underlying kernel for p

Definition at line 137 of file KernelIndependenceTest.h.

CKernel* m_kernel_q
protectedinherited

underlying kernel for q

Definition at line 140 of file KernelIndependenceTest.h.

Parameter* m_model_selection_parameters
inherited

model selection parameters

Definition at line 381 of file SGObject.h.

ENullApproximationMethod m_null_approximation_method
protectedinherited

Defines how the the null distribution is approximated

Definition at line 177 of file HypothesisTest.h.

index_t m_num_null_samples
protectedinherited

number of iterations for sampling from null-distributions

Definition at line 174 of file HypothesisTest.h.

CFeatures* m_p
protectedinherited

samples of the distribution p

Definition at line 116 of file IndependenceTest.h.

Parameter* m_parameters
inherited

parameters

Definition at line 378 of file SGObject.h.

CFeatures* m_q
protectedinherited

samples of the distribution q

Definition at line 119 of file IndependenceTest.h.

Parallel* parallel
inherited

parallel

Definition at line 372 of file SGObject.h.

Version* version
inherited

version

Definition at line 375 of file SGObject.h.

The documentation for this class was generated from the following files:
SHOGUN Machine Learning Toolbox - Documentation