Public Member Functions | Public Attributes | Protected Member Functions | Protected Attributes

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 $\textbf{P}_x\textbf{P}_y$, 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 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. 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 null-distribution. 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, 1-8.

Definition at line 67 of file HSIC.h.

Inheritance diagram for CHSIC:
Inheritance graph
[legend]

List of all members.

Public Member Functions

 CHSIC ()
 CHSIC (CKernel *kernel_p, CKernel *kernel_q, CFeatures *p_and_q, index_t m)
 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
SGVector< float64_t > fit_null_gamma ()
virtual SGVector< float64_t > bootstrap_null ()
virtual void set_p_and_q (CFeatures *p_and_q)
virtual float64_t perform_test ()
bool perform_test (float64_t alpha)
virtual void set_bootstrap_iterations (index_t bootstrap_iterations)
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 ()
void unset_generic ()
virtual void print_serializable (const char *prefix="")
virtual bool save_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=VERSION_PARAMETER)
virtual bool load_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=VERSION_PARAMETER)
DynArray< TParameter * > * load_file_parameters (const SGParamInfo *param_info, int32_t file_version, CSerializableFile *file, const char *prefix="")
DynArray< TParameter * > * load_all_file_parameters (int32_t file_version, int32_t current_version, CSerializableFile *file, const char *prefix="")
void map_parameters (DynArray< TParameter * > *param_base, int32_t &base_version, DynArray< const SGParamInfo * > *target_param_infos)
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_parameter_dictionary (CMap< TParameter *, CSGObject * > &dict)

Public Attributes

SGIO * io
Parallel * parallel
Version * version
Parameter * m_parameters
Parameter * m_model_selection_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)
virtual bool update_parameter_hash ()

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 & Destructor Documentation

CHSIC (  ) 

Constructor

Definition at line 18 of file HSIC.cpp.

CHSIC ( CKernel *  kernel_p,
CKernel *  kernel_q,
CFeatures *  p_and_q,
index_t  m 
)

Constructor

Parameters:
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

Definition at line 24 of file HSIC.cpp.

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

Parameters:
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

Definition at line 37 of file HSIC.cpp.

~CHSIC (  )  [virtual]

Definition at line 50 of file HSIC.cpp.

Member Function Documentation

SGVector< float64_t > bootstrap_null (  )  [virtual]

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.

Returns:
vector of all statistics

Reimplemented from CKernelIndependenceTestStatistic.

Definition at line 290 of file HSIC.cpp.

void build_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:
dict dictionary of parameters to be built.

Definition at line 1201 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:
statistic statistic value to compute the p-value for
Returns:
p-value parameter statistic is the (1-p) percentile of the null distribution

Reimplemented from CTwoDistributionsTestStatistic.

Definition at line 89 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 CTestStatistic.

Definition at line 60 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:
alpha test level to reject null-hypothesis
Returns:
threshold for statistics to reject null-hypothesis

Reimplemented from CTwoDistributionsTestStatistic.

Definition at line 111 of file HSIC.cpp.

virtual CSGObject* deep_copy (  )  const [virtual, inherited]

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

Definition at line 131 of file SGObject.h.

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 133 of file HSIC.cpp.

SGIO * get_global_io (  )  [inherited]

get the io object

Returns:
io object

Definition at line 224 of file SGObject.cpp.

Parallel * get_global_parallel (  )  [inherited]

get the parallel object

Returns:
parallel object

Definition at line 259 of file SGObject.cpp.

Version * get_global_version (  )  [inherited]

get the version object

Returns:
version object

Definition at line 272 of file SGObject.cpp.

SGMatrix< float64_t > get_kernel_matrix_K (  )  [protected]
Returns:
kernel matrix on samples from p. Distinguishes CustomKernels

Definition at line 219 of file HSIC.cpp.

SGMatrix< float64_t > get_kernel_matrix_L (  )  [protected]
Returns:
kernel matrix on samples from q. Distinguishes CustomKernels

Definition at line 254 of file HSIC.cpp.

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

Definition at line 1108 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_name name of the parameter
Returns:
description of the parameter

Definition at line 1132 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_name name of model selection parameter
Returns:
index of model selection parameter with provided name, -1 if there is no such

Definition at line 1145 of file SGObject.cpp.

virtual const char* get_name (  )  const [virtual]

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

Returns:
name of the SGSerializable

Implements CKernelIndependenceTestStatistic.

Definition at line 133 of file HSIC.h.

bool is_generic ( EPrimitiveType *  generic  )  const [virtual, inherited]

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

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

Definition at line 278 of file SGObject.cpp.

DynArray< TParameter * > * load_all_file_parameters ( int32_t  file_version,
int32_t  current_version,
CSerializableFile *  file,
const char *  prefix = "" 
) [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)

Parameters:
file_version parameter version of the file
current_version version from which mapping begins (you want to use VERSION_PARAMETER for this in most cases)
file file to load from
prefix prefix for members
Returns:
(sorted) array of created TParameter instances with file data

Definition at line 679 of file SGObject.cpp.

DynArray< TParameter * > * load_file_parameters ( const SGParamInfo *  param_info,
int32_t  file_version,
CSerializableFile *  file,
const char *  prefix = "" 
) [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

Parameters:
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
Returns:
new array with TParameter instances with the attached data

Definition at line 523 of file SGObject.cpp.

bool load_serializable ( CSerializableFile *  file,
const char *  prefix = "",
int32_t  param_version = VERSION_PARAMETER 
) [virtual, inherited]

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

Parameters:
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)
Returns:
TRUE if done, otherwise FALSE

Reimplemented in CModelSelectionParameters.

Definition at line 354 of file SGObject.cpp.

void load_serializable_post (  )  throw (ShogunException) [protected, virtual, inherited]

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:
ShogunException Will be thrown if an error occurres.

Reimplemented in CLinearHMM, CAlphabet, CANOVAKernel, CCircularKernel, CExponentialKernel, CGaussianKernel, CInverseMultiQuadricKernel, CKernel, CWeightedDegreePositionStringKernel, and CList.

Definition at line 1033 of file SGObject.cpp.

void load_serializable_pre (  )  throw (ShogunException) [protected, virtual, inherited]

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:
ShogunException Will be thrown if an error occurres.

Definition at line 1028 of file SGObject.cpp.

void map_parameters ( DynArray< TParameter * > *  param_base,
int32_t &  base_version,
DynArray< const SGParamInfo * > *  target_param_infos 
) [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

Parameters:
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 717 of file SGObject.cpp.

TParameter * migrate ( DynArray< TParameter * > *  param_base,
const SGParamInfo *  target 
) [protected, virtual, inherited]

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

Parameters:
param_base set of TParameter instances to use for migration
target parameter info for the resulting TParameter
Returns:
a new TParameter instance with migrated data from the base of the type which is specified by the target parameter

Definition at line 923 of file SGObject.cpp.

void one_to_one_migration_prepare ( DynArray< TParameter * > *  param_base,
const SGParamInfo *  target,
TParameter *&  replacement,
TParameter *&  to_migrate,
char *  old_name = NULL 
) [protected, virtual, inherited]

This method prepares everything for a one-to-one 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)

Parameters:
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 864 of file SGObject.cpp.

float64_t perform_test (  )  [virtual, inherited]

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 CLinearTimeMMD.

Definition at line 50 of file TestStatistic.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:
alpha test level alpha.
Returns:
true if null hypothesis is rejected and false otherwise

Definition at line 58 of file TestStatistic.cpp.

void print_modsel_params (  )  [inherited]

prints all parameter registered for model selection and their type

Definition at line 1084 of file SGObject.cpp.

void print_serializable ( const char *  prefix = ""  )  [virtual, inherited]

prints registered parameters out

Parameters:
prefix prefix for members

Definition at line 290 of file SGObject.cpp.

bool save_serializable ( CSerializableFile *  file,
const char *  prefix = "",
int32_t  param_version = VERSION_PARAMETER 
) [virtual, inherited]

Save this object to file.

Parameters:
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)
Returns:
TRUE if done, otherwise FALSE

Reimplemented in CModelSelectionParameters.

Definition at line 296 of file SGObject.cpp.

void save_serializable_post (  )  throw (ShogunException) [protected, virtual, inherited]

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:
ShogunException Will be thrown if an error occurres.

Reimplemented in CKernel.

Definition at line 1043 of file SGObject.cpp.

void save_serializable_pre (  )  throw (ShogunException) [protected, virtual, inherited]

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:
ShogunException Will be thrown if an error occurres.

Reimplemented in CKernel.

Definition at line 1038 of file SGObject.cpp.

void set_bootstrap_iterations ( index_t  bootstrap_iterations  )  [virtual, inherited]

sets the number of bootstrap iterations for bootstrap_null()

Parameters:
bootstrap_iterations how often bootstrapping shall be done

Definition at line 44 of file TestStatistic.cpp.

void set_generic< floatmax_t > (  )  [inherited]

set generic type to T

void set_global_io ( SGIO *  io  )  [inherited]

set the io object

Parameters:
io io object to use

Definition at line 217 of file SGObject.cpp.

void set_global_parallel ( Parallel *  parallel  )  [inherited]

set the parallel object

Parameters:
parallel parallel object to use

Definition at line 230 of file SGObject.cpp.

void set_global_version ( Version *  version  )  [inherited]

set the version object

Parameters:
version version object to use

Definition at line 265 of file SGObject.cpp.

void set_null_approximation_method ( ENullApproximationMethod  null_approximation_method  )  [virtual, inherited]

sets the method how to approximate the null-distribution

Parameters:
null_approximation_method method to use

Definition at line 38 of file TestStatistic.cpp.

void set_p_and_q ( CFeatures *  p_and_q  )  [virtual, inherited]

Setter for joint features

Parameters:
p_and_q joint features from p and q to set

Definition at line 144 of file TwoDistributionsTestStatistic.cpp.

virtual CSGObject* shallow_copy (  )  const [virtual, inherited]

A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.

Reimplemented in CGaussianKernel.

Definition at line 122 of file SGObject.h.

void unset_generic (  )  [inherited]

unset generic type

this has to be called in classes specializing a template class

Definition at line 285 of file SGObject.cpp.

bool update_parameter_hash (  )  [protected, virtual, inherited]

Updates the hash of current parameter combination.

Returns:
bool if parameter combination has changed since last update.

Definition at line 237 of file SGObject.cpp.

Member Data Documentation

SGIO* io [inherited]

io

Definition at line 462 of file SGObject.h.

index_t m_bootstrap_iterations [protected, inherited]

number of iterations for bootstrapping null-distributions

Definition at line 129 of file TestStatistic.h.

uint32_t m_hash [inherited]

Hash of parameter values

Definition at line 480 of file SGObject.h.

CKernel* m_kernel_p [protected, inherited]

underlying kernel for p

Definition at line 88 of file KernelIndependenceTestStatistic.h.

CKernel* m_kernel_q [protected, inherited]

underlying kernel for q

Definition at line 91 of file KernelIndependenceTestStatistic.h.

index_t m_m [protected, inherited]

defines the first index of samples of q

Definition at line 102 of file TwoDistributionsTestStatistic.h.

Parameter* m_model_selection_parameters [inherited]

model selection parameters

Definition at line 474 of file SGObject.h.

ENullApproximationMethod m_null_approximation_method [protected, inherited]

Defines how the the null distribution is approximated

Definition at line 132 of file TestStatistic.h.

CFeatures* m_p_and_q [protected, inherited]

concatenated samples of the two distributions (two blocks)

Definition at line 99 of file TwoDistributionsTestStatistic.h.

ParameterMap* m_parameter_map [inherited]

map for different parameter versions

Definition at line 477 of file SGObject.h.

Parameter* m_parameters [inherited]

parameters

Definition at line 471 of file SGObject.h.

Parallel* parallel [inherited]

parallel

Definition at line 465 of file SGObject.h.

Version* version [inherited]

version

Definition at line 468 of file SGObject.h.

The documentation for this class was generated from the following files:
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Defines
SHOGUN Machine Learning Toolbox - Documentation