SHOGUN
v2.0.0
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This class implements the Hilbert Schmidtd Independence Criterion based independence test as described in [1].
Given samples from the joint distribution , does the joint distribution factorize as ?
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:
where is a centering matrix and 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.
Public Member Functions | |
CHSIC () | |
CHSIC (CKernel *kernel_p, CKernel *kernel_q, CFeatures *p_and_q, index_t q_start) | |
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_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_q_start |
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 q_start 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 |
q_start | 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.
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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 1204 of file SGObject.cpp.
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.
statistic | statistic value to compute the p-value for |
Reimplemented from CTwoDistributionsTestStatistic.
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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 null-distribution. The threshold is the value that a statistic has to have in ordner to reject the null-hypothesis.
alpha | test level to reject null-hypothesis |
Reimplemented from CTwoDistributionsTestStatistic.
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virtualinherited |
A deep copy. All the instance variables will also be copied.
Definition at line 131 of file SGObject.h.
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.
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Definition at line 1108 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 1132 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 1145 of file SGObject.cpp.
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Returns the name of the SGSerializable instance. It MUST BE the CLASS NAME without the prefixed `C'.
Implements CKernelIndependenceTestStatistic.
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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 278 of file SGObject.cpp.
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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_PARAMETER for this in most cases) |
file | file to load from |
prefix | prefix for members |
Definition at line 679 of file SGObject.cpp.
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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 523 of file SGObject.cpp.
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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) |
Reimplemented in CModelSelectionParameters.
Definition at line 354 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 occurres. |
Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CANOVAKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.
Definition at line 1033 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 occurres. |
Definition at line 1028 of file SGObject.cpp.
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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 717 of file SGObject.cpp.
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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 923 of file SGObject.cpp.
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protectedvirtualinherited |
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)
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.
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prints all parameter registered for model selection and their type
Definition at line 1084 of file SGObject.cpp.
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prints registered parameters out
prefix | prefix for members |
Definition at line 290 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 |
param_version | (optional) a parameter version different to (this is mainly for testing, better do not use) |
Reimplemented in CModelSelectionParameters.
Definition at line 296 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::SAVE_SERIALIZABLE_POST is called.
ShogunException | Will be thrown if an error occurres. |
Reimplemented in CKernel.
Definition at line 1043 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 occurres. |
Reimplemented in CKernel.
Definition at line 1038 of file SGObject.cpp.
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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.
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set generic type to T
Definition at line 41 of file SGObject.cpp.
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set the parallel object
parallel | parallel object to use |
Definition at line 230 of file SGObject.cpp.
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set the version object
version | version object to use |
Definition at line 265 of file SGObject.cpp.
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sets the method how to approximate the null-distribution
null_approximation_method | method to use |
Definition at line 38 of file TestStatistic.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 122 of file SGObject.h.
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unset generic type
this has to be called in classes specializing a template class
Definition at line 285 of file SGObject.cpp.
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Updates the hash of current parameter combination.
Definition at line 237 of file SGObject.cpp.
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io
Definition at line 462 of file SGObject.h.
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number of iterations for bootstrapping null-distributions
Definition at line 98 of file TestStatistic.h.
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Hash of parameter values
Definition at line 480 of file SGObject.h.
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underlying kernel for p
Definition at line 88 of file KernelIndependenceTestStatistic.h.
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underlying kernel for q
Definition at line 91 of file KernelIndependenceTestStatistic.h.
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model selection parameters
Definition at line 474 of file SGObject.h.
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Defines how the the null distribution is approximated
Definition at line 101 of file TestStatistic.h.
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concatenated samples of the two distributions (two blocks)
Definition at line 94 of file TwoDistributionsTestStatistic.h.
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map for different parameter versions
Definition at line 477 of file SGObject.h.
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parameters
Definition at line 471 of file SGObject.h.
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defines the first index of samples of q
Definition at line 97 of file TwoDistributionsTestStatistic.h.
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parallel
Definition at line 465 of file SGObject.h.
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version
Definition at line 468 of file SGObject.h.