SHOGUN
3.2.1
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This class implements the linear time Maximum Mean Statistic as described in [1] for streaming data (see CStreamingMMD for description).
Given two sets of samples \(\{x_i\}_{i=1}^m\sim p\) and \(\{y_i\}_{i=1}^m\sim q\) the (unbiased) statistic is computed as
\[ \text{MMD}_l^2[\mathcal{F},X,Y]=\frac{1}{m_2}\sum_{i=1}^{m_2} h(z_{2i},z_{2i+1}) \]
where
\[ h(z_{2i},z_{2i+1})=k(x_{2i},x_{2i+1})+k(y_{2i},y_{2i+1})-k(x_{2i},y_{2i+1})- k(x_{2i+1},y_{2i}) \]
and \( m_2=\lfloor\frac{m}{2} \rfloor\).
[1]: Gretton, A., Borgwardt, K. M., Rasch, M. J., Schoelkopf, B., & Smola, A. (2012). A Kernel Two-Sample Test. Journal of Machine Learning Research, 13, 671-721.
Definition at line 64 of file LinearTimeMMD.h.
Public Member Functions | |
CLinearTimeMMD () | |
CLinearTimeMMD (CKernel *kernel, CStreamingFeatures *p, CStreamingFeatures *q, index_t m, index_t blocksize=10000) | |
virtual | ~CLinearTimeMMD () |
virtual void | compute_statistic_and_variance (SGVector< float64_t > &statistic, SGVector< float64_t > &variance, bool multiple_kernels=false) |
virtual void | compute_statistic_and_Q (SGVector< float64_t > &statistic, SGMatrix< float64_t > &Q) |
virtual EStatisticType | get_statistic_type () const |
virtual const char * | get_name () const |
virtual float64_t | compute_statistic () |
virtual SGVector< float64_t > | compute_statistic (bool multiple_kernels) |
virtual float64_t | compute_p_value (float64_t statistic) |
virtual float64_t | perform_test () |
bool | perform_test (float64_t alpha) |
virtual float64_t | compute_threshold (float64_t alpha) |
virtual float64_t | compute_variance_estimate () |
virtual SGVector< float64_t > | sample_null () |
void | set_blocksize (index_t blocksize) |
CList * | stream_data_blocks (index_t num_blocks, index_t num_this_run) |
virtual void | set_p_and_q (CFeatures *p_and_q) |
virtual CFeatures * | get_p_and_q () |
virtual CStreamingFeatures * | get_streaming_p () |
virtual CStreamingFeatures * | get_streaming_q () |
void | set_simulate_h0 (bool simulate_h0) |
virtual void | set_kernel (CKernel *kernel) |
virtual CKernel * | get_kernel () |
index_t | get_m () |
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 () |
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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::get_version_parameter()) |
virtual bool | load_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=Version::get_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_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 |
ParameterMap * | m_parameter_map |
uint32_t | m_hash |
Protected Member Functions | |
virtual SGVector< float64_t > | compute_squared_mmd (CKernel *kernel, CList *data, index_t num_this_run) |
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) |
CLinearTimeMMD | ( | ) |
default constructor
Definition at line 44 of file LinearTimeMMD.cpp.
CLinearTimeMMD | ( | CKernel * | kernel, |
CStreamingFeatures * | p, | ||
CStreamingFeatures * | q, | ||
index_t | m, | ||
index_t | blocksize = 10000 |
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) |
Constructor.
kernel | kernel to use |
p | streaming features p to use |
q | streaming features q to use |
m | number of samples from each distribution |
blocksize | size of examples that are processed at once when computing statistic/threshold. If larger than m/2, all examples will be processed at once. Memory consumption increased linearly in the blocksize. Choose as large as possible regarding available memory. |
Definition at line 48 of file LinearTimeMMD.cpp.
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virtual |
destructor
Definition at line 54 of file LinearTimeMMD.cpp.
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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 1174 of file SGObject.cpp.
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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 1291 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.
The method for computing the p-value can be set via set_null_approximation_method(). Since the null- distribution is normal, a Gaussian approximation is available.
statistic | statistic value to compute the p-value for |
Reimplemented from CTwoSampleTest.
Definition at line 119 of file StreamingMMD.cpp.
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protectedvirtual |
method that computes the squared MMD in linear time (see class description for the equation)
kernel | the kernel to be used for computing MMD. This will be useful when multiple kernels are used |
data | the list of data on which kernels are computed. The order of data in the list is \(x,x',\cdots\sim p\) followed by \(y,y',\cdots\sim q\). It is assumed that detele_data flag is set inside the list |
num_this_run | number of data points in current blocks |
Implements CStreamingMMD.
Definition at line 103 of file LinearTimeMMD.cpp.
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virtualinherited |
Computes the squared MMD for the current data. This is an unbiased estimate. This method relies on compute_statistic_and_variance which has to be defined in the subclasses
Note that the underlying streaming feature parser has to be started before this is called. Otherwise deadlock.
Implements CKernelTwoSampleTest.
Definition at line 85 of file StreamingMMD.cpp.
Same as compute_statistic(), but with the possibility to perform on multiple kernels at once
multiple_kernels | if true, and underlying kernel is K_COMBINED, method will be executed on all subkernels on the same data |
Implements CKernelTwoSampleTest.
Definition at line 95 of file StreamingMMD.cpp.
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virtual |
Same as compute_statistic_and_variance, but computes a linear time estimate of the covariance of the multiple-kernel-MMD. See [1] for details.
Implements CStreamingMMD.
Definition at line 250 of file LinearTimeMMD.cpp.
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virtual |
Computes squared MMD and a variance estimate, in linear time. If multiple_kernels is set to true, each subkernel is evaluated on the same data.
statistic | return parameter for statistic, vector with entry for each kernel. May be allocated before but doesn not have to be |
variance | return parameter for statistic, vector with entry for each kernel. May be allocated before but doesn not have to be |
multiple_kernels | optional flag, if set to true, it is assumed that the underlying kernel is of type K_COMBINED. Then, the MMD is computed on all subkernel separately rather than computing it on the combination. This is used by kernel selection strategies that need to evaluate multiple kernels on the same data. Since the linear time MMD works on streaming data, one cannot simply compute MMD, change kernel since data would be different for every kernel. |
Implements CStreamingMMD.
Definition at line 116 of file LinearTimeMMD.cpp.
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.
The method for computing the p-value can be set via set_null_approximation_method(). Since the null- distribution is normal, a Gaussian approximation is available.
alpha | test level to reject null-hypothesis |
Reimplemented from CTwoSampleTest.
Definition at line 142 of file StreamingMMD.cpp.
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virtualinherited |
computes a linear time estimate of the variance of the squared mmd, which may be used for an approximation of the null-distribution The value is the variance of the vector of which the MMD is the mean.
Definition at line 109 of file StreamingMMD.cpp.
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virtualinherited |
A deep copy. All the instance variables will also be copied.
Definition at line 126 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) |
tolerant | allows linient check on float equality (within accuracy) |
Definition at line 1195 of file SGObject.cpp.
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virtualinherited |
Definition at line 84 of file KernelTwoSampleTest.h.
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inherited |
Definition at line 122 of file TwoSampleTest.h.
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Definition at line 1066 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 1090 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 1103 of file SGObject.cpp.
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virtual |
Reimplemented from CStreamingMMD.
Definition at line 122 of file LinearTimeMMD.h.
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virtualinherited |
Not implemented for streaming MMD since it uses streaming feautres
Reimplemented from CTwoSampleTest.
Definition at line 300 of file StreamingMMD.cpp.
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returns the statistic type of this test statistic
Implements CHypothesisTest.
Definition at line 116 of file LinearTimeMMD.h.
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virtualinherited |
Getter for streaming features of p distribution.
Definition at line 307 of file StreamingMMD.cpp.
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virtualinherited |
Getter for streaming features of q distribution.
Definition at line 313 of file StreamingMMD.cpp.
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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 234 of file SGObject.cpp.
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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 639 of file SGObject.cpp.
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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 480 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) |
Definition at line 311 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 CWeightedDegreePositionStringKernel, CKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.
Definition at line 995 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. |
Reimplemented in CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 990 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 677 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 884 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 824 of file SGObject.cpp.
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Definition at line 200 of file SGObject.cpp.
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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)
alpha | test level alpha. |
Definition at line 118 of file HypothesisTest.cpp.
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virtualinherited |
Performs the complete two-sample test on current data and returns a p-value.
In case null distribution should be estimated with MMD1_GAUSSIAN, statistic and p-value are computed in the same loop, which is more efficient than first computing statistic and then computung p-values.
In case of sampling null, superclass method is called.
The method for computing the p-value can be set via set_null_approximation_method().
Reimplemented from CHypothesisTest.
Definition at line 165 of file StreamingMMD.cpp.
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prints all parameter registered for model selection and their type
Definition at line 1042 of file SGObject.cpp.
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virtualinherited |
prints registered parameters out
prefix | prefix for members |
Definition at line 246 of file SGObject.cpp.
Mimics sampling null for MMD. However, samples are not permutated but constantly streamed and then merged. Usually, this is not necessary since there is the Gaussian approximation for the null distribution. However, in certain cases this may fail and sampling the null distribution might be numerically more stable. Ovewrite superclass method that merges samples.
Reimplemented from CKernelTwoSampleTest.
Definition at line 194 of file StreamingMMD.cpp.
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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 252 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 1005 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, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 1000 of file SGObject.cpp.
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Setter for the blocksize of examples to be processed at once
blocksize | new blocksize to use |
Definition at line 224 of file StreamingMMD.h.
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Definition at line 41 of file SGObject.cpp.
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Definition at line 46 of file SGObject.cpp.
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Definition at line 51 of file SGObject.cpp.
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Definition at line 56 of file SGObject.cpp.
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Definition at line 61 of file SGObject.cpp.
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Definition at line 66 of file SGObject.cpp.
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Definition at line 71 of file SGObject.cpp.
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Definition at line 76 of file SGObject.cpp.
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Definition at line 81 of file SGObject.cpp.
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Definition at line 86 of file SGObject.cpp.
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Definition at line 91 of file SGObject.cpp.
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Definition at line 96 of file SGObject.cpp.
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Definition at line 101 of file SGObject.cpp.
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Definition at line 106 of file SGObject.cpp.
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Definition at line 111 of file SGObject.cpp.
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set generic type to T
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set the parallel object
parallel | parallel object to use |
Definition at line 180 of file SGObject.cpp.
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set the version object
version | version object to use |
Definition at line 221 of file SGObject.cpp.
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Setter for the underlying kernel
kernel | new kernel to use |
Definition at line 75 of file KernelTwoSampleTest.h.
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sets the method how to approximate the null-distribution
null_approximation_method | method to use |
Definition at line 59 of file HypothesisTest.cpp.
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sets the number of permutation iterations for sample_null()
num_null_samples | how often permutation shall be done |
Definition at line 65 of file HypothesisTest.cpp.
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virtualinherited |
Not implemented for streaming MMD since it uses streaming feautres
Reimplemented from CTwoSampleTest.
Definition at line 294 of file StreamingMMD.cpp.
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simulate_h0 | if true, samples from p and q will be mixed and permuted |
Definition at line 261 of file StreamingMMD.h.
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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 117 of file SGObject.h.
Streams num_blocks data from each distribution with blocks of size num_this_run. If m_simulate_h0 is set, it merges the blocks together, shuffles and redistributes between the blocks.
num_blocks | number of blocks to be streamed from each distribution |
num_this_run | number of data points to be streamed for one block |
Definition at line 220 of file StreamingMMD.cpp.
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unset generic type
this has to be called in classes specializing a template class
Definition at line 241 of file SGObject.cpp.
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Updates the hash of current parameter combination
Definition at line 187 of file SGObject.cpp.
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io
Definition at line 473 of file SGObject.h.
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Number of examples processed at once, i.e. in one burst
Definition at line 294 of file StreamingMMD.h.
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parameters wrt which we can compute gradients
Definition at line 488 of file SGObject.h.
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Hash of parameter values
Definition at line 494 of file SGObject.h.
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underlying kernel
Definition at line 119 of file KernelTwoSampleTest.h.
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defines the first index of samples of q
Definition at line 134 of file TwoSampleTest.h.
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model selection parameters
Definition at line 485 of file SGObject.h.
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Defines how the the null distribution is approximated
Definition at line 167 of file HypothesisTest.h.
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number of iterations for sampling from null-distributions
Definition at line 164 of file HypothesisTest.h.
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concatenated samples of the two distributions (two blocks)
Definition at line 131 of file TwoSampleTest.h.
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map for different parameter versions
Definition at line 491 of file SGObject.h.
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parameters
Definition at line 482 of file SGObject.h.
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If this is true, samples will be mixed between p and q in any method that computes the statistic
Definition at line 298 of file StreamingMMD.h.
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Streaming feature objects that are used instead of merged samples
Definition at line 288 of file StreamingMMD.h.
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protectedinherited |
Streaming feature objects that are used instead of merged samples
Definition at line 291 of file StreamingMMD.h.
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parallel
Definition at line 476 of file SGObject.h.
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version
Definition at line 479 of file SGObject.h.