Abstract base class that provides an interface for performing kernel two-sample test on streaming data using Maximum Mean Discrepancy (MMD) as the test statistic. The MMD is the distance of two probability distributions \(p\) and \(q\) in a RKHS (see [1] for formal description).
\[ \text{MMD}[\mathcal{F},p,q]^2=\textbf{E}_{x,x'}\left[ k(x,x')\right]- 2\textbf{E}_{x,y}\left[ k(x,y)\right] +\textbf{E}_{y,y'}\left[ k(y,y')\right]=||\mu_p - \mu_q||^2_\mathcal{F} \]
where \(x,x'\sim p\) and \(y,y'\sim q\). The data has to be provided as streaming features, which are processed in blocks for a given blocksize. The blocksize determines how many examples are processed at once. A method for getting a specified number of blocks of data is provided which can optionally merge and permute the data within the current burst. The exact computation of kernel functions for MMD computation is abstract and has to be defined by its subclasses, which should return a vector of function values. Please note that for streaming MMD, the number of data points from both the distributions has to be equal.
Along with the statistic comes a method to compute a p-value based on a Gaussian approximation of the null-distribution which is possible in linear time and constant space. Sampling from null is also possible (no permutations but new examples will be used here). If unsure which one to use, sampling with 250 iterations always is correct (but slow). When the sample size is large (>1000) at least, the Gaussian approximation is an accurate and much faster choice.
To choose, use set_null_approximation_method() and choose from
MMD1_GAUSSIAN: Approximates the null-distribution with a Gaussian. Only use from at least 1000 samples. If using, check if type I error equals the desired value.
PERMUTATION: For permuting available samples to sample null-distribution.
For kernel selection see CMMDKernelSelection.
[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.
在文件 StreamingMMD.h 第 86 行定义.
Public 成员函数 | |
CStreamingMMD () | |
CStreamingMMD (CKernel *kernel, CStreamingFeatures *p, CStreamingFeatures *q, index_t m, index_t blocksize=10000) | |
virtual | ~CStreamingMMD () |
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 () |
virtual float64_t | compute_threshold (float64_t alpha) |
virtual float64_t | compute_variance_estimate () |
virtual void | compute_statistic_and_variance (SGVector< float64_t > &statistic, SGVector< float64_t > &variance, bool multiple_kernels=false)=0 |
virtual void | compute_statistic_and_Q (SGVector< float64_t > &statistic, SGMatrix< float64_t > &Q)=0 |
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 const char * | get_name () const |
virtual void | set_kernel (CKernel *kernel) |
virtual CKernel * | get_kernel () |
index_t | get_m () |
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 EStatisticType | get_statistic_type () const =0 |
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="", 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 属性 | |
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 成员函数 | |
virtual SGVector< float64_t > | compute_squared_mmd (CKernel *kernel, CList *data, index_t num_this_run)=0 |
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) |
CStreamingMMD | ( | ) |
default constructor
在文件 StreamingMMD.cpp 第 40 行定义.
CStreamingMMD | ( | 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. |
在文件 StreamingMMD.cpp 第 45 行定义.
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virtual |
destructor
在文件 StreamingMMD.cpp 第 60 行定义.
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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. |
在文件 SGObject.cpp 第 1174 行定义.
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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.
在文件 SGObject.cpp 第 1291 行定义.
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 |
重载 CTwoSampleTest .
在文件 StreamingMMD.cpp 第 119 行定义.
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protectedpure virtual |
abstract method that computes the squared MMD
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 |
在 CLinearTimeMMD 内被实现.
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virtual |
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.
实现了 CKernelTwoSampleTest.
在文件 StreamingMMD.cpp 第 85 行定义.
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 |
实现了 CKernelTwoSampleTest.
在文件 StreamingMMD.cpp 第 95 行定义.
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pure 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.
在 CLinearTimeMMD 内被实现.
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pure virtual |
Abstract method that computes MMD and a linear time variance estimate. 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. |
在 CLinearTimeMMD 内被实现.
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 |
重载 CTwoSampleTest .
在文件 StreamingMMD.cpp 第 142 行定义.
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virtual |
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.
在文件 StreamingMMD.cpp 第 109 行定义.
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virtualinherited |
A deep copy. All the instance variables will also be copied.
在文件 SGObject.h 第 126 行定义.
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) |
在文件 SGObject.cpp 第 1195 行定义.
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inherited |
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inherited |
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inherited |
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virtualinherited |
在文件 KernelTwoSampleTest.h 第 84 行定义.
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inherited |
在文件 TwoSampleTest.h 第 122 行定义.
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inherited |
在文件 SGObject.cpp 第 1066 行定义.
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inherited |
Returns description of a given parameter string, if it exists. SG_ERROR otherwise
param_name | name of the parameter |
在文件 SGObject.cpp 第 1090 行定义.
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inherited |
Returns index of model selection parameter with provided index
param_name | name of model selection parameter |
在文件 SGObject.cpp 第 1103 行定义.
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virtual |
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virtual |
Not implemented for streaming MMD since it uses streaming feautres
重载 CTwoSampleTest .
在文件 StreamingMMD.cpp 第 300 行定义.
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pure virtualinherited |
returns the statistic type of this test statistic
在 CQuadraticTimeMMD, CHSIC , 以及 CLinearTimeMMD 内被实现.
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virtual |
Getter for streaming features of p distribution.
在文件 StreamingMMD.cpp 第 307 行定义.
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virtual |
Getter for streaming features of q distribution.
在文件 StreamingMMD.cpp 第 313 行定义.
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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 |
在文件 SGObject.cpp 第 234 行定义.
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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 |
在文件 SGObject.cpp 第 639 行定义.
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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 |
在文件 SGObject.cpp 第 480 行定义.
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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) |
在文件 SGObject.cpp 第 311 行定义.
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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. |
被 CWeightedDegreePositionStringKernel, CKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel , 以及 CExponentialKernel 重载.
在文件 SGObject.cpp 第 995 行定义.
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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. |
被 CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool > , 以及 CDynamicObjectArray 重载.
在文件 SGObject.cpp 第 990 行定义.
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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 |
在文件 SGObject.cpp 第 677 行定义.
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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 |
在文件 SGObject.cpp 第 884 行定义.
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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 |
在文件 SGObject.cpp 第 824 行定义.
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virtualinherited |
在文件 SGObject.cpp 第 200 行定义.
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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)
alpha | test level alpha. |
在文件 HypothesisTest.cpp 第 118 行定义.
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virtual |
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().
重载 CHypothesisTest .
在文件 StreamingMMD.cpp 第 165 行定义.
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inherited |
prints all parameter registered for model selection and their type
在文件 SGObject.cpp 第 1042 行定义.
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virtualinherited |
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.
重载 CKernelTwoSampleTest .
在文件 StreamingMMD.cpp 第 194 行定义.
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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) |
在文件 SGObject.cpp 第 252 行定义.
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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. |
被 CKernel 重载.
在文件 SGObject.cpp 第 1005 行定义.
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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. |
被 CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool > , 以及 CDynamicObjectArray 重载.
在文件 SGObject.cpp 第 1000 行定义.
void set_blocksize | ( | index_t | blocksize | ) |
Setter for the blocksize of examples to be processed at once
blocksize | new blocksize to use |
在文件 StreamingMMD.h 第 224 行定义.
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inherited |
在文件 SGObject.cpp 第 41 行定义.
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inherited |
在文件 SGObject.cpp 第 46 行定义.
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inherited |
在文件 SGObject.cpp 第 51 行定义.
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inherited |
在文件 SGObject.cpp 第 56 行定义.
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inherited |
在文件 SGObject.cpp 第 61 行定义.
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inherited |
在文件 SGObject.cpp 第 66 行定义.
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inherited |
在文件 SGObject.cpp 第 71 行定义.
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inherited |
在文件 SGObject.cpp 第 76 行定义.
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inherited |
在文件 SGObject.cpp 第 81 行定义.
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inherited |
在文件 SGObject.cpp 第 86 行定义.
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inherited |
在文件 SGObject.cpp 第 91 行定义.
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inherited |
在文件 SGObject.cpp 第 96 行定义.
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inherited |
在文件 SGObject.cpp 第 101 行定义.
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inherited |
在文件 SGObject.cpp 第 106 行定义.
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inherited |
在文件 SGObject.cpp 第 111 行定义.
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inherited |
set generic type to T
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inherited |
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inherited |
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inherited |
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virtualinherited |
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virtualinherited |
sets the method how to approximate the null-distribution
null_approximation_method | method to use |
在文件 HypothesisTest.cpp 第 59 行定义.
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virtualinherited |
sets the number of permutation iterations for sample_null()
num_null_samples | how often permutation shall be done |
在文件 HypothesisTest.cpp 第 65 行定义.
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virtual |
Not implemented for streaming MMD since it uses streaming feautres
重载 CTwoSampleTest .
在文件 StreamingMMD.cpp 第 294 行定义.
void set_simulate_h0 | ( | bool | simulate_h0 | ) |
simulate_h0 | if true, samples from p and q will be mixed and permuted |
在文件 StreamingMMD.h 第 261 行定义.
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virtualinherited |
A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.
被 CGaussianKernel 重载.
在文件 SGObject.h 第 117 行定义.
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 |
在文件 StreamingMMD.cpp 第 220 行定义.
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inherited |
unset generic type
this has to be called in classes specializing a template class
在文件 SGObject.cpp 第 241 行定义.
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virtualinherited |
Updates the hash of current parameter combination
在文件 SGObject.cpp 第 187 行定义.
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inherited |
io
在文件 SGObject.h 第 473 行定义.
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protected |
Number of examples processed at once, i.e. in one burst
在文件 StreamingMMD.h 第 294 行定义.
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inherited |
parameters wrt which we can compute gradients
在文件 SGObject.h 第 488 行定义.
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inherited |
Hash of parameter values
在文件 SGObject.h 第 494 行定义.
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protectedinherited |
underlying kernel
在文件 KernelTwoSampleTest.h 第 119 行定义.
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protectedinherited |
defines the first index of samples of q
在文件 TwoSampleTest.h 第 134 行定义.
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inherited |
model selection parameters
在文件 SGObject.h 第 485 行定义.
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protectedinherited |
Defines how the the null distribution is approximated
在文件 HypothesisTest.h 第 167 行定义.
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protectedinherited |
number of iterations for sampling from null-distributions
在文件 HypothesisTest.h 第 164 行定义.
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protectedinherited |
concatenated samples of the two distributions (two blocks)
在文件 TwoSampleTest.h 第 131 行定义.
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inherited |
map for different parameter versions
在文件 SGObject.h 第 491 行定义.
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inherited |
parameters
在文件 SGObject.h 第 482 行定义.
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protected |
If this is true, samples will be mixed between p and q in any method that computes the statistic
在文件 StreamingMMD.h 第 298 行定义.
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protected |
Streaming feature objects that are used instead of merged samples
在文件 StreamingMMD.h 第 288 行定义.
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protected |
Streaming feature objects that are used instead of merged samples
在文件 StreamingMMD.h 第 291 行定义.
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inherited |
parallel
在文件 SGObject.h 第 476 行定义.
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inherited |
version
在文件 SGObject.h 第 479 行定义.