This class implements the linear time Maximum Mean Statistic as described in [1]. This statistic is in particular suitable for streaming data. Therefore, only streaming features may be passed. To process other feature types, construct streaming features from these (see constructor documentations). A blocksize has to be specified that determines how many examples are processed at once. This should be set as large as available memory allows to ensure faster computations.
The MMD is the distance of two probability distributions \(p\) and \(q\) in a RKHS.
\[ \text{MMD}}[\mathcal{F},p,q]^2=\textbf{E}_{x,x'}\left[ k(x,x')\right]- 2\textbf{E}_{x,y}\left[ k(x,y)\right] +\textbf{E}_{y,y'}\left[ k(y,y')\right]=||\mu_p - \mu_q||^2_\mathcal{F} \]
Given two sets of samples \(\{x_i\}_{i=1}^m\sim p\) and \(\{y_i\}_{i=1}^n\sim q\) 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 \( m_2=\lfloor\frac{m}{2} \rfloor\).
Along with the statistic comes a method to compute a p-value based on a Gaussian approximation of the null-distribution which is also possible in linear time and constant space. Bootstrapping, is also possible (no permutations but new examples will be used here). If unsure which one to use, bootstrapping 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 than bootstrapping.
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.
BOOTSTRAPPING: 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 LinearTimeMMD.h 第 75 行定义.
Public 成员函数 | |
CLinearTimeMMD () | |
CLinearTimeMMD (CKernel *kernel, CStreamingFeatures *p, CStreamingFeatures *q, index_t m, index_t blocksize=10000) | |
virtual | ~CLinearTimeMMD () |
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) |
virtual void | compute_statistic_and_Q (SGVector< float64_t > &statistic, SGMatrix< float64_t > &Q) |
virtual SGVector< float64_t > | bootstrap_null () |
void | set_blocksize (index_t blocksize) |
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 () |
virtual EStatisticType | get_statistic_type () const |
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_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 () |
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 bool | update_parameter_hash () |
virtual bool | equals (CSGObject *other, float64_t accuracy=0.0) |
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 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 | ( | ) |
在文件 LinearTimeMMD.cpp 第 22 行定义.
CLinearTimeMMD | ( | CKernel * | kernel, |
CStreamingFeatures * | p, | ||
CStreamingFeatures * | q, | ||
index_t | m, | ||
index_t | blocksize = 10000 |
||
) |
Constructor.
kernel | kernel to use |
p | streaming features p to use |
q | streaming features q to use |
m | index of first sample of q |
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. |
在文件 LinearTimeMMD.cpp 第 28 行定义.
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virtual |
在文件 LinearTimeMMD.cpp 第 43 行定义.
Mimics bootstrapping for the linear time 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 CKernelTwoSampleTestStatistic .
在文件 LinearTimeMMD.cpp 第 683 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 1156 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 1273 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 CTwoDistributionsTestStatistic .
在文件 LinearTimeMMD.cpp 第 608 行定义.
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virtual |
Computes the squared linear time MMD for the current data. This is an unbiased estimate.
Note that the underlying streaming feature parser has to be started before this is called. Otherwise deadlock.
实现了 CKernelTwoSampleTestStatistic.
在文件 LinearTimeMMD.cpp 第 573 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 CKernelTwoSampleTestStatistic.
在文件 LinearTimeMMD.cpp 第 583 行定义.
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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.
在文件 LinearTimeMMD.cpp 第 274 行定义.
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virtual |
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. |
在文件 LinearTimeMMD.cpp 第 68 行定义.
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 CTwoDistributionsTestStatistic .
在文件 LinearTimeMMD.cpp 第 631 行定义.
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virtual |
computes a linear time estimate of the variance of the squared linear time mmd, which may be used for an approximation of the null-distribution The value is the variance of the vector of which the linear time MMD is the mean.
在文件 LinearTimeMMD.cpp 第 598 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) |
在文件 SGObject.cpp 第 1177 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 KernelTwoSampleTestStatistic.h 第 80 行定义.
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inherited |
在文件 TwoDistributionsTestStatistic.h 第 98 行定义.
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inherited |
在文件 SGObject.cpp 第 1060 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 1084 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 1097 行定义.
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virtual |
Returns the name of the SGSerializable instance. It MUST BE the CLASS NAME without the prefixed `C'.
实现了 CKernelTwoSampleTestStatistic.
在文件 LinearTimeMMD.h 第 242 行定义.
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virtual |
Not implemented for linear time MMD since it uses streaming feautres
重载 CTwoDistributionsTestStatistic .
在文件 LinearTimeMMD.cpp 第 715 行定义.
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virtual |
returns the statistic type of this test statistic
实现了 CTestStatistic.
在文件 LinearTimeMMD.h 第 231 行定义.
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virtual |
Getter for streaming features of p distribution.
在文件 LinearTimeMMD.cpp 第 722 行定义.
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virtual |
Getter for streaming features of q distribution.
在文件 LinearTimeMMD.cpp 第 728 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 228 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 633 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 474 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 305 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 989 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 984 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 671 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 878 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 818 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 TestStatistic.cpp 第 58 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 bootstrapping, superclass method is called.
The method for computing the p-value can be set via set_null_approximation_method().
重载 CTestStatistic .
在文件 LinearTimeMMD.cpp 第 654 行定义.
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inherited |
prints all parameter registered for model selection and their type
在文件 SGObject.cpp 第 1036 行定义.
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virtualinherited |
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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 246 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 999 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 994 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 LinearTimeMMD.h 第 212 行定义.
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virtualinherited |
sets the number of bootstrap iterations for bootstrap_null()
bootstrap_iterations | how often bootstrapping shall be done |
在文件 TestStatistic.cpp 第 44 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 |
Setter for the underlying kernel
kernel | new kernel to use |
在文件 KernelTwoSampleTestStatistic.h 第 71 行定义.
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virtualinherited |
sets the method how to approximate the null-distribution
null_approximation_method | method to use |
在文件 TestStatistic.cpp 第 38 行定义.
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virtual |
Not implemented for linear time MMD since it uses streaming feautres
重载 CTwoDistributionsTestStatistic .
在文件 LinearTimeMMD.cpp 第 709 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 LinearTimeMMD.h 第 239 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.
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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 235 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 LinearTimeMMD.h 第 258 行定义.
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protectedinherited |
number of iterations for bootstrapping null-distributions
在文件 TestStatistic.h 第 138 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 KernelTwoSampleTestStatistic.h 第 115 行定义.
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protectedinherited |
defines the first index of samples of q
在文件 TwoDistributionsTestStatistic.h 第 110 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 TestStatistic.h 第 141 行定义.
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protectedinherited |
concatenated samples of the two distributions (two blocks)
在文件 TwoDistributionsTestStatistic.h 第 107 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 ind any method that computes the statistic
在文件 LinearTimeMMD.h 第 262 行定义.
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protected |
Streaming feature objects that are used instead of merged samples
在文件 LinearTimeMMD.h 第 252 行定义.
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protected |
Streaming feature objects that are used instead of merged samples
在文件 LinearTimeMMD.h 第 255 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.