SHOGUN
v3.0.0
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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.
Definition at line 75 of file LinearTimeMMD.h.
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 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 | ( | ) |
Definition at line 22 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 | 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. |
Definition at line 28 of file LinearTimeMMD.cpp.
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Definition at line 43 of file LinearTimeMMD.cpp.
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.
Reimplemented from CKernelTwoSampleTestStatistic.
Definition at line 683 of file LinearTimeMMD.cpp.
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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 1196 of file SGObject.cpp.
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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 1313 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 CTwoDistributionsTestStatistic.
Definition at line 608 of file LinearTimeMMD.cpp.
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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.
Implements CKernelTwoSampleTestStatistic.
Definition at line 573 of file LinearTimeMMD.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 CKernelTwoSampleTestStatistic.
Definition at line 583 of file LinearTimeMMD.cpp.
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Same as compute_statistic_and_variance, but computes a linear time estimate of the covariance of the multiple-kernel-MMD. See [1] for details.
Definition at line 274 of file LinearTimeMMD.cpp.
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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. |
Definition at line 68 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 CTwoDistributionsTestStatistic.
Definition at line 631 of file LinearTimeMMD.cpp.
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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.
Definition at line 598 of file LinearTimeMMD.cpp.
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A deep copy. All the instance variables will also be copied.
Definition at line 160 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) |
Definition at line 1217 of file SGObject.cpp.
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virtualinherited |
Definition at line 80 of file KernelTwoSampleTestStatistic.h.
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Definition at line 98 of file TwoDistributionsTestStatistic.h.
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Definition at line 1100 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 1124 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 1137 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 CKernelTwoSampleTestStatistic.
Definition at line 242 of file LinearTimeMMD.h.
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Not implemented for linear time MMD since it uses streaming feautres
Reimplemented from CTwoDistributionsTestStatistic.
Definition at line 715 of file LinearTimeMMD.cpp.
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returns the statistic type of this test statistic
Implements CTestStatistic.
Definition at line 231 of file LinearTimeMMD.h.
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Getter for streaming features of p distribution.
Definition at line 722 of file LinearTimeMMD.cpp.
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Getter for streaming features of q distribution.
Definition at line 728 of file LinearTimeMMD.cpp.
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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 268 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::get_version_parameter() for this in most cases) |
file | file to load from |
prefix | prefix for members |
Definition at line 673 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 514 of file SGObject.cpp.
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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 345 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, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.
Definition at line 1029 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 >, CDynamicArray< uint64_t >, and CDynamicObjectArray.
Definition at line 1024 of file SGObject.cpp.
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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 711 of file SGObject.cpp.
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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 918 of file SGObject.cpp.
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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 858 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 58 of file TestStatistic.cpp.
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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().
Reimplemented from CTestStatistic.
Definition at line 654 of file LinearTimeMMD.cpp.
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prints all parameter registered for model selection and their type
Definition at line 1076 of file SGObject.cpp.
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prints registered parameters out
prefix | prefix for members |
Definition at line 280 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) |
Definition at line 286 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 1039 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 >, CDynamicArray< uint64_t >, and CDynamicObjectArray.
Definition at line 1034 of file SGObject.cpp.
void set_blocksize | ( | index_t | blocksize | ) |
Setter for the blocksize of examples to be processed at once
blocksize | new blocksize to use |
Definition at line 212 of file LinearTimeMMD.h.
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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 220 of file SGObject.cpp.
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set the version object
version | version object to use |
Definition at line 255 of file SGObject.cpp.
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Setter for the underlying kernel
kernel | new kernel to use |
Definition at line 71 of file KernelTwoSampleTestStatistic.h.
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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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Not implemented for linear time MMD since it uses streaming feautres
Reimplemented from CTwoDistributionsTestStatistic.
Definition at line 709 of file LinearTimeMMD.cpp.
void set_simulate_h0 | ( | bool | simulate_h0 | ) |
simulate_h0 | if true, samples from p and q will be mixed and permuted |
Definition at line 239 of file LinearTimeMMD.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 151 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 275 of file SGObject.cpp.
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Updates the hash of current parameter combination.
Definition at line 227 of file SGObject.cpp.
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io
Definition at line 514 of file SGObject.h.
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Number of examples processed at once, i.e. in one burst
Definition at line 258 of file LinearTimeMMD.h.
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number of iterations for bootstrapping null-distributions
Definition at line 138 of file TestStatistic.h.
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parameters wrt which we can compute gradients
Definition at line 529 of file SGObject.h.
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Hash of parameter values
Definition at line 535 of file SGObject.h.
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underlying kernel
Definition at line 115 of file KernelTwoSampleTestStatistic.h.
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defines the first index of samples of q
Definition at line 110 of file TwoDistributionsTestStatistic.h.
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model selection parameters
Definition at line 526 of file SGObject.h.
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Defines how the the null distribution is approximated
Definition at line 141 of file TestStatistic.h.
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concatenated samples of the two distributions (two blocks)
Definition at line 107 of file TwoDistributionsTestStatistic.h.
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map for different parameter versions
Definition at line 532 of file SGObject.h.
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parameters
Definition at line 523 of file SGObject.h.
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If this is true, samples will be mixed between p and q ind any method that computes the statistic
Definition at line 262 of file LinearTimeMMD.h.
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Streaming feature objects that are used instead of merged samples
Definition at line 252 of file LinearTimeMMD.h.
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Streaming feature objects that are used instead of merged samples
Definition at line 255 of file LinearTimeMMD.h.
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parallel
Definition at line 517 of file SGObject.h.
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version
Definition at line 520 of file SGObject.h.