SHOGUN  4.1.0
CLinearTimeMMD Class Reference

## Detailed Description

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 66 of file LinearTimeMMD.h.

Inheritance diagram for CLinearTimeMMD:
[legend]

## 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_tcompute_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_tsample_null ()

void set_blocksize (index_t blocksize)

CListstream_data_blocks (index_t num_blocks, index_t num_this_run)

virtual void set_p_and_q (CFeatures *p_and_q)

virtual CFeaturesget_p_and_q ()

virtual CStreamingFeaturesget_streaming_p ()

virtual CStreamingFeaturesget_streaming_q ()

void set_simulate_h0 (bool simulate_h0)

virtual void set_kernel (CKernel *kernel)

virtual CKernelget_kernel ()

void set_m (index_t m)

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 CSGObjectshallow_copy () const

virtual CSGObjectdeep_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="")

virtual bool load_serializable (CSerializableFile *file, const char *prefix="")

void set_global_io (SGIO *io)

SGIOget_global_io ()

void set_global_parallel (Parallel *parallel)

Parallelget_global_parallel ()

void set_global_version (Version *version)

Versionget_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 CSGObjectclone ()

## Public Attributes

SGIOio

Parallelparallel

Versionversion

Parameterm_parameters

Parameterm_model_selection_parameters

uint32_t m_hash

## Protected Member Functions

virtual SGVector< float64_tcompute_squared_mmd (CKernel *kernel, CList *data, index_t num_this_run)

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)

## Protected Attributes

CStreamingFeaturesm_streaming_p

CStreamingFeaturesm_streaming_q

index_t m_blocksize

bool m_simulate_h0

CKernelm_kernel

CFeaturesm_p_and_q

index_t m_m

index_t m_num_null_samples

ENullApproximationMethod m_null_approximation_method

## Constructor & Destructor Documentation

 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 )

Constructor.

Parameters
 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.

 ~CLinearTimeMMD ( )
virtual

destructor

Definition at line 54 of file LinearTimeMMD.cpp.

## Member Function Documentation

 void build_gradient_parameter_dictionary ( CMap< TParameter *, CSGObject * > * dict )
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.

Parameters
 dict dictionary of parameters to be built.

Definition at line 597 of file SGObject.cpp.

 CSGObject * clone ( )
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.

Returns
an identical copy of the given object, which is disjoint in memory. NULL if the clone fails. Note that the returned object is SG_REF'ed

Definition at line 714 of file SGObject.cpp.

 float64_t compute_p_value ( float64_t statistic )
virtualinherited

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.

Parameters
 statistic statistic value to compute the p-value for
Returns
p-value parameter statistic is the (1-p) percentile of the null distribution

Reimplemented from CTwoSampleTest.

Definition at line 119 of file StreamingMMD.cpp.

 SGVector< float64_t > compute_squared_mmd ( CKernel * kernel, CList * data, index_t num_this_run )
protectedvirtual

method that computes the squared MMD in linear time (see class description for the equation)

Parameters
 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
Returns
the MMD values (the h-vectors)

Implements CStreamingMMD.

Definition at line 103 of file LinearTimeMMD.cpp.

 float64_t compute_statistic ( )
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.

Returns
squared MMD

Implements CKernelTwoSampleTest.

Definition at line 85 of file StreamingMMD.cpp.

 SGVector< float64_t > compute_statistic ( bool multiple_kernels )
virtualinherited

Same as compute_statistic(), but with the possibility to perform on multiple kernels at once

Parameters
 multiple_kernels if true, and underlying kernel is K_COMBINED, method will be executed on all subkernels on the same data
Returns
vector of results for subkernels

Implements CKernelTwoSampleTest.

Definition at line 95 of file StreamingMMD.cpp.

 void compute_statistic_and_Q ( SGVector< float64_t > & statistic, SGMatrix< float64_t > & Q )
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.

 void compute_statistic_and_variance ( SGVector< float64_t > & statistic, SGVector< float64_t > & variance, bool multiple_kernels = false )
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.

Parameters
 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.

 float64_t compute_threshold ( float64_t alpha )
virtualinherited

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.

Parameters
 alpha test level to reject null-hypothesis
Returns
threshold for statistics to reject null-hypothesis

Reimplemented from CTwoSampleTest.

Definition at line 142 of file StreamingMMD.cpp.

 float64_t compute_variance_estimate ( )
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.

Returns
variance estimate

Definition at line 109 of file StreamingMMD.cpp.

 CSGObject * deep_copy ( ) const
virtualinherited

A deep copy. All the instance variables will also be copied.

Definition at line 198 of file SGObject.cpp.

 bool equals ( CSGObject * other, float64_t accuracy = 0.0, bool tolerant = false )
virtualinherited

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.

Parameters
 other object to compare with accuracy accuracy to use for comparison (optional) tolerant allows linient check on float equality (within accuracy)
Returns
true if all parameters were equal, false if not

Definition at line 618 of file SGObject.cpp.

 SGIO * get_global_io ( )
inherited

get the io object

Returns
io object

Definition at line 235 of file SGObject.cpp.

 Parallel * get_global_parallel ( )
inherited

get the parallel object

Returns
parallel object

Definition at line 277 of file SGObject.cpp.

 Version * get_global_version ( )
inherited

get the version object

Returns
version object

Definition at line 290 of file SGObject.cpp.

 virtual CKernel* get_kernel ( )
virtualinherited
Returns
underlying kernel, is SG_REF'ed

Definition at line 86 of file KernelTwoSampleTest.h.

 index_t get_m ( )
inherited
Returns
number of to be used samples m

Definition at line 127 of file TwoSampleTest.h.

 SGStringList< char > get_modelsel_names ( )
inherited
Returns
vector of names of all parameters which are registered for model selection

Definition at line 498 of file SGObject.cpp.

 char * get_modsel_param_descr ( const char * param_name )
inherited

Returns description of a given parameter string, if it exists. SG_ERROR otherwise

Parameters
 param_name name of the parameter
Returns
description of the parameter

Definition at line 522 of file SGObject.cpp.

 index_t get_modsel_param_index ( const char * param_name )
inherited

Returns index of model selection parameter with provided index

Parameters
 param_name name of model selection parameter
Returns
index of model selection parameter with provided name, -1 if there is no such

Definition at line 535 of file SGObject.cpp.

 virtual const char* get_name ( ) const
virtual
Returns
the class name

Reimplemented from CStreamingMMD.

Definition at line 124 of file LinearTimeMMD.h.

 CFeatures * get_p_and_q ( )
virtualinherited

Not implemented for streaming MMD since it uses streaming feautres

Reimplemented from CTwoSampleTest.

Definition at line 307 of file StreamingMMD.cpp.

 virtual EStatisticType get_statistic_type ( ) const
virtual

returns the statistic type of this test statistic

Implements CHypothesisTest.

Definition at line 118 of file LinearTimeMMD.h.

 CStreamingFeatures * get_streaming_p ( )
virtualinherited

Getter for streaming features of p distribution.

Returns
streaming features object for p distribution, SG_REF'ed

Definition at line 314 of file StreamingMMD.cpp.

 CStreamingFeatures * get_streaming_q ( )
virtualinherited

Getter for streaming features of q distribution.

Returns
streaming features object for q distribution, SG_REF'ed

Definition at line 320 of file StreamingMMD.cpp.

 bool is_generic ( EPrimitiveType * generic ) const
virtualinherited

If the SGSerializable is a class template then TRUE will be returned and GENERIC is set to the type of the generic.

Parameters
 generic set to the type of the generic if returning TRUE
Returns
TRUE if a class template.

Definition at line 296 of file SGObject.cpp.

 bool load_serializable ( CSerializableFile * file, const char * prefix = "" )
virtualinherited

Load this object from file. If it will fail (returning FALSE) then this object will contain inconsistent data and should not be used!

Parameters
 file where to load from prefix prefix for members
Returns
TRUE if done, otherwise FALSE

Definition at line 369 of file SGObject.cpp.

 void load_serializable_post ( ) throw ( ShogunException )
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.

Exceptions
 ShogunException will be thrown if an error occurs.

Definition at line 426 of file SGObject.cpp.

 void load_serializable_pre ( ) throw ( ShogunException )
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.

Exceptions
 ShogunException will be thrown if an error occurs.

Definition at line 421 of file SGObject.cpp.

 bool parameter_hash_changed ( )
virtualinherited
Returns
whether parameter combination has changed since last update

Definition at line 262 of file SGObject.cpp.

 bool perform_test ( float64_t alpha )
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)

Parameters
 alpha test level alpha.
Returns
true if null hypothesis is rejected and false otherwise

Definition at line 121 of file HypothesisTest.cpp.

 float64_t perform_test ( )
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().

Returns
p-value such that computed statistic is the (1-p) quantile of the estimated null distribution

Reimplemented from CHypothesisTest.

Definition at line 165 of file StreamingMMD.cpp.

 void print_modsel_params ( )
inherited

prints all parameter registered for model selection and their type

Definition at line 474 of file SGObject.cpp.

 void print_serializable ( const char * prefix = "" )
virtualinherited

prints registered parameters out

Parameters
 prefix prefix for members

Definition at line 308 of file SGObject.cpp.

 SGVector< float64_t > sample_null ( )
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.

Returns
vector of all statistics

Reimplemented from CKernelTwoSampleTest.

Definition at line 194 of file StreamingMMD.cpp.

 bool save_serializable ( CSerializableFile * file, const char * prefix = "" )
virtualinherited

Save this object to file.

Parameters
 file where to save the object; will be closed during returning if PREFIX is an empty string. prefix prefix for members
Returns
TRUE if done, otherwise FALSE

Definition at line 314 of file SGObject.cpp.

 void save_serializable_post ( ) throw ( ShogunException )
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.

Exceptions
 ShogunException will be thrown if an error occurs.

Reimplemented in CKernel.

Definition at line 436 of file SGObject.cpp.

 void save_serializable_pre ( ) throw ( ShogunException )
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.

Exceptions
 ShogunException will be thrown if an error occurs.

Definition at line 431 of file SGObject.cpp.

 void set_blocksize ( index_t blocksize )
inherited

Setter for the blocksize of examples to be processed at once

Parameters
 blocksize new blocksize to use

Definition at line 226 of file StreamingMMD.h.

 void set_generic ( )
inherited

Definition at line 41 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 46 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 51 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 56 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 61 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 66 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 71 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 76 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 81 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 86 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 91 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 96 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 101 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 106 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 111 of file SGObject.cpp.

 void set_generic ( )
inherited

set generic type to T

 void set_global_io ( SGIO * io )
inherited

set the io object

Parameters
 io io object to use

Definition at line 228 of file SGObject.cpp.

 void set_global_parallel ( Parallel * parallel )
inherited

set the parallel object

Parameters
 parallel parallel object to use

Definition at line 241 of file SGObject.cpp.

 void set_global_version ( Version * version )
inherited

set the version object

Parameters
 version version object to use

Definition at line 283 of file SGObject.cpp.

 virtual void set_kernel ( CKernel * kernel )
virtualinherited

Setter for the underlying kernel

Parameters
 kernel new kernel to use

Definition at line 77 of file KernelTwoSampleTest.h.

 void set_m ( index_t m )
inherited
Parameters
 m number of samples from first distribution p

Definition at line 162 of file TwoSampleTest.cpp.

 void set_null_approximation_method ( ENullApproximationMethod null_approximation_method )
virtualinherited

sets the method how to approximate the null-distribution

Parameters
 null_approximation_method method to use

Definition at line 61 of file HypothesisTest.cpp.

 void set_num_null_samples ( index_t num_null_samples )
virtualinherited

sets the number of permutation iterations for sample_null()

Parameters
 num_null_samples how often permutation shall be done

Definition at line 67 of file HypothesisTest.cpp.

 void set_p_and_q ( CFeatures * p_and_q )
virtualinherited

Not implemented for streaming MMD since it uses streaming feautres

Reimplemented from CTwoSampleTest.

Definition at line 301 of file StreamingMMD.cpp.

 void set_simulate_h0 ( bool simulate_h0 )
inherited
Parameters
 simulate_h0 if true, samples from p and q will be mixed and permuted

Definition at line 263 of file StreamingMMD.h.

 CSGObject * shallow_copy ( ) const
virtualinherited

A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.

Reimplemented in CGaussianKernel.

Definition at line 192 of file SGObject.cpp.

 CList * stream_data_blocks ( index_t num_blocks, index_t num_this_run )
inherited

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.

Parameters
 num_blocks number of blocks to be streamed from each distribution num_this_run number of data points to be streamed for one block
Returns
an ordered list of blocks of data. The order in the list is $$x,x',\cdots\sim p$$ followed by $$y,y',\cdots\sim q$$. The features inside the list are SG_REF'ed and delete_data is set in the list, which will destroy the at CList's destructor call

Definition at line 220 of file StreamingMMD.cpp.

 void unset_generic ( )
inherited

unset generic type

this has to be called in classes specializing a template class

Definition at line 303 of file SGObject.cpp.

 void update_parameter_hash ( )
virtualinherited

Updates the hash of current parameter combination

Definition at line 248 of file SGObject.cpp.

## Member Data Documentation

 SGIO* io
inherited

io

Definition at line 369 of file SGObject.h.

 index_t m_blocksize
protectedinherited

Number of examples processed at once, i.e. in one burst

Definition at line 296 of file StreamingMMD.h.

inherited

parameters wrt which we can compute gradients

Definition at line 384 of file SGObject.h.

 uint32_t m_hash
inherited

Hash of parameter values

Definition at line 387 of file SGObject.h.

 CKernel* m_kernel
protectedinherited

underlying kernel

Definition at line 121 of file KernelTwoSampleTest.h.

 index_t m_m
protectedinherited

defines the first index of samples of q

Definition at line 139 of file TwoSampleTest.h.

 Parameter* m_model_selection_parameters
inherited

model selection parameters

Definition at line 381 of file SGObject.h.

 ENullApproximationMethod m_null_approximation_method
protectedinherited

Defines how the the null distribution is approximated

Definition at line 177 of file HypothesisTest.h.

 index_t m_num_null_samples
protectedinherited

number of iterations for sampling from null-distributions

Definition at line 174 of file HypothesisTest.h.

 CFeatures* m_p_and_q
protectedinherited

concatenated samples of the two distributions (two blocks)

Definition at line 136 of file TwoSampleTest.h.

 Parameter* m_parameters
inherited

parameters

Definition at line 378 of file SGObject.h.

 bool m_simulate_h0
protectedinherited

If this is true, samples will be mixed between p and q in any method that computes the statistic

Definition at line 300 of file StreamingMMD.h.

 CStreamingFeatures* m_streaming_p
protectedinherited

Streaming feature objects that are used instead of merged samples

Definition at line 290 of file StreamingMMD.h.

 CStreamingFeatures* m_streaming_q
protectedinherited

Streaming feature objects that are used instead of merged samples

Definition at line 293 of file StreamingMMD.h.

 Parallel* parallel
inherited

parallel

Definition at line 372 of file SGObject.h.

 Version* version
inherited

version

Definition at line 375 of file SGObject.h.

The documentation for this class was generated from the following files:

SHOGUN Machine Learning Toolbox - Documentation