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.
在文件 LinearTimeMMD.h 第 66 行定义.
Public 属性 | |
SGIO * | io |
Parallel * | parallel |
Version * | version |
Parameter * | m_parameters |
Parameter * | m_model_selection_parameters |
Parameter * | m_gradient_parameters |
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) |
virtual void | load_serializable_pre () throw (ShogunException) |
virtual void | load_serializable_post () throw (ShogunException) |
virtual void | save_serializable_pre () throw (ShogunException) |
virtual void | save_serializable_post () throw (ShogunException) |
CLinearTimeMMD | ( | ) |
default constructor
在文件 LinearTimeMMD.cpp 第 44 行定义.
CLinearTimeMMD | ( | CKernel * | kernel, |
CStreamingFeatures * | p, | ||
CStreamingFeatures * | q, | ||
index_t | m, | ||
index_t | blocksize = 10000 |
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) |
Constructor.
kernel | kernel to use |
p | streaming features p to use |
q | streaming features q to use |
m | number of samples from each distribution |
blocksize | size of examples that are processed at once when computing statistic/threshold. If larger than m/2, all examples will be processed at once. Memory consumption increased linearly in the blocksize. Choose as large as possible regarding available memory. |
在文件 LinearTimeMMD.cpp 第 48 行定义.
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virtual |
destructor
在文件 LinearTimeMMD.cpp 第 54 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 597 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 714 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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protectedvirtual |
method that computes the squared MMD in linear time (see class description for the equation)
kernel | the kernel to be used for computing MMD. This will be useful when multiple kernels are used |
data | the list of data on which kernels are computed. The order of data in the list is \(x,x',\cdots\sim p\) followed by \(y,y',\cdots\sim q\). It is assumed that detele_data flag is set inside the list |
num_this_run | number of data points in current blocks |
实现了 CStreamingMMD.
在文件 LinearTimeMMD.cpp 第 103 行定义.
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virtualinherited |
Computes the squared MMD for the current data. This is an unbiased estimate. This method relies on compute_statistic_and_variance which has to be defined in the subclasses
Note that the underlying streaming feature parser has to be started before this is called. Otherwise deadlock.
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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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.
实现了 CStreamingMMD.
在文件 LinearTimeMMD.cpp 第 250 行定义.
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virtual |
Computes squared MMD and a variance estimate, in linear time. If multiple_kernels is set to true, each subkernel is evaluated on the same data.
statistic | return parameter for statistic, vector with entry for each kernel. May be allocated before but doesn not have to be |
variance | return parameter for statistic, vector with entry for each kernel. May be allocated before but doesn not have to be |
multiple_kernels | optional flag, if set to true, it is assumed that the underlying kernel is of type K_COMBINED. Then, the MMD is computed on all subkernel separately rather than computing it on the combination. This is used by kernel selection strategies that need to evaluate multiple kernels on the same data. Since the linear time MMD works on streaming data, one cannot simply compute MMD, change kernel since data would be different for every kernel. |
实现了 CStreamingMMD.
在文件 LinearTimeMMD.cpp 第 116 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 CTwoSampleTest .
在文件 StreamingMMD.cpp 第 142 行定义.
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virtualinherited |
computes a linear time estimate of the variance of the squared mmd, which may be used for an approximation of the null-distribution The value is the variance of the vector of which the MMD is the mean.
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.cpp 第 198 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 618 行定义.
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virtualinherited |
在文件 KernelTwoSampleTest.h 第 86 行定义.
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inherited |
在文件 TwoSampleTest.h 第 127 行定义.
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inherited |
在文件 SGObject.cpp 第 498 行定义.
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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 522 行定义.
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Returns index of model selection parameter with provided index
param_name | name of model selection parameter |
在文件 SGObject.cpp 第 535 行定义.
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virtual |
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virtualinherited |
Not implemented for streaming MMD since it uses streaming feautres
重载 CTwoSampleTest .
在文件 StreamingMMD.cpp 第 307 行定义.
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virtual |
returns the statistic type of this test statistic
实现了 CHypothesisTest.
在文件 LinearTimeMMD.h 第 118 行定义.
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virtualinherited |
Getter for streaming features of p distribution.
在文件 StreamingMMD.cpp 第 314 行定义.
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virtualinherited |
Getter for streaming features of q distribution.
在文件 StreamingMMD.cpp 第 320 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 296 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 |
在文件 SGObject.cpp 第 369 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 occurs. |
被 CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel , 以及 CExponentialKernel 重载.
在文件 SGObject.cpp 第 426 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 occurs. |
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 421 行定义.
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virtualinherited |
在文件 SGObject.cpp 第 262 行定义.
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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. |
在文件 HypothesisTest.cpp 第 121 行定义.
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virtualinherited |
Performs the complete two-sample test on current data and returns a p-value.
In case null distribution should be estimated with MMD1_GAUSSIAN, statistic and p-value are computed in the same loop, which is more efficient than first computing statistic and then computung p-values.
In case of sampling null, superclass method is called.
The method for computing the p-value can be set via set_null_approximation_method().
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 474 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 |
在文件 SGObject.cpp 第 314 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 occurs. |
被 CKernel 重载.
在文件 SGObject.cpp 第 436 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 occurs. |
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 431 行定义.
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inherited |
Setter for the blocksize of examples to be processed at once
blocksize | new blocksize to use |
在文件 StreamingMMD.h 第 226 行定义.
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inherited |
在文件 SGObject.cpp 第 41 行定义.
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在文件 SGObject.cpp 第 46 行定义.
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在文件 SGObject.cpp 第 51 行定义.
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在文件 SGObject.cpp 第 56 行定义.
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在文件 SGObject.cpp 第 61 行定义.
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在文件 SGObject.cpp 第 66 行定义.
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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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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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在文件 SGObject.cpp 第 91 行定义.
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在文件 SGObject.cpp 第 96 行定义.
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在文件 SGObject.cpp 第 101 行定义.
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在文件 SGObject.cpp 第 106 行定义.
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在文件 SGObject.cpp 第 111 行定义.
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set generic type to T
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virtualinherited |
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m | number of samples from first distribution p |
在文件 TwoSampleTest.cpp 第 162 行定义.
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sets the method how to approximate the null-distribution
null_approximation_method | method to use |
在文件 HypothesisTest.cpp 第 61 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 67 行定义.
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virtualinherited |
Not implemented for streaming MMD since it uses streaming feautres
重载 CTwoSampleTest .
在文件 StreamingMMD.cpp 第 301 行定义.
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inherited |
simulate_h0 | if true, samples from p and q will be mixed and permuted |
在文件 StreamingMMD.h 第 263 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.cpp 第 192 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 303 行定义.
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virtualinherited |
Updates the hash of current parameter combination
在文件 SGObject.cpp 第 248 行定义.
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io
在文件 SGObject.h 第 369 行定义.
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protectedinherited |
Number of examples processed at once, i.e. in one burst
在文件 StreamingMMD.h 第 296 行定义.
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parameters wrt which we can compute gradients
在文件 SGObject.h 第 384 行定义.
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Hash of parameter values
在文件 SGObject.h 第 387 行定义.
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protectedinherited |
underlying kernel
在文件 KernelTwoSampleTest.h 第 121 行定义.
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protectedinherited |
defines the first index of samples of q
在文件 TwoSampleTest.h 第 139 行定义.
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model selection parameters
在文件 SGObject.h 第 381 行定义.
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Defines how the the null distribution is approximated
在文件 HypothesisTest.h 第 177 行定义.
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protectedinherited |
number of iterations for sampling from null-distributions
在文件 HypothesisTest.h 第 174 行定义.
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protectedinherited |
concatenated samples of the two distributions (two blocks)
在文件 TwoSampleTest.h 第 136 行定义.
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parameters
在文件 SGObject.h 第 378 行定义.
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protectedinherited |
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 300 行定义.
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protectedinherited |
Streaming feature objects that are used instead of merged samples
在文件 StreamingMMD.h 第 290 行定义.
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protectedinherited |
Streaming feature objects that are used instead of merged samples
在文件 StreamingMMD.h 第 293 行定义.
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parallel
在文件 SGObject.h 第 372 行定义.
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version
在文件 SGObject.h 第 375 行定义.