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SHOGUN
4.2.0
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SHOGUN
4.2.0
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Class that contains certain functions related to statistics, such as probability/cumulative distribution functions, different statistics, etc.
Definition at line 30 of file Statistics.h.
Classes | |
| struct | SigmoidParamters |
Public Member Functions | |
| virtual const char * | get_name () const |
| template<> | |
| floatmax_t | mean (SGVector< complex128_t > vec) |
| mean not implemented for complex128_t, returns 0.0 instead More... | |
| 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="") |
| virtual bool | load_serializable (CSerializableFile *file, const char *prefix="") |
| 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) |
| bool | has (const std::string &name) const |
| template<typename T > | |
| bool | has (const Tag< T > &tag) const |
| template<typename T , typename U = void> | |
| bool | has (const std::string &name) const |
| template<typename T > | |
| void | set (const Tag< T > &_tag, const T &value) |
| template<typename T , typename U = void> | |
| void | set (const std::string &name, const T &value) |
| template<typename T > | |
| T | get (const Tag< T > &_tag) const |
| template<typename T , typename U = void> | |
| T | get (const std::string &name) const |
| virtual void | update_parameter_hash () |
| virtual bool | parameter_hash_changed () |
| virtual bool | equals (CSGObject *other, float64_t accuracy=0.0, bool tolerant=false) |
| virtual CSGObject * | clone () |
Public Attributes | |
| SGIO * | io |
| Parallel * | parallel |
| Version * | version |
| Parameter * | m_parameters |
| Parameter * | m_model_selection_parameters |
| Parameter * | m_gradient_parameters |
| uint32_t | m_hash |
Static Public Attributes | |
| static const float64_t | ERFC_CASE1 =0.0492 |
| static const float64_t | ERFC_CASE2 =-11.3137 |
Protected Member Functions | |
| 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) |
| template<typename T > | |
| void | register_param (Tag< T > &_tag, const T &value) |
| template<typename T > | |
| void | register_param (const std::string &name, const T &value) |
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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 630 of file SGObject.cpp.
Evaluates the CDF of the chi square distribution with parameter k at \(x\).
| x | position to evaluate |
| k | parameter |
Definition at line 374 of file Statistics.cpp.
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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.
Definition at line 747 of file SGObject.cpp.
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Computes the empirical estimate of the DxD covariance matrix of the given data which is organized as num_cols variables with num_rows observations. Normalizes by N-1 for N observations
Data is centered before matrix is computed. May be done in place. In this case, the observation matrix is changed (centered).
| observations | Data matrix |
| in_place | Optional, if set to true, observations matrix will be centered, if false, a copy will be created an centered. |
Definition at line 135 of file Statistics.cpp.
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virtualinherited |
A deep copy. All the instance variables will also be copied.
Definition at line 231 of file SGObject.cpp.
Derivative of the log gamma function.
| x | input |
Definition at line 558 of file Statistics.cpp.
Definition at line 312 of file Statistics.cpp.
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) |
Definition at line 651 of file SGObject.cpp.
Use to estimates erfc(x) valid for -100 < x < -8
| x | real value |
Definition at line 464 of file Statistics.cpp.
Evaluates the CDF of the F-distribution with parameters \(d1,d2\) at \(x\). Based on Wikipedia definition.
| x | position to evaluate |
| d1 | parameter 1 |
| d2 | parameter 2 |
Definition at line 537 of file Statistics.cpp.
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fisher's test for multiple 2x3 tables
| tables |
Definition at line 168 of file Statistics.cpp.
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Converts a given vector of scores to calibrated probabilities by fitting a sigmoid function using the method described in Lin, H., Lin, C., and Weng, R. (2007). A note on Platt's probabilistic outputs for support vector machines.
This can be used to transform scores to probabilities as setting \(pf=x*a+b\) for a given score \(x\) and computing \(\frac{\exp(-f)}{1+}exp(-f)}\) if \(f\geq 0\) and \(\frac{1}{(1+\exp(f)}\) otherwise
| scores | scores to fit the sigmoid to |
Definition at line 821 of file Statistics.cpp.
Evaluates the CDF of the gamma distribution, parametrized with shape and rate parameters \(\alpha, \beta\) at \(x\).
\[ \frac{\beta^\alpha}{\Gamma(\alpha)}\int _{-\infty}^x x^{\alpha-1}\exp(-t \beta)dt \]
| x | Argument \(x\) to evaluate. |
| a | Shape parameter \(\alpha\) |
| b | Rate parameter \(\beta\) |
Definition at line 395 of file Statistics.cpp.
Inverse of Gamma cumulative distribution function, parametrized with shape and rate parameters \(\alpha, \beta\), given by
\[ \frac{\beta^\alpha}{\Gamma(\alpha)}\int _{-\infty}^x x^{\alpha-1}\exp(-t \beta)dt \]
Returns the argument \(x\) for which the CDF is equal to \(y\).
| p | CDF value \(y\). |
| a | Shape parameter \(\alpha\) |
| b | Rate parameter \(\beta\) |
Definition at line 513 of file Statistics.cpp.
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Getter for a class parameter, identified by a Tag. Throws an exception if the class does not have such a parameter.
| _tag | name and type information of parameter |
Definition at line 367 of file SGObject.h.
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Getter for a class parameter, identified by a name. Throws an exception if the class does not have such a parameter.
| name | name of the parameter |
Definition at line 388 of file SGObject.h.
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Definition at line 531 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 555 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 568 of file SGObject.cpp.
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Checks if object has a class parameter identified by a name.
| name | name of the parameter |
Definition at line 289 of file SGObject.h.
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Checks if object has a class parameter identified by a Tag.
| tag | tag of the parameter containing name and type information |
Definition at line 301 of file SGObject.h.
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Checks if a type exists for a class parameter identified by a name.
| name | name of the parameter |
Definition at line 312 of file SGObject.h.
Inverse of Normal cumulative distribution function with mean \(\mu\) and standard deviation \(\sigma\), given by
\[ y=\frac{1}{\sigma \sqrt {2\pi }} \int_{-\infty}^x \exp\left(-\frac{(t-\mu)^2}{2\sigma^2}\right)dt \]
Returns the argument \(x\) for which CDF is equal to \(y\).
| y0 | CDF value \(y\). |
| mean | Mean \(\mu\). Default value is 0. |
| std_dev | Standard deviation \(\sigma\). Default value is 1. |
Definition at line 348 of file Statistics.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 329 of file SGObject.cpp.
Definition at line 131 of file Statistics.h.
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Definition at line 138 of file Statistics.h.
Returns logarithm of the cumulative distribution function (CDF) of Gaussian distribution \(N(0, 1)\):
\[ \text{lnormal\_cdf}(x)=log\left(\frac{1}{2}+ \frac{1}{2}\text{error\_function}(\frac{x}{\sqrt{2}})\right) \]
| x | Evaluate CDF here |
Definition at line 418 of file Statistics.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 |
Definition at line 402 of file SGObject.cpp.
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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. |
Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.
Definition at line 459 of file SGObject.cpp.
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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. |
Reimplemented in CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 454 of file SGObject.cpp.
The log determinant of a dense matrix
The log determinant of a positive definite symmetric real valued matrix is calculated as
\[ \text{log\_determinant}(M) = \text{log}(\text{determinant}(L)\times\text{determinant}(L')) = 2\times \sum_{i}\text{log}(L_{i,i}) \]
Where, \(M = L\times L'\) as per Cholesky decomposition.
| m | input matrix |
Definition at line 660 of file Statistics.cpp.
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The log determinant of a sparse matrix
The log determinant of symmetric positive definite sparse matrix is calculated in a similar way as the dense case. But using cholesky decomposition on sparse matrices may suffer from fill-in phenomenon, i.e. the factors may not be as sparse. The SimplicialCholesky module for sparse matrix in eigen3 library uses an approach called approximate minimum degree reordering, or amd, which permutes the matrix beforehand and results in much sparser factors. If \(P\) is the permutation matrix, it computes \(\text{LLT}(P\times M\times P^{-1}) = L\times L'\).
| m | input sparse matrix |
Definition at line 683 of file Statistics.cpp.
The log determinant of a dense matrix
If determinant of the input matrix is positive, it returns the logarithm of the value. If not, it returns CMath::INFTY Note that the input matrix is not required to be symmetric positive definite. This method is slower than log_det() if input matrix is known to be symmetric positive definite
It is adapted from Gaussian Process Machine Learning Toolbox http://www.gaussianprocess.org/gpml/code/matlab/doc/
| A | input matrix |
Definition at line 606 of file Statistics.cpp.
Calculates mean of given values. Given \(\{x_1, ..., x_m\}\), this is \(\frac{1}{m}\sum_{i=1}^m x_i\)
Computes the mean for each row/col of matrix
| values | vector of values |
| col_wise | if true, every column vector will be used, row vectors otherwise |
Definition at line 43 of file Statistics.cpp.
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Calculates unbiased empirical standard deviation estimator of given values. Given \(\{x_1, ..., x_m\}\), this is \(\sqrt{\frac{1}{m-1}\sum_{i=1}^m (x-\bar{x})^2}\) where \(\bar x=\frac{1}{m}\sum_{i=1}^m x_i\)
Computes the variance for each row/col of matrix
| values | vector of values |
| col_wise | if true, every column vector will be used, row vectors otherwise |
Definition at line 125 of file Statistics.cpp.
Calculates unbiased empirical variance estimator of given values. Given \(\{x_1, ..., x_m\}\), this is \(\frac{1}{m-1}\sum_{i=1}^m (x-\bar{x})^2\) where \(\bar x=\frac{1}{m}\sum_{i=1}^m x_i\)
Computes the variance for each row/col of matrix
| values | vector of values |
| col_wise | if true, every column vector will be used, row vectors otherwise |
Definition at line 80 of file Statistics.cpp.
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Calculates mean of given values. Given \(\{x_1, ..., x_m\}\), this is \(\frac{1}{m}\sum_{i=1}^m x_i\)
| vec | vector of values |
Definition at line 42 of file Statistics.h.
| floatmax_t mean | ( | SGVector< complex128_t > | vec | ) |
mean not implemented for complex128_t, returns 0.0 instead
Definition at line 414 of file Statistics.h.
Definition at line 291 of file Statistics.cpp.
Evaluates the CDF of the Normal distribution, with mean \(\mu\) and standard deviation \(\sigma\), given by
\[ y=\frac{1}{\sigma \sqrt {2\pi }} \int_{-\infty}^x \exp\left(-\frac{(t-\mu)^2}{2\sigma^2}\right)dt \]
| x | Argument \(x\) to evaluate. |
| std_dev | Standard deviation \(\sigma\). Default value is 1. |
Definition at line 508 of file Statistics.cpp.
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Definition at line 295 of file SGObject.cpp.
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prints all parameter registered for model selection and their type
Definition at line 507 of file SGObject.cpp.
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prints registered parameters out
| prefix | prefix for members |
Definition at line 341 of file SGObject.cpp.
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Registers a class parameter which is identified by a tag. This enables the parameter to be modified by set() and retrieved by get(). Parameters can be registered in the constructor of the class.
| _tag | name and type information of parameter |
| value | value of the parameter |
Definition at line 439 of file SGObject.h.
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Registers a class parameter which is identified by a name. This enables the parameter to be modified by set() and retrieved by get(). Parameters can be registered in the constructor of the class.
| name | name of the parameter |
| value | value of the parameter along with type information |
Definition at line 452 of file SGObject.h.
Definition at line 302 of file Statistics.cpp.
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Sampling from a multivariate Gaussian distribution with dense covariance matrix
Sampling is performed by taking samples from \(N(0, I)\), then using cholesky factor of the covariance matrix, \(\Sigma\) and performing
\[S_{N(\mu,\Sigma)}=S_{N(0,I)}*L^{T}+\mu\]
where \(\Sigma=L*L^{T}\) and \(\mu\) is the mean vector.
| mean | the mean vector |
| cov | the covariance matrix |
| N | number of samples |
| precision_matrix | if true, sample from N(mu,C^-1) |
Definition at line 703 of file Statistics.cpp.
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Sampling from a multivariate Gaussian distribution with sparse covariance matrix
Sampling is performed in similar way as of dense covariance matrix, but direct cholesky factorization of sparse matrices could be inefficient. So, this method uses permutation matrix for factorization and then permutes back the final samples before adding the mean.
| mean | the mean vector |
| cov | the covariance matrix |
| N | number of samples |
| precision_matrix | if true, sample from N(mu,C^-1) |
Definition at line 753 of file Statistics.cpp.
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sample indices
| sample_size | size of sample to pick |
| N | total number of indices |
Definition at line 322 of file Statistics.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 |
Definition at line 347 of file SGObject.cpp.
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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. |
Reimplemented in CKernel.
Definition at line 469 of file SGObject.cpp.
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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. |
Reimplemented in CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 464 of file SGObject.cpp.
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Setter for a class parameter, identified by a Tag. Throws an exception if the class does not have such a parameter.
| _tag | name and type information of parameter |
| value | value of the parameter |
Definition at line 328 of file SGObject.h.
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Setter for a class parameter, identified by a name. Throws an exception if the class does not have such a parameter.
| name | name of the parameter |
| value | value of the parameter along with type information |
Definition at line 354 of file SGObject.h.
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Definition at line 74 of file SGObject.cpp.
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Definition at line 79 of file SGObject.cpp.
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Definition at line 84 of file SGObject.cpp.
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Definition at line 89 of file SGObject.cpp.
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Definition at line 94 of file SGObject.cpp.
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Definition at line 99 of file SGObject.cpp.
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Definition at line 104 of file SGObject.cpp.
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Definition at line 109 of file SGObject.cpp.
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Definition at line 114 of file SGObject.cpp.
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Definition at line 119 of file SGObject.cpp.
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Definition at line 124 of file SGObject.cpp.
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Definition at line 129 of file SGObject.cpp.
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Definition at line 134 of file SGObject.cpp.
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Definition at line 139 of file SGObject.cpp.
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Definition at line 144 of file SGObject.cpp.
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set generic type to T
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set the parallel object
| parallel | parallel object to use |
Definition at line 274 of file SGObject.cpp.
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set the version object
| version | version object to use |
Definition at line 316 of file SGObject.cpp.
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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 225 of file SGObject.cpp.
Calculates unbiased empirical standard deviation estimator of given values. Given \(\{x_1, ..., x_m\}\), this is \(\sqrt{\frac{1}{m-1}\sum_{i=1}^m (x-\bar{x})^2}\) where \(\bar x=\frac{1}{m}\sum_{i=1}^m x_i\)
| values | vector of values |
Definition at line 120 of file Statistics.cpp.
Definition at line 148 of file Statistics.h.
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unset generic type
this has to be called in classes specializing a template class
Definition at line 336 of file SGObject.cpp.
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Updates the hash of current parameter combination
Definition at line 281 of file SGObject.cpp.
Calculates unbiased empirical variance estimator of given values. Given \(\{x_1, ..., x_m\}\), this is \(\frac{1}{m-1}\sum_{i=1}^m (x-\bar{x})^2\) where \(\bar x=\frac{1}{m}\sum_{i=1}^m x_i\)
| values | vector of values |
Definition at line 29 of file Statistics.cpp.
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Magic number for computing lnormal_cdf
Definition at line 404 of file Statistics.h.
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Magic number for computing lnormal_cdf
Definition at line 407 of file Statistics.h.
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io
Definition at line 537 of file SGObject.h.
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parameters wrt which we can compute gradients
Definition at line 552 of file SGObject.h.
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Hash of parameter values
Definition at line 555 of file SGObject.h.
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model selection parameters
Definition at line 549 of file SGObject.h.
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parameters
Definition at line 546 of file SGObject.h.
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parallel
Definition at line 540 of file SGObject.h.
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version
Definition at line 543 of file SGObject.h.