SHOGUN  6.1.3
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CStatistics Class Reference

Detailed Description

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.

Inheritance diagram for CStatistics:
[legend]

Classes

struct  SigmoidParamters
 

Public Types

typedef rxcpp::subjects::subject< ObservedValueSGSubject
 
typedef rxcpp::observable< ObservedValue, rxcpp::dynamic_observable< ObservedValue > > SGObservable
 
typedef rxcpp::subscriber< ObservedValue, rxcpp::observer< ObservedValue, void, void, void, void > > SGSubscriber
 

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...
 
int32_t ref ()
 
int32_t ref_count ()
 
int32_t unref ()
 
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)
 
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 >
get (const Tag< T > &_tag) const
 
template<typename T , typename U = void>
get (const std::string &name) const
 
SGObservableget_parameters_observable ()
 
void subscribe_to_parameters (ParameterObserverInterface *obs)
 
void list_observable_parameters ()
 
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 ()
 

Static Public Member Functions

template<class T >
static floatmax_t mean (SGVector< T > vec)
 
static float64_t variance (SGVector< float64_t > values)
 
static float64_t std_deviation (SGVector< float64_t > values)
 
static SGVector< float64_tmatrix_mean (SGMatrix< float64_t > values, bool col_wise=true)
 
static SGVector< float64_tmatrix_variance (SGMatrix< float64_t > values, bool col_wise=true)
 
static SGVector< float64_tmatrix_std_deviation (SGMatrix< float64_t > values, bool col_wise=true)
 
static SGMatrix< float64_tcovariance_matrix (SGMatrix< float64_t > observations, bool in_place=false)
 
static float64_t lgamma (float64_t x)
 
static floatmax_t lgammal (floatmax_t x)
 
static float64_t tgamma (float64_t x)
 
static float64_t gamma_cdf (float64_t x, float64_t a, float64_t b)
 
static float64_t gamma_inverse_cdf (float64_t p, float64_t a, float64_t b)
 
static float64_t normal_cdf (float64_t x, float64_t std_dev=1)
 
static float64_t inverse_normal_cdf (float64_t y0, float64_t mean=0, float64_t std_dev=1)
 
static float64_t lnormal_cdf (float64_t x)
 
static float64_t chi2_cdf (float64_t x, float64_t k)
 
static float64_t fdistribution_cdf (float64_t x, float64_t d1, float64_t d2)
 
static float64_t erfc8_weighted_sum (float64_t x)
 
static float64_t mutual_info (float64_t *p1, float64_t *p2, int32_t len)
 
static float64_t relative_entropy (float64_t *p, float64_t *q, int32_t len)
 
static float64_t entropy (float64_t *p, int32_t len)
 
static SGVector< float64_tfishers_exact_test_for_multiple_2x3_tables (SGMatrix< float64_t > tables)
 
static float64_t fishers_exact_test_for_2x3_table (SGMatrix< float64_t > table)
 
static SGVector< int32_t > sample_indices (int32_t sample_size, int32_t N)
 
static float64_t dlgamma (float64_t x)
 
static SigmoidParamters fit_sigmoid (SGVector< float64_t > scores)
 
static float64_t log_det_general (const SGMatrix< float64_t > A)
 
static float64_t log_det (SGMatrix< float64_t > m)
 
static float64_t log_det (const SGSparseMatrix< float64_t > m)
 
static SGMatrix< float64_tsample_from_gaussian (SGVector< float64_t > mean, SGMatrix< float64_t > cov, int32_t N=1, bool precision_matrix=false)
 
static SGMatrix< float64_tsample_from_gaussian (SGVector< float64_t > mean, SGSparseMatrix< float64_t > cov, int32_t N=1, bool precision_matrix=false)
 

Public Attributes

SGIOio
 
Parallelparallel
 
Versionversion
 
Parameterm_parameters
 
Parameterm_model_selection_parameters
 
Parameterm_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)
 
bool clone_parameters (CSGObject *other)
 
void observe (const ObservedValue value)
 
void register_observable_param (const std::string &name, const SG_OBS_VALUE_TYPE type, const std::string &description)
 

Member Typedef Documentation

◆ SGObservable

Definition at line 130 of file SGObject.h.

◆ SGSubject

Definition at line 127 of file SGObject.h.

◆ SGSubscriber

typedef rxcpp::subscriber< ObservedValue, rxcpp::observer<ObservedValue, void, void, void, void> > SGSubscriber
inherited

Definition at line 133 of file SGObject.h.

Member Function Documentation

◆ build_gradient_parameter_dictionary()

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
dictdictionary of parameters to be built.

Definition at line 635 of file SGObject.cpp.

◆ chi2_cdf()

float64_t chi2_cdf ( float64_t  x,
float64_t  k 
)
static

Evaluates the CDF of the chi square distribution with parameter k at \(x\).

Parameters
xposition to evaluate
kparameter
Returns
chi square CDF at \(x\)

Definition at line 377 of file Statistics.cpp.

◆ clone()

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

Reimplemented in CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, CDynamicObjectArray, CAlphabet, and CMKL.

Definition at line 734 of file SGObject.cpp.

◆ clone_parameters()

bool clone_parameters ( CSGObject other)
protectedinherited

Definition at line 759 of file SGObject.cpp.

◆ covariance_matrix()

SGMatrix< float64_t > covariance_matrix ( SGMatrix< float64_t observations,
bool  in_place = false 
)
static

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).

Parameters
observationsData matrix
in_placeOptional, if set to true, observations matrix will be centered, if false, a copy will be created an centered.
Returns
DxD covariance matrix

Definition at line 138 of file Statistics.cpp.

◆ deep_copy()

CSGObject * deep_copy ( ) const
virtualinherited

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

Definition at line 232 of file SGObject.cpp.

◆ dlgamma()

float64_t dlgamma ( float64_t  x)
static

Derivative of the log gamma function.

Parameters
xinput
Returns
derivative of the log gamma input

Definition at line 561 of file Statistics.cpp.

◆ entropy()

float64_t entropy ( float64_t p,
int32_t  len 
)
static
Returns
entropy of \(p\) which is given in logspace

Definition at line 315 of file Statistics.cpp.

◆ equals()

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
otherobject to compare with
accuracyaccuracy to use for comparison (optional)
tolerantallows linient check on float equality (within accuracy)
Returns
true if all parameters were equal, false if not

Definition at line 656 of file SGObject.cpp.

◆ erfc8_weighted_sum()

float64_t erfc8_weighted_sum ( float64_t  x)
static

Use to estimates erfc(x) valid for -100 < x < -8

Parameters
xreal value
Returns
weighted sum

Definition at line 467 of file Statistics.cpp.

◆ fdistribution_cdf()

float64_t fdistribution_cdf ( float64_t  x,
float64_t  d1,
float64_t  d2 
)
static

Evaluates the CDF of the F-distribution with parameters \(d1,d2\) at \(x\). Based on Wikipedia definition.

Parameters
xposition to evaluate
d1parameter 1
d2parameter 2
Returns
F-distribution CDF at \(x\)

Definition at line 540 of file Statistics.cpp.

◆ fishers_exact_test_for_2x3_table()

float64_t fishers_exact_test_for_2x3_table ( SGMatrix< float64_t table)
static

fisher's test for 2x3 table

Parameters
table

Definition at line 186 of file Statistics.cpp.

◆ fishers_exact_test_for_multiple_2x3_tables()

SGVector< float64_t > fishers_exact_test_for_multiple_2x3_tables ( SGMatrix< float64_t tables)
static

fisher's test for multiple 2x3 tables

Parameters
tables

Definition at line 171 of file Statistics.cpp.

◆ fit_sigmoid()

CStatistics::SigmoidParamters fit_sigmoid ( SGVector< float64_t scores)
static

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

Parameters
scoresscores to fit the sigmoid to
Returns
struct containing the sigmoid's shape parameters a and b

Definition at line 824 of file Statistics.cpp.

◆ gamma_cdf()

float64_t gamma_cdf ( float64_t  x,
float64_t  a,
float64_t  b 
)
static

Evaluates the CDF of the gamma distribution, parametrized with shape and rate parameters \(\alpha, \beta\) at \(x\).

\[ \frac{\beta^\alpha}{\Gamma(\alpha)}\int _{-\infty}^x x^{\alpha-1}\exp(-t \beta)dt \]

Parameters
xArgument \(x\) to evaluate.
aShape parameter \(\alpha\)
bRate parameter \(\beta\)
Returns
Gamma CDF at \(x\)

Definition at line 398 of file Statistics.cpp.

◆ gamma_inverse_cdf()

float64_t gamma_inverse_cdf ( float64_t  p,
float64_t  a,
float64_t  b 
)
static

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 \(y\).

Parameters
pCDF value \(y\).
aShape parameter \(\alpha\)
bRate parameter \(\beta\)
Returns
Argument \(x\) that produces \(y\).

Definition at line 516 of file Statistics.cpp.

◆ get() [1/2]

T get ( const Tag< T > &  _tag) const
inherited

Getter for a class parameter, identified by a Tag. Throws an exception if the class does not have such a parameter.

Parameters
_tagname and type information of parameter
Returns
value of the parameter identified by the input tag

Definition at line 381 of file SGObject.h.

◆ get() [2/2]

T get ( const std::string &  name) const
inherited

Getter for a class parameter, identified by a name. Throws an exception if the class does not have such a parameter.

Parameters
namename of the parameter
Returns
value of the parameter corresponding to the input name and type

Definition at line 404 of file SGObject.h.

◆ get_global_io()

SGIO * get_global_io ( )
inherited

get the io object

Returns
io object

Definition at line 269 of file SGObject.cpp.

◆ get_global_parallel()

Parallel * get_global_parallel ( )
inherited

get the parallel object

Returns
parallel object

Definition at line 311 of file SGObject.cpp.

◆ get_global_version()

Version * get_global_version ( )
inherited

get the version object

Returns
version object

Definition at line 324 of file SGObject.cpp.

◆ get_modelsel_names()

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

Definition at line 536 of file SGObject.cpp.

◆ get_modsel_param_descr()

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_namename of the parameter
Returns
description of the parameter

Definition at line 560 of file SGObject.cpp.

◆ get_modsel_param_index()

index_t get_modsel_param_index ( const char *  param_name)
inherited

Returns index of model selection parameter with provided index

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

Definition at line 573 of file SGObject.cpp.

◆ get_name()

virtual const char* get_name ( ) const
virtual
Returns
object name

Implements CSGObject.

Definition at line 281 of file Statistics.h.

◆ get_parameters_observable()

SGObservable* get_parameters_observable ( )
inherited

Get parameters observable

Returns
RxCpp observable

Definition at line 415 of file SGObject.h.

◆ has() [1/3]

bool has ( const std::string &  name) const
inherited

Checks if object has a class parameter identified by a name.

Parameters
namename of the parameter
Returns
true if the parameter exists with the input name

Definition at line 304 of file SGObject.h.

◆ has() [2/3]

bool has ( const Tag< T > &  tag) const
inherited

Checks if object has a class parameter identified by a Tag.

Parameters
tagtag of the parameter containing name and type information
Returns
true if the parameter exists with the input tag

Definition at line 315 of file SGObject.h.

◆ has() [3/3]

bool has ( const std::string &  name) const
inherited

Checks if a type exists for a class parameter identified by a name.

Parameters
namename of the parameter
Returns
true if the parameter exists with the input name and type

Definition at line 326 of file SGObject.h.

◆ inverse_normal_cdf()

float64_t inverse_normal_cdf ( float64_t  y0,
float64_t  mean = 0,
float64_t  std_dev = 1 
)
static

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 \(y\).

Parameters
y0CDF value \(y\).
meanMean \(\mu\). Default value is 0.
std_devStandard deviation \(\sigma\). Default value is 1.
Returns
Argument \(x\) that produces \(y\).

Definition at line 351 of file Statistics.cpp.

◆ is_generic()

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

Definition at line 330 of file SGObject.cpp.

◆ lgamma()

static float64_t lgamma ( float64_t  x)
static
Returns
natural logarithm of the gamma function of input

Definition at line 131 of file Statistics.h.

◆ lgammal()

static floatmax_t lgammal ( floatmax_t  x)
static
Returns
natural logarithm of the gamma function of input for large numbers

Definition at line 138 of file Statistics.h.

◆ list_observable_parameters()

void list_observable_parameters ( )
inherited

Print to stdout a list of observable parameters

Definition at line 878 of file SGObject.cpp.

◆ lnormal_cdf()

float64_t lnormal_cdf ( float64_t  x)
static

Returns logarithm of the cumulative distribution function (CDF) of Gaussian distribution \(N(0, 1)\):

\[ \text{lnormal\_cdf}(x)=log\left(\frac{1}{2}+ \frac{1}{2}\text{error\_function}(\frac{x}{\sqrt{2}})\right) \]

Parameters
xEvaluate CDF here
Returns
\(log(\text{normal\_cdf}(x))\)

Definition at line 421 of file Statistics.cpp.

◆ load_serializable()

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
filewhere to load from
prefixprefix for members
Returns
TRUE if done, otherwise FALSE

Definition at line 403 of file SGObject.cpp.

◆ load_serializable_post()

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
ShogunExceptionwill be thrown if an error occurs.

Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.

Definition at line 460 of file SGObject.cpp.

◆ load_serializable_pre()

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
ShogunExceptionwill 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 455 of file SGObject.cpp.

◆ log_det() [1/2]

float64_t log_det ( SGMatrix< float64_t m)
static

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.

Parameters
minput matrix
Returns
the log determinant value

Definition at line 663 of file Statistics.cpp.

◆ log_det() [2/2]

float64_t log_det ( const SGSparseMatrix< float64_t m)
static

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 \(\text{LLT}(P\times M\times P^{-1}) = L\times L'\).

Parameters
minput sparse matrix
Returns
the log determinant value

Definition at line 686 of file Statistics.cpp.

◆ log_det_general()

float64_t log_det_general ( const SGMatrix< float64_t A)
static

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/

Parameters
Ainput matrix
Returns
the log determinant value

Definition at line 609 of file Statistics.cpp.

◆ matrix_mean()

SGVector< float64_t > matrix_mean ( SGMatrix< float64_t values,
bool  col_wise = true 
)
static

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

Parameters
valuesvector of values
col_wiseif true, every column vector will be used, row vectors otherwise
Returns
mean of given values

Definition at line 46 of file Statistics.cpp.

◆ matrix_std_deviation()

SGVector< float64_t > matrix_std_deviation ( SGMatrix< float64_t values,
bool  col_wise = true 
)
static

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

Parameters
valuesvector of values
col_wiseif true, every column vector will be used, row vectors otherwise
Returns
variance of given values

Definition at line 128 of file Statistics.cpp.

◆ matrix_variance()

SGVector< float64_t > matrix_variance ( SGMatrix< float64_t values,
bool  col_wise = true 
)
static

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

Parameters
valuesvector of values
col_wiseif true, every column vector will be used, row vectors otherwise
Returns
variance of given values

Definition at line 83 of file Statistics.cpp.

◆ mean() [1/2]

static floatmax_t mean ( SGVector< T >  vec)
static

Calculates mean of given values. Given \(\{x_1, ..., x_m\}\), this is \(\frac{1}{m}\sum_{i=1}^m x_i\)

Parameters
vecvector of values
Returns
mean of given values

Definition at line 42 of file Statistics.h.

◆ mean() [2/2]

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.

◆ mutual_info()

float64_t mutual_info ( float64_t p1,
float64_t p2,
int32_t  len 
)
static
Returns
mutual information of \(p\) which is given in logspace where \(p,q\) are given in logspace

Definition at line 294 of file Statistics.cpp.

◆ normal_cdf()

float64_t normal_cdf ( float64_t  x,
float64_t  std_dev = 1 
)
static

Evaluates the CDF of the Normal distribution, with mean \(\mu\) and standard deviation \(\sigma\), given by

\[ y=\frac{1}{\sigma \sqrt {2\pi }} \int_{-\infty}^x \exp\left(-\frac{(t-\mu)^2}{2\sigma^2}\right)dt \]

Parameters
xArgument \(x\) to evaluate.
std_devStandard deviation \(\sigma\). Default value is 1.
Returns
Gamma CDF at \(x\)

Definition at line 511 of file Statistics.cpp.

◆ observe()

void observe ( const ObservedValue  value)
protectedinherited

Observe a parameter value and emit them to observer.

Parameters
valueObserved parameter's value

Definition at line 828 of file SGObject.cpp.

◆ parameter_hash_changed()

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

Definition at line 296 of file SGObject.cpp.

◆ print_modsel_params()

void print_modsel_params ( )
inherited

prints all parameter registered for model selection and their type

Definition at line 512 of file SGObject.cpp.

◆ print_serializable()

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

prints registered parameters out

Parameters
prefixprefix for members

Definition at line 342 of file SGObject.cpp.

◆ ref()

int32_t ref ( )
inherited

increase reference counter

Returns
reference count

Definition at line 186 of file SGObject.cpp.

◆ ref_count()

int32_t ref_count ( )
inherited

display reference counter

Returns
reference count

Definition at line 193 of file SGObject.cpp.

◆ register_observable_param()

void register_observable_param ( const std::string &  name,
const SG_OBS_VALUE_TYPE  type,
const std::string &  description 
)
protectedinherited

Register which params this object can emit.

Parameters
namethe param name
typethe param type
descriptiona user oriented description

Definition at line 871 of file SGObject.cpp.

◆ register_param() [1/2]

void register_param ( Tag< T > &  _tag,
const T &  value 
)
protectedinherited

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.

Parameters
_tagname and type information of parameter
valuevalue of the parameter

Definition at line 472 of file SGObject.h.

◆ register_param() [2/2]

void register_param ( const std::string &  name,
const T &  value 
)
protectedinherited

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.

Parameters
namename of the parameter
valuevalue of the parameter along with type information

Definition at line 485 of file SGObject.h.

◆ relative_entropy()

float64_t relative_entropy ( float64_t p,
float64_t q,
int32_t  len 
)
static
Returns
relative entropy \(H(P||Q)\) where \(p,q\) are given in logspace

Definition at line 305 of file Statistics.cpp.

◆ sample_from_gaussian() [1/2]

SGMatrix< float64_t > sample_from_gaussian ( SGVector< float64_t mean,
SGMatrix< float64_t cov,
int32_t  N = 1,
bool  precision_matrix = false 
)
static

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.

Parameters
meanthe mean vector
covthe covariance matrix
Nnumber of samples
precision_matrixif true, sample from N(mu,C^-1)
Returns
the sample matrix of size \(N\times dim\)

Definition at line 706 of file Statistics.cpp.

◆ sample_from_gaussian() [2/2]

SGMatrix< float64_t > sample_from_gaussian ( SGVector< float64_t mean,
SGSparseMatrix< float64_t cov,
int32_t  N = 1,
bool  precision_matrix = false 
)
static

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.

Parameters
meanthe mean vector
covthe covariance matrix
Nnumber of samples
precision_matrixif true, sample from N(mu,C^-1)
Returns
the sample matrix of size \(N\times dim\)

Definition at line 756 of file Statistics.cpp.

◆ sample_indices()

SGVector< int32_t > sample_indices ( int32_t  sample_size,
int32_t  N 
)
static

sample indices

Parameters
sample_sizesize of sample to pick
Ntotal number of indices

Definition at line 325 of file Statistics.cpp.

◆ save_serializable()

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

Save this object to file.

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

Definition at line 348 of file SGObject.cpp.

◆ save_serializable_post()

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
ShogunExceptionwill be thrown if an error occurs.

Reimplemented in CKernel.

Definition at line 470 of file SGObject.cpp.

◆ save_serializable_pre()

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
ShogunExceptionwill 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 465 of file SGObject.cpp.

◆ set() [1/2]

void set ( const Tag< T > &  _tag,
const T &  value 
)
inherited

Setter for a class parameter, identified by a Tag. Throws an exception if the class does not have such a parameter.

Parameters
_tagname and type information of parameter
valuevalue of the parameter

Definition at line 342 of file SGObject.h.

◆ set() [2/2]

void set ( const std::string &  name,
const T &  value 
)
inherited

Setter for a class parameter, identified by a name. Throws an exception if the class does not have such a parameter.

Parameters
namename of the parameter
valuevalue of the parameter along with type information

Definition at line 368 of file SGObject.h.

◆ set_generic() [1/16]

void set_generic ( )
inherited

Definition at line 73 of file SGObject.cpp.

◆ set_generic() [2/16]

void set_generic ( )
inherited

Definition at line 78 of file SGObject.cpp.

◆ set_generic() [3/16]

void set_generic ( )
inherited

Definition at line 83 of file SGObject.cpp.

◆ set_generic() [4/16]

void set_generic ( )
inherited

Definition at line 88 of file SGObject.cpp.

◆ set_generic() [5/16]

void set_generic ( )
inherited

Definition at line 93 of file SGObject.cpp.

◆ set_generic() [6/16]

void set_generic ( )
inherited

Definition at line 98 of file SGObject.cpp.

◆ set_generic() [7/16]

void set_generic ( )
inherited

Definition at line 103 of file SGObject.cpp.

◆ set_generic() [8/16]

void set_generic ( )
inherited

Definition at line 108 of file SGObject.cpp.

◆ set_generic() [9/16]

void set_generic ( )
inherited

Definition at line 113 of file SGObject.cpp.

◆ set_generic() [10/16]

void set_generic ( )
inherited

Definition at line 118 of file SGObject.cpp.

◆ set_generic() [11/16]

void set_generic ( )
inherited

Definition at line 123 of file SGObject.cpp.

◆ set_generic() [12/16]

void set_generic ( )
inherited

Definition at line 128 of file SGObject.cpp.

◆ set_generic() [13/16]

void set_generic ( )
inherited

Definition at line 133 of file SGObject.cpp.

◆ set_generic() [14/16]

void set_generic ( )
inherited

Definition at line 138 of file SGObject.cpp.

◆ set_generic() [15/16]

void set_generic ( )
inherited

Definition at line 143 of file SGObject.cpp.

◆ set_generic() [16/16]

void set_generic ( )
inherited

set generic type to T

◆ set_global_io()

void set_global_io ( SGIO io)
inherited

set the io object

Parameters
ioio object to use

Definition at line 262 of file SGObject.cpp.

◆ set_global_parallel()

void set_global_parallel ( Parallel parallel)
inherited

set the parallel object

Parameters
parallelparallel object to use

Definition at line 275 of file SGObject.cpp.

◆ set_global_version()

void set_global_version ( Version version)
inherited

set the version object

Parameters
versionversion object to use

Definition at line 317 of file SGObject.cpp.

◆ shallow_copy()

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 226 of file SGObject.cpp.

◆ std_deviation()

float64_t std_deviation ( SGVector< float64_t values)
static

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 \(\bar x=\frac{1}{m}\sum_{i=1}^m x_i\)

Parameters
valuesvector of values
Returns
variance of given values

Definition at line 123 of file Statistics.cpp.

◆ subscribe_to_parameters()

void subscribe_to_parameters ( ParameterObserverInterface obs)
inherited

Subscribe a parameter observer to watch over params

Definition at line 811 of file SGObject.cpp.

◆ tgamma()

static float64_t tgamma ( float64_t  x)
static
Returns
gamma function of input

Definition at line 148 of file Statistics.h.

◆ unref()

int32_t unref ( )
inherited

decrement reference counter and deallocate object if refcount is zero before or after decrementing it

Returns
reference count

Definition at line 200 of file SGObject.cpp.

◆ unset_generic()

void unset_generic ( )
inherited

unset generic type

this has to be called in classes specializing a template class

Definition at line 337 of file SGObject.cpp.

◆ update_parameter_hash()

void update_parameter_hash ( )
virtualinherited

Updates the hash of current parameter combination

Definition at line 282 of file SGObject.cpp.

◆ variance()

float64_t variance ( SGVector< float64_t values)
static

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 \(\bar x=\frac{1}{m}\sum_{i=1}^m x_i\)

Parameters
valuesvector of values
Returns
variance of given values

Definition at line 32 of file Statistics.cpp.

Member Data Documentation

◆ ERFC_CASE1

const float64_t ERFC_CASE1 =0.0492
static

Magic number for computing lnormal_cdf

Definition at line 404 of file Statistics.h.

◆ ERFC_CASE2

const float64_t ERFC_CASE2 =-11.3137
static

Magic number for computing lnormal_cdf

Definition at line 407 of file Statistics.h.

◆ io

SGIO* io
inherited

io

Definition at line 600 of file SGObject.h.

◆ m_gradient_parameters

Parameter* m_gradient_parameters
inherited

parameters wrt which we can compute gradients

Definition at line 615 of file SGObject.h.

◆ m_hash

uint32_t m_hash
inherited

Hash of parameter values

Definition at line 618 of file SGObject.h.

◆ m_model_selection_parameters

Parameter* m_model_selection_parameters
inherited

model selection parameters

Definition at line 612 of file SGObject.h.

◆ m_parameters

Parameter* m_parameters
inherited

parameters

Definition at line 609 of file SGObject.h.

◆ parallel

Parallel* parallel
inherited

parallel

Definition at line 603 of file SGObject.h.

◆ version

Version* version
inherited

version

Definition at line 606 of file SGObject.h.


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

SHOGUN Machine Learning Toolbox - Documentation