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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 31 of file Statistics.h.

Inheritance diagram for CStatistics:
Inheritance graph
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Classes

struct  SigmoidParamters

Public Member Functions

virtual const char * get_name () const
virtual CSGObjectshallow_copy () const
virtual CSGObjectdeep_copy () const
virtual bool is_generic (EPrimitiveType *generic) const
template<class T >
void set_generic ()
void unset_generic ()
virtual void print_serializable (const char *prefix="")
virtual bool save_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=Version::get_version_parameter())
virtual bool load_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=Version::get_version_parameter())
DynArray< TParameter * > * load_file_parameters (const SGParamInfo *param_info, int32_t file_version, CSerializableFile *file, const char *prefix="")
DynArray< TParameter * > * load_all_file_parameters (int32_t file_version, int32_t current_version, CSerializableFile *file, const char *prefix="")
void map_parameters (DynArray< TParameter * > *param_base, int32_t &base_version, DynArray< const SGParamInfo * > *target_param_infos)
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 ()

Static Public Member Functions

static float64_t mean (SGVector< float64_t > values)
static float64_t median (SGVector< float64_t > values, bool modify=false, bool in_place=false)
static float64_t matrix_median (SGMatrix< float64_t > values, bool modify=false, bool in_place=false)
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 confidence_intervals_mean (SGVector< float64_t > values, float64_t alpha, float64_t &conf_int_low, float64_t &conf_int_up)
static float64_t inverse_student_t (int32_t k, float64_t p)
static float64_t inverse_incomplete_beta (float64_t a, float64_t b, float64_t y)
static float64_t incomplete_beta (float64_t a, float64_t b, float64_t x)
static float64_t inverse_normal_cdf (float64_t y0)
static float64_t inverse_normal_cdf (float64_t y0, float64_t mean, float64_t std_dev)
static float64_t lgamma (float64_t x)
static floatmax_t lgammal (floatmax_t x)
static float64_t tgamma (float64_t x)
static float64_t incomplete_gamma (float64_t a, float64_t x)
static float64_t incomplete_gamma_completed (float64_t a, float64_t x)
static float64_t gamma_cdf (float64_t x, float64_t a, float64_t b)
static float64_t inverse_gamma_cdf (float64_t p, float64_t a, float64_t b)
static float64_t inverse_incomplete_gamma_completed (float64_t a, float64_t y0)
static float64_t normal_cdf (float64_t x, 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 error_function (float64_t x)
static float64_t error_function_complement (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
ParameterMapm_parameter_map
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 TParametermigrate (DynArray< TParameter * > *param_base, const SGParamInfo *target)
virtual void one_to_one_migration_prepare (DynArray< TParameter * > *param_base, const SGParamInfo *target, TParameter *&replacement, TParameter *&to_migrate, char *old_name=NULL)
virtual void load_serializable_pre () throw (ShogunException)
virtual void load_serializable_post () throw (ShogunException)
virtual void save_serializable_pre () throw (ShogunException)
virtual void save_serializable_post () throw (ShogunException)

Static Protected Member Functions

static float64_t ibetaf_incompletebetaps (float64_t a, float64_t b, float64_t x, float64_t maxgam)
static float64_t ibetaf_incompletebetafe (float64_t a, float64_t b, float64_t x, float64_t big, float64_t biginv)
static float64_t ibetaf_incompletebetafe2 (float64_t a, float64_t b, float64_t x, float64_t big, float64_t biginv)
static bool equal (float64_t a, float64_t b)
static bool not_equal (float64_t a, float64_t b)
static bool less (float64_t a, float64_t b)
static bool less_equal (float64_t a, float64_t b)
static bool greater (float64_t a, float64_t b)
static bool greater_equal (float64_t a, float64_t b)

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
dictdictionary of parameters to be built.

Definition at line 1189 of file SGObject.cpp.

float64_t chi2_cdf ( float64_t  x,
float64_t  k 
)
static

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

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

Definition at line 1763 of file Statistics.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 1306 of file SGObject.cpp.

float64_t confidence_intervals_mean ( SGVector< float64_t values,
float64_t  alpha,
float64_t conf_int_low,
float64_t conf_int_up 
)
static

Calculates the sample mean of a given set of samples and also computes the confidence interval for the actual mean for a given p-value, assuming that the actual variance and mean are unknown (These are estimated by the samples). Based on Student's t-distribution.

Only for normally distributed data

Parameters
valuesvector of values that are used for calculations
alphaactual mean lies in confidence interval with (1-alpha)*100%
conf_int_lowlower confidence interval border is written here
conf_int_upupper confidence interval border is written here
Returns
sample mean

Definition at line 347 of file Statistics.cpp.

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

Computes the empirical estimate of the covariance matrix of the given data which is organized as num_cols variables with num_rows observations.

Data is centered before matrix is computed. May be done in place. In this case, the observation matrix is changed (centered).

Given sample matrix \(X\), first, column mean is removed to create \(\bar X\). Then \(\text{cov}(X)=(X-\bar X)^T(X - \bar X)\) is returned.

Needs SHOGUN to be compiled with LAPACK.

Parameters
observationsdata matrix organized as one variable per column
in_placeoptional, if set to true, observations matrix will be centered, if false, a copy will be created an centered.
Returns
covariance matrix empirical estimate

Definition at line 323 of file Statistics.cpp.

CSGObject * deep_copy ( ) const
virtualinherited

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

Definition at line 146 of file SGObject.cpp.

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 2083 of file Statistics.cpp.

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

Definition at line 2047 of file Statistics.cpp.

static bool equal ( float64_t  a,
float64_t  b 
)
staticprotected

method to make ALGLIB integration easier

Definition at line 639 of file Statistics.h.

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 1210 of file SGObject.cpp.

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 1775 of file Statistics.cpp.

float64_t error_function ( float64_t  x)
static

Error function

The integral is

\[ \text{error\_function}(x)= \frac{2}{\sqrt{pi}}\int_0^x \exp (-t^2) dt \]

For \(0 \leq |x| < 1, \text{error\_function}(x) = x \frac{P4(x^2)}{Q5(x^2)}\) otherwise \(\text{error\_function}(x) = 1 - \text{error\_function\_complement}(x)\).

Taken from ALGLIB under gpl2+

Definition at line 1821 of file Statistics.cpp.

float64_t error_function_complement ( float64_t  x)
static

Complementary error function

\[ 1 - \text{error\_function}(x) = \text{error\_function\_complement}(x)= \frac{2}{\sqrt{\pi}}\int_x^\infty \exp\left(-t^2 \right)dt \]

For small \(x\), \(\text{error\_function\_complement}(x) = 1 - \text{error\_function}(x)\); otherwise rational approximations are computed.

Taken from ALGLIB under gpl2+

Definition at line 1860 of file Statistics.cpp.

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 1769 of file Statistics.cpp.

float64_t fishers_exact_test_for_2x3_table ( SGMatrix< float64_t table)
static

fisher's test for 2x3 table

Parameters
table

Definition at line 1918 of file Statistics.cpp.

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 1903 of file Statistics.cpp.

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 2348 of file Statistics.cpp.

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

Evaluates the CDF of the gamma distribution with given parameters \(a, b\) at \(x\). Based on Wikipedia definition and ALGLIB routines.

Parameters
xposition to evaluate
ashape parameter
bscale parameter
Returns
gamma CDF at \(x\)

Definition at line 1520 of file Statistics.cpp.

SGIO * get_global_io ( )
inherited

get the io object

Returns
io object

Definition at line 183 of file SGObject.cpp.

Parallel * get_global_parallel ( )
inherited

get the parallel object

Returns
parallel object

Definition at line 224 of file SGObject.cpp.

Version * get_global_version ( )
inherited

get the version object

Returns
version object

Definition at line 237 of file SGObject.cpp.

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

Definition at line 1081 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_namename of the parameter
Returns
description of the parameter

Definition at line 1105 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_namename of model selection parameter
Returns
index of model selection parameter with provided name, -1 if there is no such

Definition at line 1118 of file SGObject.cpp.

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

Implements CSGObject.

Definition at line 485 of file Statistics.h.

static bool greater ( float64_t  a,
float64_t  b 
)
staticprotected

method to make ALGLIB integration easier

Definition at line 651 of file Statistics.h.

static bool greater_equal ( float64_t  a,
float64_t  b 
)
staticprotected

method to make ALGLIB integration easier

Definition at line 654 of file Statistics.h.

float64_t ibetaf_incompletebetafe ( float64_t  a,
float64_t  b,
float64_t  x,
float64_t  big,
float64_t  biginv 
)
staticprotected

Continued fraction expansion #1 for incomplete beta integral

Taken from ALGLIB under gpl2+

Definition at line 1187 of file Statistics.cpp.

float64_t ibetaf_incompletebetafe2 ( float64_t  a,
float64_t  b,
float64_t  x,
float64_t  big,
float64_t  biginv 
)
staticprotected

Continued fraction expansion #2 for incomplete beta integral

Taken from ALGLIB under gpl2+

Definition at line 1290 of file Statistics.cpp.

float64_t ibetaf_incompletebetaps ( float64_t  a,
float64_t  b,
float64_t  x,
float64_t  maxgam 
)
staticprotected

Power series for incomplete beta integral. Use when \(bx\) is small and \(x\) not too close to \(1\).

Taken from ALGLIB under gpl2+

Definition at line 1133 of file Statistics.cpp.

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

Incomplete beta integral

Returns incomplete beta integral of the arguments, evaluated from zero to \(x\). The function is defined as

\[ \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}\int_0^x t^{a-1} (1-t)^{b-1} dt. \]

The domain of definition is \(0 \leq x \leq 1\). In this implementation \(a\) and \(b\) are restricted to positive values. The integral from \(x\) to \(1\) may be obtained by the symmetry relation

\[ 1-\text{incomplete\_beta}(a,b,x)=\text{incomplete\_beta}(b,a,1-x). \]

The integral is evaluated by a continued fraction expansion or, when \(b\cdot x\) is small, by a power series.

Taken from ALGLIB under gpl2+

Definition at line 874 of file Statistics.cpp.

float64_t incomplete_gamma ( float64_t  a,
float64_t  x 
)
static

Incomplete gamma integral

Given \(p\), the function finds \(x\) such that

\[ \text{incomplete\_gamma}(a,x)=\frac{1}{\Gamma(a)}}\int_0^x e^{-t} t^{a-1} dt. \]

In this implementation both arguments must be positive. The integral is evaluated by either a power series or continued fraction expansion, depending on the relative values of \(a\) and \(x\).

Taken from ALGLIB under gpl2+

Definition at line 1395 of file Statistics.cpp.

float64_t incomplete_gamma_completed ( float64_t  a,
float64_t  x 
)
static

Complemented incomplete gamma integral

The function is defined by

\[ \text{incomplete\_gamma\_completed}(a,x)=1-\text{incomplete\_gamma}(a,x) = \frac{1}{\Gamma (a)}\int_x^\infty e^{-t} t^{a-1} dt \]

In this implementation both arguments must be positive. The integral is evaluated by either a power series or continued fraction expansion, depending on the relative values of \(a\) and \(x\).

Taken from ALGLIB under gpl2+

Definition at line 1436 of file Statistics.cpp.

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

Evaluates the inverse CDF of the gamma distribution with given parameters \(a\), \(b\) at \(x\), such that result equals \(\text{gamma\_cdf}(x,a,b)\).

Parameters
pposition to evaluate
ashape parameter
bscale parameter
Returns
\(x\) such that result equals \(\text{gamma\_cdf}(x,a,b)\).

Definition at line 1526 of file Statistics.cpp.

float64_t inverse_incomplete_beta ( float64_t  a,
float64_t  b,
float64_t  y 
)
static

Inverse of incomplete beta integral

Given \(y\), the function finds \(x\) such that

\(\text{inverse\_incomplete\_beta}( a, b, x ) = y .\)

The routine performs interval halving or Newton iterations to find the root of \(\text{inverse\_incomplete\_beta}( a, b, x )-y=0.\)

Taken from ALGLIB under gpl2+

Definition at line 422 of file Statistics.cpp.

float64_t inverse_incomplete_gamma_completed ( float64_t  a,
float64_t  y0 
)
static

Inverse of complemented incomplete gamma integral

Given \(p\), the function finds \(x\) such that

\(\text{inverse\_incomplete\_gamma\_completed}( a, x ) = p.\)

Starting with the approximate value \( x=a t^3\), where \( t = 1 - d - \text{ndtri}(p) \sqrt{d} \) and \( d = \frac{1}{9}a \)

The routine performs up to 10 Newton iterations to find the root of \( \text{inverse\_incomplete\_gamma\_completed}( a, x )-p=0\)

Taken from ALGLIB under gpl2+

Definition at line 1534 of file Statistics.cpp.

float64_t inverse_normal_cdf ( float64_t  y0)
static

Inverse of Normal distribution function

Returns the argument, \(x\), for which the area under the Gaussian probability density function (integrated from minus infinity to \(x\)) is equal to \(y\).

For small arguments \(0 < y < \exp(-2)\), the program computes \(z = \sqrt{ -2.0 \log(y) }\); then the approximation is \(x = z - \frac{log(z)}{z} - \frac{1}{z} \frac{P(\frac{1}{z})}{ Q(\frac{1}{z}}\). There are two rational functions \(\frac{P}{Q}\), one for \(0 < y < \exp(-32)\) and the other for \(y\) up to \(\exp(-2)\). For larger arguments, \(w = y - 0.5\), and \(\frac{x}{\sqrt{2\pi}} = w + w^3 R(\frac{w^2)}{S(w^2)})\).

Taken from ALGLIB under gpl2+

Definition at line 1016 of file Statistics.cpp.

float64_t inverse_normal_cdf ( float64_t  y0,
float64_t  mean,
float64_t  std_dev 
)
static

same as other version, but with custom mean and variance

Definition at line 1010 of file Statistics.cpp.

float64_t inverse_student_t ( int32_t  k,
float64_t  p 
)
static

Functional inverse of Student's t distribution

Given probability \(p\), finds the argument \(t\) such that \(\text{student\_t}(k,t)=p\)

Taken from ALGLIB under gpl2+

Definition at line 374 of file Statistics.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
genericset to the type of the generic if returning TRUE
Returns
TRUE if a class template.

Definition at line 243 of file SGObject.cpp.

static bool less ( float64_t  a,
float64_t  b 
)
staticprotected

method to make ALGLIB integration easier

Definition at line 645 of file Statistics.h.

static bool less_equal ( float64_t  a,
float64_t  b 
)
staticprotected

method to make ALGLIB integration easier

Definition at line 648 of file Statistics.h.

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

Definition at line 265 of file Statistics.h.

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

Definition at line 272 of file Statistics.h.

float64_t lnormal_cdf ( float64_t  x)
static

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

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

This method uses asymptotic expansion for \(x<-10.0\), otherwise it returns \(log(\text{normal\_cdf}(x))\).

Parameters
xreal value
Returns
\(log(\text{normal\_cdf}(x))\)

Definition at line 1703 of file Statistics.cpp.

DynArray< TParameter * > * load_all_file_parameters ( int32_t  file_version,
int32_t  current_version,
CSerializableFile file,
const char *  prefix = "" 
)
inherited

maps all parameters of this instance to the provided file version and loads all parameter data from the file into an array, which is sorted (basically calls load_file_parameter(...) for all parameters and puts all results into a sorted array)

Parameters
file_versionparameter version of the file
current_versionversion from which mapping begins (you want to use Version::get_version_parameter() for this in most cases)
filefile to load from
prefixprefix for members
Returns
(sorted) array of created TParameter instances with file data

Definition at line 650 of file SGObject.cpp.

DynArray< TParameter * > * load_file_parameters ( const SGParamInfo param_info,
int32_t  file_version,
CSerializableFile file,
const char *  prefix = "" 
)
inherited

loads some specified parameters from a file with a specified version The provided parameter info has a version which is recursively mapped until the file parameter version is reached. Note that there may be possibly multiple parameters in the mapping, therefore, a set of TParameter instances is returned

Parameters
param_infoinformation of parameter
file_versionparameter version of the file, must be <= provided parameter version
filefile to load from
prefixprefix for members
Returns
new array with TParameter instances with the attached data

Definition at line 491 of file SGObject.cpp.

bool load_serializable ( CSerializableFile file,
const char *  prefix = "",
int32_t  param_version = Version::get_version_parameter() 
)
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
param_version(optional) a parameter version different to (this is mainly for testing, better do not use)
Returns
TRUE if done, otherwise FALSE

Definition at line 320 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
ShogunExceptionwill be thrown if an error occurs.

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

Definition at line 1008 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
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 1003 of file SGObject.cpp.

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 2186 of file Statistics.cpp.

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 2209 of file Statistics.cpp.

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 2132 of file Statistics.cpp.

void map_parameters ( DynArray< TParameter * > *  param_base,
int32_t &  base_version,
DynArray< const SGParamInfo * > *  target_param_infos 
)
inherited

Takes a set of TParameter instances (base) with a certain version and a set of target parameter infos and recursively maps the base level wise to the current version using CSGObject::migrate(...). The base is replaced. After this call, the base version containing parameters should be of same version/type as the initial target parameter infos. Note for this to work, the migrate methods and all the internal parameter mappings have to match

Parameters
param_baseset of TParameter instances that are mapped to the provided target parameter infos
base_versionversion of the parameter base
target_param_infosset of SGParamInfo instances that specify the target parameter base

Definition at line 688 of file SGObject.cpp.

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 230 of file Statistics.cpp.

float64_t matrix_median ( SGMatrix< float64_t values,
bool  modify = false,
bool  in_place = false 
)
static

Calculates median of given values. Matrix is seen as a long vector for this. The median is the value that one gets when the input vector is sorted and then selects the middle value.

This method is just a wrapper for median(). See this method for license of QuickSelect and Torben.

Parameters
valuesvector of values
modifyif false, array is modified while median is computed (Using QuickSelect). If true, median is computed without modifications, which is slower. There are two methods to choose from.
in_placeif set false, the vector is copied and then computed using QuickSelect. If set true, median is computed in-place using Torben method.
Returns
median of given values

Definition at line 204 of file Statistics.cpp.

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 312 of file Statistics.cpp.

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 267 of file Statistics.cpp.

float64_t mean ( SGVector< float64_t values)
static

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

Parameters
valuesvector of values
Returns
mean of given values

Definition at line 40 of file Statistics.cpp.

float64_t median ( SGVector< float64_t values,
bool  modify = false,
bool  in_place = false 
)
static

Calculates median of given values. The median is the value that one gets when the input vector is sorted and then selects the middle value.

QuickSelect method copyright: This Quickselect routine is based on the algorithm described in "Numerical recipes in C", Second Edition, Cambridge University Press, 1992, Section 8.5, ISBN 0-521-43108-5 This code by Nicolas Devillard - 1998. Public domain.

Torben method copyright: The following code is public domain. Algorithm by Torben Mogensen, implementation by N. Devillard. Public domain.

Both methods adapted to SHOGUN by Heiko Strathmann.

Parameters
valuesvector of values
modifyif false, array is modified while median is computed (Using QuickSelect). If true, median is computed without modifications, which is slower. There are two methods to choose from.
in_placeif set false, the vector is copied and then computed using QuickSelect. If set true, median is computed in-place using Torben method.
Returns
median of given values

Definition at line 52 of file Statistics.cpp.

TParameter * migrate ( DynArray< TParameter * > *  param_base,
const SGParamInfo target 
)
protectedvirtualinherited

creates a new TParameter instance, which contains migrated data from the version that is provided. The provided parameter data base is used for migration, this base is a collection of all parameter data of the previous version. Migration is done FROM the data in param_base TO the provided param info Migration is always one version step. Method has to be implemented in subclasses, if no match is found, base method has to be called.

If there is an element in the param_base which equals the target, a copy of the element is returned. This represents the case when nothing has changed and therefore, the migrate method is not overloaded in a subclass

Parameters
param_baseset of TParameter instances to use for migration
targetparameter info for the resulting TParameter
Returns
a new TParameter instance with migrated data from the base of the type which is specified by the target parameter

Definition at line 895 of file SGObject.cpp.

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 2026 of file Statistics.cpp.

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

Normal distribution function

Returns the area under the Gaussian probability density function, integrated from minus infinity to \(x\):

\[ \text{normal\_cdf}(x)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^x \exp \left( -\frac{t^2}{2} \right) dt = \frac{1+\text{error\_function}(z) }{2} \]

where \( z = \frac{x}{\sqrt{2} \sigma}\) and \( \sigma \) is the standard deviation. Computation is via the functions \(\text{error\_function}\) and \(\text{error\_function\_completement}\).

Taken from ALGLIB under gpl2+ Custom variance added by Heiko Strathmann

Definition at line 1693 of file Statistics.cpp.

static bool not_equal ( float64_t  a,
float64_t  b 
)
staticprotected

method to make ALGLIB integration easier

Definition at line 642 of file Statistics.h.

void one_to_one_migration_prepare ( DynArray< TParameter * > *  param_base,
const SGParamInfo target,
TParameter *&  replacement,
TParameter *&  to_migrate,
char *  old_name = NULL 
)
protectedvirtualinherited

This method prepares everything for a one-to-one parameter migration. One to one here means that only ONE element of the parameter base is needed for the migration (the one with the same name as the target). Data is allocated for the target (in the type as provided in the target SGParamInfo), and a corresponding new TParameter instance is written to replacement. The to_migrate pointer points to the single needed TParameter instance needed for migration. If a name change happened, the old name may be specified by old_name. In addition, the m_delete_data flag of to_migrate is set to true. So if you want to migrate data, the only thing to do after this call is converting the data in the m_parameter fields. If unsure how to use - have a look into an example for this. (base_migration_type_conversion.cpp for example)

Parameters
param_baseset of TParameter instances to use for migration
targetparameter info for the resulting TParameter
replacement(used as output) here the TParameter instance which is returned by migration is created into
to_migratethe only source that is used for migration
old_namewith this parameter, a name change may be specified

Definition at line 835 of file SGObject.cpp.

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

Definition at line 209 of file SGObject.cpp.

void print_modsel_params ( )
inherited

prints all parameter registered for model selection and their type

Definition at line 1057 of file SGObject.cpp.

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

prints registered parameters out

Parameters
prefixprefix for members

Definition at line 255 of file SGObject.cpp.

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 2037 of file Statistics.cpp.

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 2229 of file Statistics.cpp.

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 2279 of file Statistics.cpp.

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 2057 of file Statistics.cpp.

bool save_serializable ( CSerializableFile file,
const char *  prefix = "",
int32_t  param_version = Version::get_version_parameter() 
)
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
param_version(optional) a parameter version different to (this is mainly for testing, better do not use)
Returns
TRUE if done, otherwise FALSE

Definition at line 261 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
ShogunExceptionwill be thrown if an error occurs.

Reimplemented in CKernel.

Definition at line 1018 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
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 1013 of file SGObject.cpp.

void set_generic< complex128_t > ( )
inherited

set generic type to T

Definition at line 38 of file SGObject.cpp.

void set_global_io ( SGIO io)
inherited

set the io object

Parameters
ioio object to use

Definition at line 176 of file SGObject.cpp.

void set_global_parallel ( Parallel parallel)
inherited

set the parallel object

Parameters
parallelparallel object to use

Definition at line 189 of file SGObject.cpp.

void set_global_version ( Version version)
inherited

set the version object

Parameters
versionversion object to use

Definition at line 230 of file SGObject.cpp.

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 140 of file SGObject.cpp.

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 307 of file Statistics.cpp.

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

Definition at line 282 of file Statistics.h.

void unset_generic ( )
inherited

unset generic type

this has to be called in classes specializing a template class

Definition at line 250 of file SGObject.cpp.

void update_parameter_hash ( )
virtualinherited

Updates the hash of current parameter combination

Definition at line 196 of file SGObject.cpp.

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 216 of file Statistics.cpp.

Member Data Documentation

const float64_t ERFC_CASE1 = 0.0492
static

Magic number for computing lnormal_cdf

Definition at line 610 of file Statistics.h.

const float64_t ERFC_CASE2 = -11.3137
static

Magic number for computing lnormal_cdf

Definition at line 613 of file Statistics.h.

SGIO* io
inherited

io

Definition at line 457 of file SGObject.h.

Parameter* m_gradient_parameters
inherited

parameters wrt which we can compute gradients

Definition at line 472 of file SGObject.h.

uint32_t m_hash
inherited

Hash of parameter values

Definition at line 478 of file SGObject.h.

Parameter* m_model_selection_parameters
inherited

model selection parameters

Definition at line 469 of file SGObject.h.

ParameterMap* m_parameter_map
inherited

map for different parameter versions

Definition at line 475 of file SGObject.h.

Parameter* m_parameters
inherited

parameters

Definition at line 466 of file SGObject.h.

Parallel* parallel
inherited

parallel

Definition at line 460 of file SGObject.h.

Version* version
inherited

version

Definition at line 463 of file SGObject.h.


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

SHOGUN Machine Learning Toolbox - Documentation