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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
[legend]

List of all members.

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 bool update_parameter_hash ()
virtual bool equals (CSGObject *other, float64_t accuracy=0.0)
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 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 (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

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 1156 of file SGObject.cpp.

CSGObject * clone ( ) [virtual, inherited]

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 1273 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 341 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 317 of file Statistics.cpp.

virtual CSGObject* deep_copy ( ) const [virtual, inherited]

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

Definition at line 126 of file SGObject.h.

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 1970 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 1934 of file Statistics.cpp.

static bool equal ( float64_t  a,
float64_t  b 
) [static, protected]

method to make ALGLIB integration easier

Definition at line 592 of file Statistics.h.

bool equals ( CSGObject other,
float64_t  accuracy = 0.0 
) [virtual, inherited]

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)
Returns:
true if all parameters were equal, false if not

Definition at line 1177 of file SGObject.cpp.

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 1708 of file Statistics.cpp.

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 1747 of file Statistics.cpp.

fisher's test for 2x3 table

Parameters:
table

Definition at line 1805 of file Statistics.cpp.

fisher's test for multiple 2x3 tables

Parameters:
tables

Definition at line 1790 of file Statistics.cpp.

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 2191 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 1514 of file Statistics.cpp.

SGIO * get_global_io ( ) [inherited]

get the io object

Returns:
io object

Definition at line 174 of file SGObject.cpp.

Parallel * get_global_parallel ( ) [inherited]

get the parallel object

Returns:
parallel object

Definition at line 209 of file SGObject.cpp.

Version * get_global_version ( ) [inherited]

get the version object

Returns:
version object

Definition at line 222 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 1060 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 1084 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 1097 of file SGObject.cpp.

virtual const char* get_name ( ) const [virtual]
Returns:
object name

Implements CSGObject.

Definition at line 459 of file Statistics.h.

static bool greater ( float64_t  a,
float64_t  b 
) [static, protected]

method to make ALGLIB integration easier

Definition at line 604 of file Statistics.h.

static bool greater_equal ( float64_t  a,
float64_t  b 
) [static, protected]

method to make ALGLIB integration easier

Definition at line 607 of file Statistics.h.

float64_t ibetaf_incompletebetafe ( float64_t  a,
float64_t  b,
float64_t  x,
float64_t  big,
float64_t  biginv 
) [static, protected]

Continued fraction expansion #1 for incomplete beta integral

Taken from ALGLIB under gpl2+

Definition at line 1181 of file Statistics.cpp.

float64_t ibetaf_incompletebetafe2 ( float64_t  a,
float64_t  b,
float64_t  x,
float64_t  big,
float64_t  biginv 
) [static, protected]

Continued fraction expansion #2 for incomplete beta integral

Taken from ALGLIB under gpl2+

Definition at line 1284 of file Statistics.cpp.

float64_t ibetaf_incompletebetaps ( float64_t  a,
float64_t  b,
float64_t  x,
float64_t  maxgam 
) [static, protected]

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 1127 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 868 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 1389 of file Statistics.cpp.

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 1430 of file Statistics.cpp.

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 1520 of file Statistics.cpp.

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 416 of file Statistics.cpp.

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 1528 of file Statistics.cpp.

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 1010 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 1004 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 368 of file Statistics.cpp.

bool is_generic ( EPrimitiveType *  generic) const [virtual, inherited]

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 228 of file SGObject.cpp.

static bool less ( float64_t  a,
float64_t  b 
) [static, protected]

method to make ALGLIB integration easier

Definition at line 598 of file Statistics.h.

static bool less_equal ( float64_t  a,
float64_t  b 
) [static, protected]

method to make ALGLIB integration easier

Definition at line 601 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 1692 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 633 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 474 of file SGObject.cpp.

bool load_serializable ( CSerializableFile file,
const char *  prefix = "",
int32_t  param_version = Version::get_version_parameter() 
) [virtual, inherited]

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 305 of file SGObject.cpp.

void load_serializable_post ( ) throw (ShogunException) [protected, virtual, inherited]

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 occurres.

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

Definition at line 989 of file SGObject.cpp.

void load_serializable_pre ( ) throw (ShogunException) [protected, virtual, inherited]

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 occurres.

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

Definition at line 984 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 2019 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 2042 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 671 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 224 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 198 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 306 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 261 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 34 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 46 of file Statistics.cpp.

TParameter * migrate ( DynArray< TParameter * > *  param_base,
const SGParamInfo target 
) [protected, virtual, inherited]

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 878 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 1913 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 1687 of file Statistics.cpp.

static bool not_equal ( float64_t  a,
float64_t  b 
) [static, protected]

method to make ALGLIB integration easier

Definition at line 595 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 
) [protected, virtual, inherited]

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 818 of file SGObject.cpp.

void print_modsel_params ( ) [inherited]

prints all parameter registered for model selection and their type

Definition at line 1036 of file SGObject.cpp.

void print_serializable ( const char *  prefix = "") [virtual, inherited]

prints registered parameters out

Parameters:
prefixprefix for members

Definition at line 240 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 1924 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 2062 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 2122 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 1944 of file Statistics.cpp.

bool save_serializable ( CSerializableFile file,
const char *  prefix = "",
int32_t  param_version = Version::get_version_parameter() 
) [virtual, inherited]

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 246 of file SGObject.cpp.

void save_serializable_post ( ) throw (ShogunException) [protected, virtual, inherited]

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 occurres.

Reimplemented in CKernel.

Definition at line 999 of file SGObject.cpp.

void save_serializable_pre ( ) throw (ShogunException) [protected, virtual, inherited]

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 occurres.

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

Definition at line 994 of file SGObject.cpp.

void set_generic< complex128_t > ( ) [inherited]

set generic type to T

Definition at line 41 of file SGObject.cpp.

void set_global_io ( SGIO io) [inherited]

set the io object

Parameters:
ioio object to use

Definition at line 167 of file SGObject.cpp.

void set_global_parallel ( Parallel parallel) [inherited]

set the parallel object

Parameters:
parallelparallel object to use

Definition at line 180 of file SGObject.cpp.

void set_global_version ( Version version) [inherited]

set the version object

Parameters:
versionversion object to use

Definition at line 215 of file SGObject.cpp.

virtual CSGObject* shallow_copy ( ) const [virtual, inherited]

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

Reimplemented in CGaussianKernel.

Definition at line 117 of file SGObject.h.

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 301 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 235 of file SGObject.cpp.

bool update_parameter_hash ( ) [virtual, inherited]

Updates the hash of current parameter combination.

Returns:
bool if parameter combination has changed since last update.

Definition at line 187 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 210 of file Statistics.cpp.


Member Data Documentation

SGIO* io [inherited]

io

Definition at line 473 of file SGObject.h.

parameters wrt which we can compute gradients

Definition at line 488 of file SGObject.h.

uint32_t m_hash [inherited]

Hash of parameter values

Definition at line 494 of file SGObject.h.

model selection parameters

Definition at line 485 of file SGObject.h.

map for different parameter versions

Definition at line 491 of file SGObject.h.

Parameter* m_parameters [inherited]

parameters

Definition at line 482 of file SGObject.h.

Parallel* parallel [inherited]

parallel

Definition at line 476 of file SGObject.h.

Version* version [inherited]

version

Definition at line 479 of file SGObject.h.


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