Class that contains certain functions related to statistics, such as probability/cumulative distribution functions, different statistics, etc.
在文件 Statistics.h 第 32 行定义.
类 | |
struct | SigmoidParamters |
Public 成员函数 | |
virtual const char * | get_name () const |
template<> | |
floatmax_t | mean (SGVector< complex128_t > vec) |
mean not implemented for complex128_t, returns 0.0 instead 更多... | |
virtual CSGObject * | shallow_copy () const |
virtual CSGObject * | deep_copy () const |
virtual bool | is_generic (EPrimitiveType *generic) const |
template<class T > | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
template<> | |
void | set_generic () |
void | unset_generic () |
virtual void | print_serializable (const char *prefix="") |
virtual bool | save_serializable (CSerializableFile *file, const char *prefix="") |
virtual bool | load_serializable (CSerializableFile *file, const char *prefix="") |
void | set_global_io (SGIO *io) |
SGIO * | get_global_io () |
void | set_global_parallel (Parallel *parallel) |
Parallel * | get_global_parallel () |
void | set_global_version (Version *version) |
Version * | get_global_version () |
SGStringList< char > | get_modelsel_names () |
void | print_modsel_params () |
char * | get_modsel_param_descr (const char *param_name) |
index_t | get_modsel_param_index (const char *param_name) |
void | build_gradient_parameter_dictionary (CMap< TParameter *, CSGObject * > *dict) |
virtual void | update_parameter_hash () |
virtual bool | parameter_hash_changed () |
virtual bool | equals (CSGObject *other, float64_t accuracy=0.0, bool tolerant=false) |
virtual CSGObject * | clone () |
Public 属性 | |
SGIO * | io |
Parallel * | parallel |
Version * | version |
Parameter * | m_parameters |
Parameter * | m_model_selection_parameters |
Parameter * | m_gradient_parameters |
uint32_t | m_hash |
静态 Public 属性 | |
static const float64_t | ERFC_CASE1 =0.0492 |
static const float64_t | ERFC_CASE2 =-11.3137 |
Protected 成员函数 | |
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) |
静态 Protected 成员函数 | |
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) |
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Builds a dictionary of all parameters in SGObject as well of those of SGObjects that are parameters of this object. Dictionary maps parameters to the objects that own them.
dict | dictionary of parameters to be built. |
在文件 SGObject.cpp 第 597 行定义.
Evaluates the CDF of the chi square distribution with parameter k at \(x\). Based on Wikipedia definition.
x | position to evaluate |
k | parameter |
在文件 Statistics.cpp 第 1751 行定义.
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virtualinherited |
Creates a clone of the current object. This is done via recursively traversing all parameters, which corresponds to a deep copy. Calling equals on the cloned object always returns true although none of the memory of both objects overlaps.
在文件 SGObject.cpp 第 714 行定义.
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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
values | vector of values that are used for calculations |
alpha | actual mean lies in confidence interval with (1-alpha)*100% |
conf_int_low | lower confidence interval border is written here |
conf_int_up | upper confidence interval border is written here |
在文件 Statistics.cpp 第 335 行定义.
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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.
observations | data matrix organized as one variable per column |
in_place | optional, if set to true, observations matrix will be centered, if false, a copy will be created an centered. |
在文件 Statistics.cpp 第 311 行定义.
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virtualinherited |
A deep copy. All the instance variables will also be copied.
在文件 SGObject.cpp 第 198 行定义.
Derivative of the log gamma function.
x | input |
在文件 Statistics.cpp 第 2071 行定义.
在文件 Statistics.cpp 第 2035 行定义.
method to make ALGLIB integration easier
在文件 Statistics.h 第 649 行定义.
Recursively compares the current SGObject to another one. Compares all registered numerical parameters, recursion upon complex (SGObject) parameters. Does not compare pointers!
May be overwritten but please do with care! Should not be necessary in most cases.
other | object to compare with |
accuracy | accuracy to use for comparison (optional) |
tolerant | allows linient check on float equality (within accuracy) |
在文件 SGObject.cpp 第 618 行定义.
Use to estimates erfc(x) valid for -100 < x < -8
x | real value |
在文件 Statistics.cpp 第 1763 行定义.
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+
在文件 Statistics.cpp 第 1809 行定义.
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+
在文件 Statistics.cpp 第 1848 行定义.
Evaluates the CDF of the F-distribution with parameters \(d1,d2\) at \(x\). Based on Wikipedia definition.
x | position to evaluate |
d1 | parameter 1 |
d2 | parameter 2 |
在文件 Statistics.cpp 第 1757 行定义.
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Converts a given vector of scores to calibrated probabilities by fitting a sigmoid function using the method described in Lin, H., Lin, C., and Weng, R. (2007). A note on Platt's probabilistic outputs for support vector machines.
This can be used to transform scores to probabilities as setting \(pf=x*a+b\) for a given score \(x\) and computing \(\frac{\exp(-f)}{1+}exp(-f)}\) if \(f\geq 0\) and \(\frac{1}{(1+\exp(f)}\) otherwise
scores | scores to fit the sigmoid to |
在文件 Statistics.cpp 第 2336 行定义.
Evaluates the CDF of the gamma distribution with given parameters \(a, b\) at \(x\). Based on Wikipedia definition and ALGLIB routines.
x | position to evaluate |
a | shape parameter |
b | scale parameter |
在文件 Statistics.cpp 第 1508 行定义.
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inherited |
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inherited |
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inherited |
在文件 SGObject.cpp 第 498 行定义.
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Returns description of a given parameter string, if it exists. SG_ERROR otherwise
param_name | name of the parameter |
在文件 SGObject.cpp 第 522 行定义.
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inherited |
Returns index of model selection parameter with provided index
param_name | name of model selection parameter |
在文件 SGObject.cpp 第 535 行定义.
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method to make ALGLIB integration easier
在文件 Statistics.h 第 661 行定义.
method to make ALGLIB integration easier
在文件 Statistics.h 第 664 行定义.
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Continued fraction expansion #1 for incomplete beta integral
Taken from ALGLIB under gpl2+
在文件 Statistics.cpp 第 1175 行定义.
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Continued fraction expansion #2 for incomplete beta integral
Taken from ALGLIB under gpl2+
在文件 Statistics.cpp 第 1278 行定义.
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Power series for incomplete beta integral. Use when \(bx\) is small and \(x\) not too close to \(1\).
Taken from ALGLIB under gpl2+
在文件 Statistics.cpp 第 1121 行定义.
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+
在文件 Statistics.cpp 第 862 行定义.
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+
在文件 Statistics.cpp 第 1383 行定义.
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+
在文件 Statistics.cpp 第 1424 行定义.
Evaluates the inverse CDF of the gamma distribution with given parameters \(a\), \(b\) at \(x\), such that result equals \(\text{gamma\_cdf}(x,a,b)\).
p | position to evaluate |
a | shape parameter |
b | scale parameter |
在文件 Statistics.cpp 第 1514 行定义.
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+
在文件 Statistics.cpp 第 410 行定义.
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+
在文件 Statistics.cpp 第 1522 行定义.
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+
在文件 Statistics.cpp 第 1004 行定义.
same as other version, but with custom mean and variance
在文件 Statistics.cpp 第 998 行定义.
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+
在文件 Statistics.cpp 第 362 行定义.
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virtualinherited |
If the SGSerializable is a class template then TRUE will be returned and GENERIC is set to the type of the generic.
generic | set to the type of the generic if returning TRUE |
在文件 SGObject.cpp 第 296 行定义.
method to make ALGLIB integration easier
在文件 Statistics.h 第 655 行定义.
method to make ALGLIB integration easier
在文件 Statistics.h 第 658 行定义.
在文件 Statistics.h 第 275 行定义.
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在文件 Statistics.h 第 282 行定义.
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 \(log(\text{normal\_cdf}(x))\).
x | real value |
在文件 Statistics.cpp 第 1691 行定义.
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Load this object from file. If it will fail (returning FALSE) then this object will contain inconsistent data and should not be used!
file | where to load from |
prefix | prefix for members |
在文件 SGObject.cpp 第 369 行定义.
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protectedvirtualinherited |
Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_POST is called.
ShogunException | will be thrown if an error occurs. |
被 CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel , 以及 CExponentialKernel 重载.
在文件 SGObject.cpp 第 426 行定义.
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protectedvirtualinherited |
Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_PRE is called.
ShogunException | will be thrown if an error occurs. |
被 CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool > , 以及 CDynamicObjectArray 重载.
在文件 SGObject.cpp 第 421 行定义.
The log determinant of a dense matrix
The log determinant of a positive definite symmetric real valued matrix is calculated as
\[ \text{log\_determinant}(M) = \text{log}(\text{determinant}(L)\times\text{determinant}(L')) = 2\times \sum_{i}\text{log}(L_{i,i}) \]
Where, \(M = L\times L'\) as per Cholesky decomposition.
m | input matrix |
在文件 Statistics.cpp 第 2174 行定义.
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The log determinant of a sparse matrix
The log determinant of symmetric positive definite sparse matrix is calculated in a similar way as the dense case. But using cholesky decomposition on sparse matrices may suffer from fill-in phenomenon, i.e. the factors may not be as sparse. The SimplicialCholesky module for sparse matrix in eigen3 library uses an approach called approximate minimum degree reordering, or amd, which permutes the matrix beforehand and results in much sparser factors. If \(P\) is the permutation matrix, it computes \(\text{LLT}(P\times M\times P^{-1}) = L\times L'\).
m | input sparse matrix |
在文件 Statistics.cpp 第 2197 行定义.
The log determinant of a dense matrix
If determinant of the input matrix is positive, it returns the logarithm of the value. If not, it returns CMath::INFTY Note that the input matrix is not required to be symmetric positive definite. This method is slower than log_det() if input matrix is known to be symmetric positive definite
It is adapted from Gaussian Process Machine Learning Toolbox http://www.gaussianprocess.org/gpml/code/matlab/doc/
A | input matrix |
在文件 Statistics.cpp 第 2120 行定义.
Calculates mean of given values. Given \(\{x_1, ..., x_m\}\), this is \(\frac{1}{m}\sum_{i=1}^m x_i\)
Computes the mean for each row/col of matrix
values | vector of values |
col_wise | if true, every column vector will be used, row vectors otherwise |
在文件 Statistics.cpp 第 218 行定义.
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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.
values | vector of values |
modify | if 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_place | if set false, the vector is copied and then computed using QuickSelect. If set true, median is computed in-place using Torben method. |
在文件 Statistics.cpp 第 192 行定义.
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Calculates unbiased empirical standard deviation estimator of given values. Given \(\{x_1, ..., x_m\}\), this is \(\sqrt{\frac{1}{m-1}\sum_{i=1}^m (x-\bar{x})^2}\) where \(\bar x=\frac{1}{m}\sum_{i=1}^m x_i\)
Computes the variance for each row/col of matrix
values | vector of values |
col_wise | if true, every column vector will be used, row vectors otherwise |
在文件 Statistics.cpp 第 300 行定义.
Calculates unbiased empirical variance estimator of given values. Given \(\{x_1, ..., x_m\}\), this is \(\frac{1}{m-1}\sum_{i=1}^m (x-\bar{x})^2\) where \(\bar x=\frac{1}{m}\sum_{i=1}^m x_i\)
Computes the variance for each row/col of matrix
values | vector of values |
col_wise | if true, every column vector will be used, row vectors otherwise |
在文件 Statistics.cpp 第 255 行定义.
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Calculates mean of given values. Given \(\{x_1, ..., x_m\}\), this is \(\frac{1}{m}\sum_{i=1}^m x_i\)
vec | vector of values |
在文件 Statistics.h 第 44 行定义.
floatmax_t mean | ( | SGVector< complex128_t > | vec | ) |
mean not implemented for complex128_t, returns 0.0 instead
在文件 Statistics.h 第 669 行定义.
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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.
values | vector of values |
modify | if 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_place | if set false, the vector is copied and then computed using QuickSelect. If set true, median is computed in-place using Torben method. |
在文件 Statistics.cpp 第 40 行定义.
在文件 Statistics.cpp 第 2014 行定义.
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
在文件 Statistics.cpp 第 1681 行定义.
method to make ALGLIB integration easier
在文件 Statistics.h 第 652 行定义.
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在文件 SGObject.cpp 第 262 行定义.
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prints all parameter registered for model selection and their type
在文件 SGObject.cpp 第 474 行定义.
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在文件 Statistics.cpp 第 2025 行定义.
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Sampling from a multivariate Gaussian distribution with dense covariance matrix
Sampling is performed by taking samples from \(N(0, I)\), then using cholesky factor of the covariance matrix, \(\Sigma\) and performing
\[S_{N(\mu,\Sigma)}=S_{N(0,I)}*L^{T}+\mu\]
where \(\Sigma=L*L^{T}\) and \(\mu\) is the mean vector.
mean | the mean vector |
cov | the covariance matrix |
N | number of samples |
precision_matrix | if true, sample from N(mu,C^-1) |
在文件 Statistics.cpp 第 2217 行定义.
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Sampling from a multivariate Gaussian distribution with sparse covariance matrix
Sampling is performed in similar way as of dense covariance matrix, but direct cholesky factorization of sparse matrices could be inefficient. So, this method uses permutation matrix for factorization and then permutes back the final samples before adding the mean.
mean | the mean vector |
cov | the covariance matrix |
N | number of samples |
precision_matrix | if true, sample from N(mu,C^-1) |
在文件 Statistics.cpp 第 2267 行定义.
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sample indices
sample_size | size of sample to pick |
N | total number of indices |
在文件 Statistics.cpp 第 2045 行定义.
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Save this object to file.
file | where to save the object; will be closed during returning if PREFIX is an empty string. |
prefix | prefix for members |
在文件 SGObject.cpp 第 314 行定义.
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Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_POST is called.
ShogunException | will be thrown if an error occurs. |
被 CKernel 重载.
在文件 SGObject.cpp 第 436 行定义.
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protectedvirtualinherited |
Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_PRE is called.
ShogunException | will be thrown if an error occurs. |
被 CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool > , 以及 CDynamicObjectArray 重载.
在文件 SGObject.cpp 第 431 行定义.
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在文件 SGObject.cpp 第 41 行定义.
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在文件 SGObject.cpp 第 46 行定义.
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在文件 SGObject.cpp 第 51 行定义.
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在文件 SGObject.cpp 第 56 行定义.
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在文件 SGObject.cpp 第 61 行定义.
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在文件 SGObject.cpp 第 66 行定义.
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在文件 SGObject.cpp 第 71 行定义.
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在文件 SGObject.cpp 第 76 行定义.
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在文件 SGObject.cpp 第 81 行定义.
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在文件 SGObject.cpp 第 86 行定义.
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在文件 SGObject.cpp 第 91 行定义.
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在文件 SGObject.cpp 第 96 行定义.
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在文件 SGObject.cpp 第 101 行定义.
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在文件 SGObject.cpp 第 106 行定义.
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在文件 SGObject.cpp 第 111 行定义.
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set generic type to T
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A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.
被 CGaussianKernel 重载.
在文件 SGObject.cpp 第 192 行定义.
Calculates unbiased empirical standard deviation estimator of given values. Given \(\{x_1, ..., x_m\}\), this is \(\sqrt{\frac{1}{m-1}\sum_{i=1}^m (x-\bar{x})^2}\) where \(\bar x=\frac{1}{m}\sum_{i=1}^m x_i\)
values | vector of values |
在文件 Statistics.cpp 第 295 行定义.
在文件 Statistics.h 第 292 行定义.
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unset generic type
this has to be called in classes specializing a template class
在文件 SGObject.cpp 第 303 行定义.
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Updates the hash of current parameter combination
在文件 SGObject.cpp 第 248 行定义.
Calculates unbiased empirical variance estimator of given values. Given \(\{x_1, ..., x_m\}\), this is \(\frac{1}{m-1}\sum_{i=1}^m (x-\bar{x})^2\) where \(\bar x=\frac{1}{m}\sum_{i=1}^m x_i\)
values | vector of values |
在文件 Statistics.cpp 第 204 行定义.
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Magic number for computing lnormal_cdf
在文件 Statistics.h 第 620 行定义.
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Magic number for computing lnormal_cdf
在文件 Statistics.h 第 623 行定义.
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io
在文件 SGObject.h 第 369 行定义.
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inherited |
parameters wrt which we can compute gradients
在文件 SGObject.h 第 384 行定义.
|
inherited |
Hash of parameter values
在文件 SGObject.h 第 387 行定义.
|
inherited |
model selection parameters
在文件 SGObject.h 第 381 行定义.
|
inherited |
parameters
在文件 SGObject.h 第 378 行定义.
|
inherited |
parallel
在文件 SGObject.h 第 372 行定义.
|
inherited |
version
在文件 SGObject.h 第 375 行定义.