Regression

The project Regress proposes a set of classes for computing usual linear and non-linear regressions. More...

Namespaces
namespace	STK::Regress
	This namespace encloses all variables and constant specific to the Regress project.

Classes
class	STK::AdditiveBSplineCoefficients< Array >
	Compute the regression splines coefficients of an additive model. More...
class	STK::AdditiveBSplineRegression< YArray, XArray, Weights >
	Compute an additive BSpline, multivalued, regression function using BSpline basis. More...
class	STK::IBasis< Data, Coefs >
	Interface base class for all basis function. More...
class	STK::IRegression< YArray, XArray, Weights >
	Interface base class for Regression methods. More...

Enumerations
enum	STK::Basis::TypeBasisFunction {   STK::Basis::bspline_ , STK::Basis::sines_ , STK::Basis::cosines_ , STK::Basis::trigonometric_ ,   STK::Basis::chebyshev_ , STK::Basis::unknown_basis_ = -1 }
	function basis function to use for functional and non-linear regression More...
enum	STK::Basis::KnotsPosition { STK::Basis::uniformKnotsPositions_ , STK::Basis::periodicKnotsPositions_ , STK::Basis::densityKnotsPositions_ , STK::Basis::unknown_Knots_Position_ = -1 }
	Method to use for positioning the knots in BSpline basis. More...
enum	STK::Regress::TypeBasisFunction {   STK::Regress::unknown_basis_ = -1 , STK::Regress::bspline_ , STK::Regress::sines_ , STK::Regress::cosines_ ,   STK::Regress::trigonometric_ , STK::Regress::chebyshev }
	functional basis coefficients to use for fonctional and non-linear regression More...
enum	STK::Regress::TypeRegression { STK::Regress::unknown_regression_ = -1 , STK::Regress::linear_ , STK::Regress::additiveBSpline_ , STK::Regress::adaptiveBSpline_ }
	Regression method to use. More...
enum	STK::Regress::KnotsPosition { STK::Regress::uniformKnotsPositions_ , STK::Regress::periodicKnotsPositions_ , STK::Regress::densityKnotsPositions_ , STK::Regress::unknown_Knots_Position_ = -1 }
	Method to use for positioning the knots for BSpline basis. More...

Functions
KnotsPosition	STK::Basis::stringToKnotsPosition (String const &type)
	convert a String to a KnotsPosition.
String	STK::Basis::knotsPositionToString (KnotsPosition const &type)
	convert a KnotsPosition to a String.
TypeBasisFunction	STK::Basis::stringToTypeBasisFunction (String const &type)
	convert a String to a TypeBasisFunction.
String	STK::Basis::typeBasisFunctionToString (TypeBasisFunction const &type)
	convert a TypeBasisFunction to a String.
TypeRegression	STK::Regress::stringToTypeRegression (String const &type)
	Convert a String to a TypeRegression.
String	STK::Regress::typeRegressionToString (TypeRegression const &type)
	Convert a TypeRegression to a String.
String	STK::Regress::knotsPositionToString (KnotsPosition const &type)
	convert a KnotsPosition to a String.

Detailed Description

The project Regress proposes a set of classes for computing usual linear and non-linear regressions.

In statistics, regression analysis includes any techniques for modeling and analyzing several variables, when the focus is on the relationship between a set of dependent variables and one or more independent variables. More specifically, regression analysis helps one understand how the typical values of the dependent variables changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variables given the independent variables — that is, the average value of the dependent variable when the independent variables are held fixed.

In regression analysis, it is also of interest to characterize the variation of the dependent variables around the regression function, which can be described by a probability distribution.

Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables.

A large body of techniques for carrying out regression analysis has been developed. Familiar methods such as linear regression and ordinary least squares regression are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data. Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinite-dimensional.

Enumeration Type Documentation

KnotsPosition [1/2]

enum STK::Basis::KnotsPosition

Method to use for positioning the knots in BSpline basis.

Enumerator
uniformKnotsPositions_	uniform knots
periodicKnotsPositions_	periodic knots
densityKnotsPositions_	knots using density of the data
unknown_Knots_Position_	unknown positions

Definition at line 72 of file STK_Basis_Util.h.

{
   uniformKnotsPositions_         
 , periodicKnotsPositions_        
 , densityKnotsPositions_         
 , unknown_Knots_Position_ = -1   
};

KnotsPosition [2/2]

enum STK::Regress::KnotsPosition

Method to use for positioning the knots for BSpline basis.

Enumerator
uniformKnotsPositions_	uniform knots
periodicKnotsPositions_	periodic knots
densityKnotsPositions_	knots using density of the data
unknown_Knots_Position_	unknown positions

Definition at line 102 of file STK_Regress_Util.h.

{
  uniformKnotsPositions_  
 , periodicKnotsPositions_ 
 , densityKnotsPositions_  
 , unknown_Knots_Position_ = -1  
};

TypeBasisFunction [1/2]

enum STK::Basis::TypeBasisFunction

function basis function to use for functional and non-linear regression

Enumerator
bspline_	BSpline basis. Sines basis
sines_	cosines basis
cosines_	trigonometric basis (sines and cosines)
trigonometric_	Chebyshev basis.
chebyshev_	unknown basis
unknown_basis_

Definition at line 53 of file STK_Basis_Util.h.

{
  bspline_
  , sines_
  , cosines_
  , trigonometric_
  , chebyshev_
  , unknown_basis_ = -1
};

TypeBasisFunction [2/2]

enum STK::Regress::TypeBasisFunction

functional basis coefficients to use for fonctional and non-linear regression

Enumerator
unknown_basis_	unknown coefficients
bspline_	Sines coefficients.
sines_	cosines coefficients
cosines_	trigonometric coefficients (sines and cosines)
trigonometric_	Chebyshev coefficients.
chebyshev

Definition at line 54 of file STK_Regress_Util.h.

{
  unknown_basis_ = -1
  , bspline_
  , sines_
  , cosines_
  , trigonometric_
  , chebyshev
};

TypeRegression

enum STK::Regress::TypeRegression

Regression method to use.

Enumerator
unknown_regression_	unknown regression
linear_	additive BSpline regression
additiveBSpline_	adaptive BSpline regression
adaptiveBSpline_

Definition at line 72 of file STK_Regress_Util.h.

{
  unknown_regression_ = -1
  , linear_
  , additiveBSpline_
  , adaptiveBSpline_
};

Function Documentation

knotsPositionToString() [1/2]

String STK::Basis::knotsPositionToString ( KnotsPosition const &  type )

inline

convert a KnotsPosition to a String.

Parameters

type	the KnotsPosition we want to convert to a string

Returns

the string associated to this KnotsPosition

Definition at line 129 of file STK_Basis_Util.h.

{
  if (type == uniformKnotsPositions_)  return String(_T("uniform"));
  if (type == periodicKnotsPositions_) return String(_T("periodic"));
  if (type == densityKnotsPositions_) return String(_T("density"));
  return String(_T("unknown"));
}

References _T, STK::Basis::densityKnotsPositions_, STK::Basis::periodicKnotsPositions_, and STK::Basis::uniformKnotsPositions_.

knotsPositionToString() [2/2]

String STK::Regress::knotsPositionToString ( KnotsPosition const &  type )

inline

convert a KnotsPosition to a String.

Parameters

type	the KnotsPosition we want to convert to a string

Returns

the string associated to this KnotsPosition

Definition at line 145 of file STK_Regress_Util.h.

{
  if (type == uniformKnotsPositions_)  return String(_T("uniform"));
  if (type == periodicKnotsPositions_) return String(_T("periodic"));
  if (type == densityKnotsPositions_) return String(_T("density"));
  return String(_T("unknown"));
}

References _T, STK::Regress::densityKnotsPositions_, STK::Regress::periodicKnotsPositions_, and STK::Regress::uniformKnotsPositions_.

stringToKnotsPosition()

KnotsPosition STK::Basis::stringToKnotsPosition ( String const &  type )

inline

convert a String to a KnotsPosition.

Parameters

type	the type of KnotsPosition in a string

Returns

the KnotsPosition represented by the String type. If the string does not match any known name, the unknown_regression_ type is returned.

Definition at line 117 of file STK_Basis_Util.h.

{
  if (toUpperString(type) == toUpperString(_T("uniform")))  return uniformKnotsPositions_;
  if (toUpperString(type) == toUpperString(_T("periodic"))) return periodicKnotsPositions_;
  if (toUpperString(type) == toUpperString(_T("density")))  return densityKnotsPositions_;
  return unknown_Knots_Position_;
}

References _T, STK::Basis::densityKnotsPositions_, STK::Basis::periodicKnotsPositions_, STK::toUpperString(), STK::Basis::uniformKnotsPositions_, and STK::Basis::unknown_Knots_Position_.

stringToTypeBasisFunction()

TypeBasisFunction STK::Basis::stringToTypeBasisFunction ( String const &  type )

inline

convert a String to a TypeBasisFunction.

Parameters

type	the type of TypeBasisFunction in a string

Returns

the TypeBasisFunction represented by the String type. If the string does not match any known name, the unknown_basis_ type is returned.

Definition at line 143 of file STK_Basis_Util.h.

{
  if (toUpperString(type) == toUpperString(_T("bspline")))       return bspline_;
  if (toUpperString(type) == toUpperString(_T("sines")))         return sines_;
  if (toUpperString(type) == toUpperString(_T("cosines")))       return cosines_;
  if (toUpperString(type) == toUpperString(_T("trigonometric"))) return trigonometric_;
  if (toUpperString(type) == toUpperString(_T("chebyshev")))     return chebyshev_;
  return unknown_basis_;
}

References _T, STK::Basis::bspline_, STK::Basis::chebyshev_, STK::Basis::cosines_, STK::Basis::sines_, STK::toUpperString(), STK::Basis::trigonometric_, and STK::Basis::unknown_basis_.

stringToTypeRegression()

TypeRegression STK::Regress::stringToTypeRegression ( String const &  type )

inline

Convert a String to a TypeRegression.

Parameters

type	the String we want to convert

Returns

the TypeRegression represented by the String type. if the string does not match any known name, the unknown_regression_ type is returned.

Definition at line 158 of file STK_Regress_Util.h.

{
  if (toUpperString(type) == toUpperString(_T("unknown"))) return unknown_regression_;
  if (toUpperString(type) == toUpperString(_T("linear")))  return linear_;
  if (toUpperString(type) == toUpperString(_T("additiveBSpline"))) return additiveBSpline_;
  if (toUpperString(type) == toUpperString(_T("adaptiveBSpline"))) return adaptiveBSpline_;
  return unknown_regression_;
}

References _T, STK::Regress::adaptiveBSpline_, STK::Regress::additiveBSpline_, STK::Regress::linear_, STK::toUpperString(), and STK::Regress::unknown_regression_.

typeBasisFunctionToString()

String STK::Basis::typeBasisFunctionToString ( TypeBasisFunction const &  type )

inline

convert a TypeBasisFunction to a String.

Parameters

type	the TypeBasisFunction we want to convert to a string

Returns

the string associated to this TypeBasisFunction

Definition at line 159 of file STK_Basis_Util.h.

{
  if (type == bspline_)       return String(_T("bspline"));
  if (type == sines_)         return String(_T("sines"));
  if (type == cosines_)       return String(_T("cosines"));
  if (type == trigonometric_) return String(_T("trigonometric"));
  if (type == chebyshev_)     return String(_T("chebyshev"));
  return String(_T("unknown"));
}

References _T, STK::Basis::bspline_, STK::Basis::chebyshev_, STK::Basis::cosines_, STK::Basis::sines_, and STK::Basis::trigonometric_.

typeRegressionToString()

String STK::Regress::typeRegressionToString ( TypeRegression const &  type )

inline

Convert a TypeRegression to a String.

Parameters

type	the type of regression we want to convert

Returns

the string associated to this type.

Definition at line 171 of file STK_Regress_Util.h.

{
  if (type == linear_)  return String(_T("linear"));
  if (type == additiveBSpline_) return String(_T("additiveBSpline"));
  if (type == adaptiveBSpline_) return String(_T("adaptiveBSpline"));
  return String(_T("unknown"));
}

References _T, STK::Regress::adaptiveBSpline_, STK::Regress::additiveBSpline_, and STK::Regress::linear_.