Interface base class for Regression methods. More...

#include <STK_IRegression.h>

Inheritance diagram for STK::IRegression< YArray, XArray, Weights >:

Public Member Functions
virtual	~IRegression ()
	virtual destructor.

YArray const &	predicted () const

YArray const &	residuals () const

YArray *	p_predicted ()

YArray *	p_residuals ()

int	nbFreeParameter () const

virtual bool	run ()
	run the computations.

virtual bool	run (Weights const &weights)
	run the weighted computations.

virtual YArray	extrapolate (XArray const &x) const =0

Public Member Functions inherited from STK::IRunnerSupervised< YArray, XArray, Weights >
virtual void	setX (XArray const &x)
	set the x data set (predictors).

virtual void	setY (YArray const &y)
	set the data set.

virtual void	setData (YArray const &y, XArray const &x)
	set the data set.

Public Member Functions inherited from STK::IRunnerBase
String const &	error () const
	get the last error message.

Protected Types
typedef IRunnerSupervised< YArray, XArray, Weights >	Base

Protected Member Functions
	IRegression ()
	Default constructor.

	IRegression (ArrayBase< YArray > const p_y, ArrayBase< XArray > const p_x)
	constructor

	IRegression (ArrayBase< YArray > const &y, ArrayBase< XArray > const &x)
	Constructor.

virtual bool	initializeStep ()
	perform any computation needed before the call of the regression method.

virtual bool	finalizeStep ()
	perform any computation needed after the call of the regression method.

bool	residualsStep ()
	Compute the residuals of the model.

Protected Member Functions inherited from STK::IRunnerSupervised< YArray, XArray, Weights >
	IRunnerSupervised ()
	default constructor

	IRunnerSupervised (YArray const const &p_y, XArray const const &p_x)
	constructor

	IRunnerSupervised (YArray const &y, XArray const &x)
	default constructor

	IRunnerSupervised (IRunnerSupervised const &runner)
	copy constructor

	~IRunnerSupervised ()
	destructor

virtual void	updateY ()
	update the runner when y data set is set.

virtual void	updateX ()
	update the runner when x data set is set.

virtual void	update ()
	update the runner.

Protected Member Functions inherited from STK::IRunnerBase
	IRunnerBase ()
	default constructor

	IRunnerBase (IRunnerBase const &runner)
	copy constructor

virtual	~IRunnerBase ()
	destructor

Protected Attributes
YArray	predicted_
	Container of the predicted output.

YArray	residuals_
	Container of the residuals.

Protected Attributes inherited from STK::IRunnerSupervised< YArray, XArray, Weights >
YArray const *	p_y_
	A pointer on the y data set.

XArray const *	p_x_
	A pointer on the x data set.

Protected Attributes inherited from STK::IRunnerBase
String	msg_error_
	String with the last error message.

bool	hasRun_
	`true` if run has been used, `false` otherwise

Private Member Functions
virtual bool	regressionStep ()=0
	compute the regression function.

virtual bool	regressionStep (Weights const &weights)=0
	compute the weighted regression function.

virtual bool	predictionStep ()=0
	Compute the predicted outputs by the regression function and store the result in the p_predicted_ array.

virtual int	computeNbFreeParameter () const =0
	Compute the number of parameter of the regression function.

Private Attributes
int	nbFreeParameter_
	number of parameter of the regression method.

Detailed Description

template<class YArray, class XArray, class Weights>
class STK::IRegression< YArray, XArray, Weights >

Interface base class for Regression methods.

Regression models involve the following variables:

The unknown parameters, denoted as β, which may represent a scalar or a vector.
The independent variables, X.
The dependent variable, Y.

In various fields of application, different terminologies are used in place of dependent and independent variables. A regression model relates Y to a function of X and β. $Y \approx f (\mathbf {X}, \boldsymbol{\beta} )$

The approximation is usually formalized as $E(Y|X)=f(X,\beta)$ . To carry out regression analysis, the form of the function f must be specified. Sometimes the form of this function is based on knowledge about the relationship between Y and X that does not rely on the data. If no such knowledge is available, a flexible or convenient form for f is chosen.

Assume now that the vector of unknown parameters β is of length k. In order to perform a regression analysis the user must provide information about the dependent variable Y:

If N data points of the form (Y,X) are observed, where N < k, most classical approaches to regression analysis cannot be performed: since the system of equations defining the regression model is under-determined, there is not enough data to recover β. If exactly N=k data points are observed, and the function f is linear, the equations Y=f(X, β) can be solved exactly rather than approximately. This reduces to solving a set of N equations with N unknowns (the elements of β), which has a unique solution as long as the X are linearly independent. If f is nonlinear, a solution may not exist, or many solutions may exist.
The most common situation is where N > k data points are observed. In this case, there is enough information in the data to estimate a unique value for β that best fits the data in some sense, and the regression model when applied to the data can be viewed as an overdetermined system in β.

In the last case, the regression analysis provides the tools for: #- Finding a solution for unknown parameters β that will, for example, minimize the distance between the measured and predicted values of the dependent variable Y (also known as method of least squares). #- Under certain statistical assumptions, the regression analysis uses the surplus of information to provide statistical information about the unknown parameters β and predicted values of the dependent variable Y.

In this interface, the pure virtual function to implement are

virtual bool regressionStep()=0;
virtual bool regressionStep( Weights const& weights) =0;
virtual bool predictionStep() =0;
virtual int computeNbFreeParameter() const =0;
virtual bool extrapolate( XArray const& x, YArray& y) const =0;

The virtual function

virtual void initializeStep();

STK::IRegression::initializeStep

virtual bool initializeStep()

perform any computation needed before the call of the regression method.

Definition STK_IRegression.h:168

can be overloaded.

Definition at line 107 of file STK_IRegression.h.

Member Typedef Documentation

◆ Base

template<class YArray , class XArray , class Weights >

typedef IRunnerSupervised<YArray, XArray, Weights> STK::IRegression< YArray, XArray, Weights >::Base

protected

Definition at line 110 of file STK_IRegression.h.

Constructor & Destructor Documentation

◆ IRegression() [1/3]

template<class YArray , class XArray , class Weights >

STK::IRegression< YArray, XArray, Weights >::IRegression ( )

inlineprotected

Default constructor.

Initialize the data members.

Definition at line 114 of file STK_IRegression.h.

114: Base(), predicted_(), residuals_(), nbFreeParameter_(0) {}

STK::IRegression::nbFreeParameter_

int nbFreeParameter_

number of parameter of the regression method.

Definition STK_IRegression.h:190

STK::IRegression::residuals_

YArray residuals_

Container of the residuals.

Definition STK_IRegression.h:186

STK::IRegression::predicted_

YArray predicted_

Container of the predicted output.

Definition STK_IRegression.h:184

STK::IRegression::Base

IRunnerSupervised< YArray, XArray, Weights > Base

Definition STK_IRegression.h:110

◆ IRegression() [2/3]

template<class YArray , class XArray , class Weights >

STK::IRegression< YArray, XArray, Weights >::IRegression	(	ArrayBase< YArray > const *	p_y,
		ArrayBase< XArray > const *	p_x
	)

inlineprotected

constructor

Parameters

p_y,p_x pointers on the y and x data sets

Definition at line 118 of file STK_IRegression.h.

              : Base((p_y == 0) ? 0 : p_y->asPtrDerived(), (p_x == 0) ? 0 : p_x->asPtrDerived())
               , predicted_()
               , residuals_()
               , nbFreeParameter_(0)
     {}

◆ IRegression() [3/3]

template<class YArray , class XArray , class Weights >

STK::IRegression< YArray, XArray, Weights >::IRegression	(	ArrayBase< YArray > const &	y,
		ArrayBase< XArray > const &	x
	)

inlineprotected

Constructor.

Initialize the data members.

Parameters

y,x	arrays with the observed output and inputs of the model

Definition at line 127 of file STK_IRegression.h.

              : Base(y.asDerived(), x.asDerived())
               , predicted_()
               , residuals_()
               , nbFreeParameter_(0)
     {}

◆ ~IRegression()

template<class YArray , class XArray , class Weights >

virtual STK::IRegression< YArray, XArray, Weights >::~IRegression ( )

inlinevirtual

virtual destructor.

Definition at line 136 of file STK_IRegression.h.

136{}

Member Function Documentation

◆ computeNbFreeParameter()

template<class YArray , class XArray , class Weights >

virtual int STK::IRegression< YArray, XArray, Weights >::computeNbFreeParameter ( ) const

privatepure virtual

Compute the number of parameter of the regression function.

Returns: the number of parameter of the regression function

Implemented in STK::AdditiveBSplineRegression< YArray, XArray, Weights >, STK::BSplineRegression< YArray, XVector, Weights >, and STK::MultidimRegression< Array, Weight >.

◆ extrapolate()

template<class YArray , class XArray , class Weights >

virtual YArray STK::IRegression< YArray, XArray, Weights >::extrapolate ( XArray const & x ) const

pure virtual

Returns: the compute values of y from the value x using the model. Given the data set x will compute the values $y = \hat{f}(x)$ . The regression function f has to be estimated previously.

Parameters

x	the input data set

Implemented in STK::MultidimRegression< Array, Weight >, and STK::AdditiveBSplineRegression< YArray, XArray, Weights >.

◆ finalizeStep()

template<class YArray , class XArray , class Weights >

virtual bool STK::IRegression< YArray, XArray, Weights >::finalizeStep ( )

inlineprotectedvirtual

perform any computation needed after the call of the regression method.

Default implementation is do nothing.

Definition at line 172 of file STK_IRegression.h.

172{ return true;}

Referenced by STK::IMixtureBridge< Derived >::finalizeStep(), STK::MixtureComposer::finalizeStep(), and STK::MixtureLearner::finalizeStep().

◆ initializeStep()

template<class YArray , class XArray , class Weights >

virtual bool STK::IRegression< YArray, XArray, Weights >::initializeStep ( )

inlineprotectedvirtual

perform any computation needed before the call of the regression method.

Default implementation is do nothing.

Reimplemented in STK::AdditiveBSplineRegression< YArray, XArray, Weights >, and STK::BSplineRegression< YArray, XVector, Weights >.

Definition at line 168 of file STK_IRegression.h.

168{ return true;}

Referenced by STK::MixtureLearner::createLearner().

◆ nbFreeParameter()

template<class YArray , class XArray , class Weights >

int STK::IRegression< YArray, XArray, Weights >::nbFreeParameter ( ) const

inline

Returns: the number of parameter of the regression function

Definition at line 149 of file STK_IRegression.h.

149{ return nbFreeParameter_;}

References STK::IRegression< YArray, XArray, Weights >::nbFreeParameter_.

Referenced by STK::IMixtureStatModel::registerMixture().

◆ p_predicted()

template<class YArray , class XArray , class Weights >

YArray * STK::IRegression< YArray, XArray, Weights >::p_predicted ( )

inline

Returns: the pointer on the predicted values

Definition at line 144 of file STK_IRegression.h.

144{ return &predicted_;}

References STK::IRegression< YArray, XArray, Weights >::predicted_.

◆ p_residuals()

template<class YArray , class XArray , class Weights >

YArray * STK::IRegression< YArray, XArray, Weights >::p_residuals ( )

inline

Returns: the pointer on the residuals

Definition at line 146 of file STK_IRegression.h.

146{ return &residuals_;}

References STK::IRegression< YArray, XArray, Weights >::residuals_.

◆ predicted()

template<class YArray , class XArray , class Weights >

YArray const & STK::IRegression< YArray, XArray, Weights >::predicted ( ) const

inline

Returns: the predicted values

Definition at line 139 of file STK_IRegression.h.

139{ return predicted_;}

References STK::IRegression< YArray, XArray, Weights >::predicted_.

◆ predictionStep()

template<class YArray , class XArray , class Weights >

virtual bool STK::IRegression< YArray, XArray, Weights >::predictionStep ( )

privatepure virtual

Compute the predicted outputs by the regression function and store the result in the p_predicted_ array.

Implemented in STK::AdditiveBSplineRegression< YArray, XArray, Weights >, STK::BSplineRegression< YArray, XVector, Weights >, and STK::MultidimRegression< Array, Weight >.

◆ regressionStep() [1/2]

template<class YArray , class XArray , class Weights >

virtual bool STK::IRegression< YArray, XArray, Weights >::regressionStep ( )

privatepure virtual

compute the regression function.

Implemented in STK::AdditiveBSplineRegression< YArray, XArray, Weights >, STK::BSplineRegression< YArray, XVector, Weights >, and STK::MultidimRegression< Array, Weight >.

◆ regressionStep() [2/2]

template<class YArray , class XArray , class Weights >

virtual bool STK::IRegression< YArray, XArray, Weights >::regressionStep ( Weights const & weights )

privatepure virtual

compute the weighted regression function.

Parameters

weights the weights of the samples

Implemented in STK::MultidimRegression< Array, Weight >, STK::AdditiveBSplineRegression< YArray, XArray, Weights >, and STK::BSplineRegression< YArray, XVector, Weights >.

◆ residuals()

template<class YArray , class XArray , class Weights >

YArray const & STK::IRegression< YArray, XArray, Weights >::residuals ( ) const

inline

Returns: the residuals

Definition at line 141 of file STK_IRegression.h.

141{ return residuals_;}

References STK::IRegression< YArray, XArray, Weights >::residuals_.

◆ residualsStep()

template<class YArray , class XArray , class Weights >

bool STK::IRegression< YArray, XArray, Weights >::residualsStep ( )

inlineprotected

Compute the residuals of the model.

The residuals of the model are computed by computing the difference between the observed outputs and the predicted outputs of the model.

Definition at line 177 of file STK_IRegression.h.

    {
      residuals_ = *p_y_ - predicted_;
      return true;
    }

References STK::IRunnerSupervised< YArray, XArray, Weights >::p_y_, STK::IRegression< YArray, XArray, Weights >::predicted_, and STK::IRegression< YArray, XArray, Weights >::residuals_.

◆ run() [1/2]

template<class YArray , class XArray , class Weights >

bool STK::IRegression< YArray, XArray, Weights >::run ( )

virtual

run the computations.

Default Implementation.

Implements STK::IRunnerSupervised< YArray, XArray, Weights >.

Definition at line 208 of file STK_IRegression.h.

{
  // perform any initialization step needed before the regression step
  if (!initializeStep()) { return false;}
  // compute the regression
  if (!regressionStep()) { return false;}
  // Compute the number of parameter of the regression function.
  nbFreeParameter_ = computeNbFreeParameter();
  // compute predictions
  predictionStep();
  // compute residuals
  residualsStep();
  // perform any post-operation needed before the regression step
  finalizeStep();
  // return the result of the computations
  this->hasRun_ = true;
  return true;
}

References STK::MultidimRegression< Array, Weight >::computeNbFreeParameter(), STK::IRegression< Array, Array, Weight >::finalizeStep(), STK::IRunnerBase::hasRun_, STK::IRegression< Array, Array, Weight >::initializeStep(), STK::IRegression< Array, Array, Weight >::nbFreeParameter_, STK::MultidimRegression< Array, Weight >::predictionStep(), STK::MultidimRegression< Array, Weight >::regressionStep(), and STK::IRegression< Array, Array, Weight >::residualsStep().

Referenced by STK::LocalVariance< Array >::computeAxis(), STK::ProjectedVariance< Array >::computeAxis(), STK::LocalVariance< Array >::computeCovarianceMatrices(), STK::LocalVariance< Array >::computeCovarianceMatrices(), STK::AdditiveBSplineRegression< YArray, XArray, Weights >::regressionStep(), STK::AdditiveBSplineRegression< YArray, XArray, Weights >::regressionStep(), STK::WeightedSvd< Array, WRows, WCols >::run(), STK::MultiLeastSquare< ArrayB, ArrayA >::runImpl(), STK::MultiLeastSquare< ArrayB, ArrayA >::runImpl(), and STK::MultiLaw::Normal< RowVector >::setParameters().

◆ run() [2/2]

template<class YArray , class XArray , class Weights >

bool STK::IRegression< YArray, XArray, Weights >::run ( Weights const & weights )

virtual

run the weighted computations.

run the computations.

Parameters

weights weights of the samples

Default Implementation.

Implements STK::IRunnerSupervised< YArray, XArray, Weights >.

Definition at line 229 of file STK_IRegression.h.

{
  // perform any pre-operation needed before the regression step
  if (!initializeStep()) { return false;}
  // compute weighted regression
  if (!regressionStep(weights)) { return false;}
  // Compute the number of parameter of the regression function.
  nbFreeParameter_ = computeNbFreeParameter();
  // create array of the predicted value and compute prediction
  predictionStep();
  // create array of the residuals and compute them
  residualsStep();
  // perform any post-operation needed before the regression step
  finalizeStep();
  // return the result of the computations
  this->hasRun_ = true;
  return true;
}