Gaussian Auto-Associative models. More...

#include <STK_GaussianAAModel.h>

Inheritance diagram for STK::GaussianAAModel< Array >:

Public Types
typedef IStatModel< GaussianAAModel< Array > >	Base

Public Types inherited from STK::IStatModel< GaussianAAModel< Array > >
typedef hidden::ModelTraits< GaussianAAModel< Array > >::Data	Data

typedef hidden::ModelTraits< GaussianAAModel< Array > >::ParamHandler	ParamHandler

typedef Data::Type	Type
	Type of the data contained in the container.

typedef hidden::Traits< Data >::Row	Row
	Type of the row of the data container (a sample)

Public Member Functions
	GaussianAAModel (Array *p_workData)
	Constructor.

	GaussianAAModel (Array &workData)
	Constructor.

virtual	~GaussianAAModel ()
	virtual destuctor.

Real const &	projectedLnLikelihood () const

Real const &	residualLnLikelihood () const

ArraySquareX const &	projectedCovariance () const

ArraySquareX const &	residualCovariance () const

Real const &	residualVariance () const

virtual void	setWorkData (Array &workData)
	Set a new working data set.

void	computeProjectedCovariance ()
	compute the covariance matrix of the projected data set.

void	computeModelParameters ()
	compute the ln-likelihood of the model

Public Member Functions inherited from STK::IAAModel< Array >
	~IAAModel ()
	destructor.

Array const &	workData () const

Reducer *const &	p_reducer () const

Regressor *const &	p_regressor () const

Array *const &	p_reduced () const

Array *const &	p_predicted () const

Array *const &	p_residuals () const

int	dim () const

bool	isCentered () const

bool	isStandardized () const

PointX const &	mean () const

PointX const &	std () const

void	setDimension (int const &dim)

void	setWorkData (Array &workData)

void	setReducer (Reducer *p_reducer)

void	setRegressor (Regressor *p_regressor)

void	freeReducer ()
	delete the reducer set to this model by the method `setReducer`.

void	freeRegressor ()
	delete the regressor set to this model by the method `setRegressor`.

void	center ()
	center the data set workData_.

void	center (VectorX const &weights)
	weighted centering of the data set.

void	standardize ()
	standardize the data set.

void	standardize (VectorX const &weights)
	weighted standardization the data set.

void	reductionStep ()
	compute the reduction of the data set and store the result in the `p_reduced_` container.

void	reductionStep (VectorX const &weights)
	compute the weighted dimension reduction of the data set and store the result in the `p_reduced_` container.

void	regressionStep ()
	compute the regression of the original data set and set the results in `p_predicted` and `p_residuals`.

void	regressionStep (VectorX const &weights)
	compute the weighted regression of the original data set using the reduced data set as predictor and set the results in `p_predicted` and `p_residuals`.

void	uncenterResults ()
	uncenter the predicted data set.

void	unstandardizeResults ()
	unstandardize the predicted data set and the residuals.

Public Member Functions inherited from STK::IStatModel< GaussianAAModel< Array > >
	~IStatModel ()
	destructor

Data const *const	p_dataij () const

void	setData (Data const &data)
	Set the data set of the model.

void	setData (Data const *p_data)
	Set the data set of the model.

Public Member Functions inherited from STK::IStatModelBase
int	nbSample () const

Real	lnNbSample () const

int	nbVariable () const

Real	lnLikelihood () const

Real	likelihood () const

int	nbFreeParameter () const

Real	computeBIC () const

Real	computeAIC () const

Real	computeML () const

Protected Member Functions
void	computeNbFreeParameters ()
	compute the number of free parameter of the model.

void	computeResidualCovariance ()
	compute the covariance matrix of the residuals.

void	computeProjectedLnLikelihood ()
	compute the ln-likelihood of the projected data set The projected data set is assumed Gaussian with an arbitrary covariance Array.

void	computeResidualLnLikelihood ()
	compute the ln-likelihood of the projected data set.

Protected Member Functions inherited from STK::IAAModel< Array >
	IAAModel (Array *p_workData)
	Constructor.

	IAAModel (Array &workData)
	Constructor.

Protected Member Functions inherited from STK::IStatModel< GaussianAAModel< Array > >
	IStatModel (Data const &data)
	Constructor with data set.

	IStatModel (Data const *p_data)
	Constructor with a ptr on the data set.

Protected Member Functions inherited from STK::IStatModelBase
	IStatModelBase ()
	Default constructor.

	IStatModelBase (int nbSample)
	Constructor with specified dimension.

	IStatModelBase (int nbSample, int nbVariable)
	Constructor with specified dimension.

	IStatModelBase (IStatModelBase const &model)
	Copy constructor.

	~IStatModelBase ()
	destructor

void	setNbFreeParameter (int const &nbFreeParameter)
	set the number of free parameters of the model

void	setNbSample (int const &nbSample)
	set the number of samples of the model

void	setNbVariable (int const &nbVariable)
	set the number of variables of the model

void	setLnLikelihood (Real const &lnLikelihood)
	set the log-likelihood of the model

void	initialize (int nbSample, int nbVariable)
	set the dimensions of the parameters of the model

Private Attributes
ArraySquareX	projectedCovariance_
	The covariance matrix of the projected data set.

ArraySquareX	residualCovariance_
	The covariance matrix of the residuals.

Real	residualVariance_
	The total variance of the residuals.

Real	projectedLnLikelihood_
	likelihood of the projected data set.

Real	residualLnLikelihood_
	likelihood of the residuals.

Additional Inherited Members
Protected Attributes inherited from STK::IAAModel< Array >
Regressor *	p_regressor_
	pointer on the regression method.

Reducer *	p_reducer_
	pointer on the reeducer.

Array *	p_workData_
	Array of the local data set.

Array *	p_reduced_
	Array of the reduced data set : the data set is shared with `p_reducer` and set when the `regression` method is call.

Array *	p_predicted_
	Array of the predicted data set: the data set is shared with `p_regressor` and set when the `regression` method is call.

Array *	p_residuals_
	Array of the residuals: the data set is shared with `p_regressor` and set when the `regression` method is call.

Protected Attributes inherited from STK::IStatModel< GaussianAAModel< Array > >
Data const *	p_dataij_
	A pointer on the original data set.

Detailed Description

template<class Array>
class STK::GaussianAAModel< Array >

Gaussian Auto-Associative models.

A Gaussian Auto-Associative model is a p-dimensional vector $\mathbf{y}$ with projection function $\mathbf{P}$ and regression function $\mathbf{R}$ , if it can be written

$\mathbf{y} = \mathbf{Q} \left( \begin{pmatrix} x_1 \\ \vdots \\ x_d \\ \tilde{r}_{d+1}(\mathbf{x}) \\ \vdots \\ \tilde{r}_p(\mathbf{x}) \end{pmatrix} + \tilde{\varepsilon} \right) = R(\mathbf{x})+ \varepsilon,$

where the $\tilde{r}_j(\mathbf{x})$ , $d+1 \leq j \leq p$ , are arbitrary real functions from $\mathbb{R}^d$ to $\mathbb{R}$ .

The vector $\mathbf{x}$ is a $d$ -dimensional Gaussian random vector:

$\mathbf{x} \sim \mathcal{N}(\mu_x, \Sigma_x)$

with covariance matrix $\Sigma_x = \mathrm{Diag}(\sigma_1^2, \ldots, \sigma_d^2)$ .

The Gaussian noise $\tilde{\varepsilon}$ is centered with the following covariance matrix $\Sigma_\varepsilon = \mathrm{diag}(0,\ldots,0,\sigma^2,\ldots,\sigma^2)$ .

The GaussianModel class is a factory class which compute the covariance matrix of x, the residual covariance and the number of free parameters of the model. It can be sub-classed or used by any class.

Definition at line 101 of file STK_GaussianAAModel.h.

Member Typedef Documentation

◆ Base

template<class Array >

typedef IStatModel< GaussianAAModel<Array> > STK::GaussianAAModel< Array >::Base

Definition at line 105 of file STK_GaussianAAModel.h.

Constructor & Destructor Documentation

◆ GaussianAAModel() [1/2]

template<class Array >

STK::GaussianAAModel< Array >::GaussianAAModel ( Array * p_workData )

Constructor.

Parameters

p_workData a pointer on the data set to process

Definition at line 181 of file STK_GaussianAAModel.h.

                                : IAAModel<Array>(p_workData)
                                , Base(p_workData)
                                , projectedCovariance_()
                                , residualCovariance_()
                                , residualVariance_(0.)
                                , projectedLnLikelihood_(0.)
                                , residualLnLikelihood_(0.)
{ }

◆ GaussianAAModel() [2/2]

template<class Array >

STK::GaussianAAModel< Array >::GaussianAAModel ( Array & workData )

Constructor.

Parameters

workData a reference on the data set to process

Definition at line 193 of file STK_GaussianAAModel.h.

                                : IAAModel<Array>(workData)
                                , Base(workData)
                                , projectedCovariance_()
                                , residualCovariance_()
                                , residualVariance_(0.)
                                , projectedLnLikelihood_(0.)
                                , residualLnLikelihood_(0.)
{ }

◆ ~GaussianAAModel()

template<class Array >

virtual STK::GaussianAAModel< Array >::~GaussianAAModel ( )

inlinevirtual

virtual destuctor.

Definition at line 121 of file STK_GaussianAAModel.h.

121{}

Member Function Documentation

◆ computeModelParameters()

template<class Array >

void STK::GaussianAAModel< Array >::computeModelParameters ( )

compute the ln-likelihood of the model

Definition at line 215 of file STK_GaussianAAModel.h.

{
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("GaussianAAModel::computeModelParameters().\n");
#endif
  // compute the number of free parameters
  computeNbFreeParameters();
  // compute the covariance matrix of the residual and the residual variance
  computeResidualCovariance();
  // compute projected lnLikelihood
  computeProjectedLnLikelihood();
  // compute projected lnLikelihood
  computeResidualLnLikelihood();
  // compute complete nLikelihood
  this->setLnLikelihood(projectedLnLikelihood_ + residualLnLikelihood_);
 
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("GaussianAAModel::computeModelParameters() done.\n");
#endif
}

References _T, and stk_cout.

◆ computeNbFreeParameters()

template<class Array >

void STK::GaussianAAModel< Array >::computeNbFreeParameters ( )

protected

compute the number of free parameter of the model.

It is given by the number of parameter of the regression function, the number of variance and covariance of the projected data set (d * (d+1))/2 and the variance of the residuals.

Definition at line 239 of file STK_GaussianAAModel.h.

{
  this->setNbFreeParameter(p_regressor_->nbFreeParameter() + dim() * (dim()+1)/2 + 1);
}

◆ computeProjectedCovariance()

template<class Array >

void STK::GaussianAAModel< Array >::computeProjectedCovariance ( )

compute the covariance matrix of the projected data set.

This method is set public as the projected covariance can be computed only the first time the data set is projected.

Definition at line 290 of file STK_GaussianAAModel.h.

{
#ifdef STK_AAMODELS_DEBUG
  if (!p_reduced_)
  { STKRUNTIME_ERROR_NO_ARG(GaussianAAModel::computeProjectedCovariance,p_reduced_ is not set);}
#endif
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("GaussianAAModel::computeProjectedCovariance().\n");
#endif
  projectedCovariance_ = Stat::covariance(*p_reduced_);
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("GaussianAAModel::computeProjectedCovariance() done.\n");
#endif
}

References _T, STK::GaussianAAModel< Array >::computeProjectedCovariance(), STK::Stat::covariance(), stk_cout, and STKRUNTIME_ERROR_NO_ARG.

Referenced by STK::GaussianAAModel< Array >::computeProjectedCovariance().

◆ computeProjectedLnLikelihood()

template<class Array >

void STK::GaussianAAModel< Array >::computeProjectedLnLikelihood ( )

protected

compute the ln-likelihood of the projected data set The projected data set is assumed Gaussian with an arbitrary covariance Array.

Definition at line 246 of file STK_GaussianAAModel.h.

{
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("GaussianAAModel::computeProjectedLnLikelihood().\n");
#endif
  // range of the column to use
  Range cols = Range(p_reduced_->beginCols(), dim());
  // create a reference with the first columns of the reduced data
  Array reducedData(*p_reduced_, p_reduced_->rows(), cols);
  // create a reference with the first columns of the reduced data
  ArraySquareX reducedCovariance(projectedCovariance(), cols);
  // compute first part of the ln-likelihood
  PointX mean(cols, 0.);
  MultiLaw::Normal<PointX> normalP(mean, reducedCovariance);
  projectedLnLikelihood_ = normalP.lnLikelihood(reducedData);
 
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("GaussianAAModel::computeProjectedLnLikelihood() done.\n");
  stk_cout << _T("projectedLnLikelihood_ = ") << projectedLnLikelihood_ << _T("\n");
#endif
}

References _T, STK::MultiLaw::Normal< RowVector >::lnLikelihood(), STK::mean(), and stk_cout.

◆ computeResidualCovariance()

template<class Array >

void STK::GaussianAAModel< Array >::computeResidualCovariance ( )

protected

compute the covariance matrix of the residuals.

Definition at line 306 of file STK_GaussianAAModel.h.

{
#ifdef STK_AAMODELS_DEBUG
  if (!p_residuals_)
  { STKRUNTIME_ERROR_NO_ARG(GaussianAAModel::computeResidualCovariance,p_residuals_ is not set);}
#endif
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("in GaussianAAModel::computeResidualCovariance().\n");
#endif
  residualCovariance_ = Stat::covariance(*p_residuals_);
  residualVariance_ = (residualCovariance_.trace())/Real(this->nbVariable()-dim());
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("GaussianAAModel::computeResidualCovariance() done.\n");
  stk_cout << _T("residualVariance_ = ") << residualVariance_ << _T("\n");
#endif
}

References _T, STK::GaussianAAModel< Array >::computeResidualCovariance(), STK::Stat::covariance(), stk_cout, and STKRUNTIME_ERROR_NO_ARG.

Referenced by STK::GaussianAAModel< Array >::computeResidualCovariance().

◆ computeResidualLnLikelihood()

template<class Array >

void STK::GaussianAAModel< Array >::computeResidualLnLikelihood ( )

protected

compute the ln-likelihood of the projected data set.

The residuals are assumed orthogonal to the the projected data set with a single residual variance.

Definition at line 270 of file STK_GaussianAAModel.h.

{
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("GaussianAAModel::computeResidualsLnLikelihood().\n");
#endif
  // compute constant part and determinant part of the log-likelihood
  residualLnLikelihood_ = ( Const::_LNSQRT2PI_ + 0.5*std::log(residualVariance_ ))
                          * (dim() - this->nbVariable()) * this->nbSample();
  // compute second part of the log-likelihood
  for (int i=p_residuals_->beginRows(); i<p_residuals_->endRows(); i++)
  { residualLnLikelihood_ -= p_residuals_->row(i).norm2()/(2.*residualVariance_);}
 
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("GaussianAAModel::computeResidualsLnLikelihood() done.\n");
  stk_cout << _T("residualLnLikelihood_ = ") << residualLnLikelihood_ << _T("\n");
#endif
}

References _T, and stk_cout.

◆ projectedCovariance()

template<class Array >

ArraySquareX const & STK::GaussianAAModel< Array >::projectedCovariance ( ) const

inline

Returns: the covariance matrix of the projected the data set

Definition at line 127 of file STK_GaussianAAModel.h.

127{ return projectedCovariance_;}

References STK::GaussianAAModel< Array >::projectedCovariance_.

◆ projectedLnLikelihood()

template<class Array >

Real const & STK::GaussianAAModel< Array >::projectedLnLikelihood ( ) const

inline

Returns: the ln-likelihood of the projected data set

Definition at line 123 of file STK_GaussianAAModel.h.

123{ return projectedLnLikelihood_;}

References STK::GaussianAAModel< Array >::projectedLnLikelihood_.

◆ residualCovariance()

template<class Array >

ArraySquareX const & STK::GaussianAAModel< Array >::residualCovariance ( ) const

inline

Returns: the covairance matrix of the residuals

Definition at line 129 of file STK_GaussianAAModel.h.

129{ return residualCovariance_;}

References STK::GaussianAAModel< Array >::residualCovariance_.

◆ residualLnLikelihood()

template<class Array >

Real const & STK::GaussianAAModel< Array >::residualLnLikelihood ( ) const

inline

Returns: the ln-likelihood of the residuals

Definition at line 125 of file STK_GaussianAAModel.h.

125{ return residualLnLikelihood_;}

References STK::GaussianAAModel< Array >::residualLnLikelihood_.

◆ residualVariance()

template<class Array >

Real const & STK::GaussianAAModel< Array >::residualVariance ( ) const

inline

Returns: the variance of the residuals

Definition at line 131 of file STK_GaussianAAModel.h.

131{ return residualVariance_;}

References STK::GaussianAAModel< Array >::residualVariance_.

◆ setWorkData()

template<class Array >

void STK::GaussianAAModel< Array >::setWorkData ( Array & workData )

virtual

Set a new working data set.

Parameters

workData the working data set to use

Definition at line 205 of file STK_GaussianAAModel.h.

{
  // update data set and flags for the IAAModel part
  IAAModel<Array>::setWorkData(workData);
  // set dimensions to new size for the IStatModel part
  Base::setData(workData);
}

References STK::IAAModel< Array >::setWorkData().

Referenced by STK::LinearAAModel< Array >::LinearAAModel(), and STK::LinearAAModel< Array >::LinearAAModel().

Member Data Documentation

◆ projectedCovariance_

template<class Array >

ArraySquareX STK::GaussianAAModel< Array >::projectedCovariance_

private

The covariance matrix of the projected data set.

Definition at line 166 of file STK_GaussianAAModel.h.

Referenced by STK::GaussianAAModel< Array >::projectedCovariance().

◆ projectedLnLikelihood_

template<class Array >

Real STK::GaussianAAModel< Array >::projectedLnLikelihood_

private

likelihood of the projected data set.

Definition at line 172 of file STK_GaussianAAModel.h.

Referenced by STK::GaussianAAModel< Array >::projectedLnLikelihood().

◆ residualCovariance_

template<class Array >

ArraySquareX STK::GaussianAAModel< Array >::residualCovariance_

private

The covariance matrix of the residuals.

Definition at line 168 of file STK_GaussianAAModel.h.

Referenced by STK::GaussianAAModel< Array >::residualCovariance().

◆ residualLnLikelihood_

template<class Array >

Real STK::GaussianAAModel< Array >::residualLnLikelihood_

private

likelihood of the residuals.

Definition at line 174 of file STK_GaussianAAModel.h.

Referenced by STK::GaussianAAModel< Array >::residualLnLikelihood().

◆ residualVariance_

template<class Array >

Real STK::GaussianAAModel< Array >::residualVariance_

private

The total variance of the residuals.

Definition at line 170 of file STK_GaussianAAModel.h.

Referenced by STK::GaussianAAModel< Array >::residualVariance().

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

STK_GaussianAAModel.h

Public Types

Public Member Functions

Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Base

Constructor & Destructor Documentation

◆ GaussianAAModel() [1/2]

◆ GaussianAAModel() [2/2]

◆ ~GaussianAAModel()

Member Function Documentation

◆ computeModelParameters()

◆ computeNbFreeParameters()

◆ computeProjectedCovariance()

◆ computeProjectedLnLikelihood()

◆ computeResidualCovariance()

◆ computeResidualLnLikelihood()

◆ projectedCovariance()

◆ projectedLnLikelihood()

◆ residualCovariance()

◆ residualLnLikelihood()

◆ residualVariance()

◆ setWorkData()

Member Data Documentation

◆ projectedCovariance_

◆ projectedLnLikelihood_

◆ residualCovariance_

◆ residualLnLikelihood_

◆ residualVariance_