Gamma_aj_bk is a mixture model of the following form. More...

#include <STK_Gamma_aj_bk.h>

Inheritance diagram for STK::Gamma_aj_bk< Array >:

Public Types
typedef GammaBase< Gamma_aj_bk< Array > >	Base

Public Types inherited from STK::GammaBase< Gamma_aj_bk< Array > >
typedef IMixtureDensity< Gamma_aj_bk< Array > >	Base

Public Types inherited from STK::IMixtureDensity< Derived >
typedef hidden::MixtureTraits< Derived >::Array	Array

typedef hidden::MixtureTraits< Derived >::Parameters	Parameters

typedef hidden::Traits< Array >::Type	Type

Public Member Functions
	Gamma_aj_bk (int nbCluster)
	default constructor

	Gamma_aj_bk (Gamma_aj_bk const &model)
	copy constructor

	~Gamma_aj_bk ()
	destructor

void	randomInit (CArrayXX const const &p_tik, CPointX const const &p_tk)
	Initialize randomly the parameters of the Gamma mixture.

bool	run (CArrayXX const const &p_tik, CPointX const const &p_tk)
	Compute the run( CArrayXX const* const& p_tik, CPointX const* const& p_tk) .

int	computeNbFreeParameters () const

Public Member Functions inherited from STK::GammaBase< Gamma_aj_bk< Array > >
Real	shape (int k, int j) const

Real	scale (int k, int j) const

void	initializeModelImpl ()
	Initialize the parameters of the model.

Real	lnComponentProbability (int i, int k) const

Real	impute (int i, int j, Weights const &pk) const

Real	rand (int i, int j, int k) const

void	getParameters (Array &params) const
	This function is used in order to get the current values of the parameters in an array of size (2*nbCluster, nbVariable).

void	writeParameters (CArrayXX const *p_tik, ostream &os) const
	This function can be used to write summary of parameters to the output stream.

Array const *const &	p_data () const

Public Member Functions inherited from STK::IMixtureDensity< Derived >
	~IMixtureDensity ()
	destructor

int	nbCluster () const

int	nbSample () const

Real	lnNbSample () const

Array const *const &	p_data () const

Parameters const &	param () const

void	setData (Array const &data)
	Set the data set.

void	setData (Array const &data, int nbRow, int nbCol, bool byRow=true)
	Set the data set and give dimensions.

bool	initializeStep ()
	This function will be called at the beginning of the estimation process once the model is created and data is set.

void	setParametersStep ()
	set the parameters obtained with the intermediate results and release the intermediate results.

void	finalizeStep ()
	This function will be called once the model is estimated.

template<class Weights >
Type	sample (int i, int j, Weights const &tk) const

Public Member Functions inherited from STK::IRecursiveTemplate< Derived >
Derived &	asDerived ()
	static cast : return a reference of this with a cast to the derived class.

Derived const &	asDerived () const
	static cast : return a const reference of this with a cast to the derived class.

Derived *	asPtrDerived ()
	static cast : return a ptr on a `Derived` of this with a cast to the derived class.

Derived const *	asPtrDerived () const
	static cast : return a ptr on a constant `Derived` of this with a cast to the derived class.

Derived *	clone () const
	create a leaf using the copy constructor of the Derived class.

Derived *	clone (bool isRef) const
	create a leaf using the copy constructor of the Derived class and a flag determining if the clone is a reference or not.

Additional Inherited Members
Public Attributes inherited from STK::GammaBase< Gamma_aj_bk< Array > >
Parameters	param_
	parameters of the derived mixture model.

Protected Member Functions inherited from STK::GammaBase< Gamma_aj_bk< Array > >
	GammaBase (int nbCluster)
	default constructor

	GammaBase (GammaBase const &model)
	copy constructor

	~GammaBase ()
	destructor

Real	qValue (CArrayXX const p_tik, CPointX const p_tk) const
	compute the Q(theta) value.

bool	moments (CArrayXX const *p_tik)
	compute the weighted moments of a gamma mixture.

Real	meanjk (int j, int k)
	get the weighted mean of the jth variable of the kth cluster.

Real	variancejk (int j, int k)
	get the weighted variance of the jth variable of the kth cluster.

Real	meank (int k)
	get the mean of the weighted means of the kth cluster.

Real	variancek (int k)
	get the mean of the weighted variances of the kth cluster.

Protected Member Functions inherited from STK::IMixtureDensity< Derived >
	IMixtureDensity (int nbCluster)
	Default constructor.

	IMixtureDensity (IMixtureDensity const &model)
	copy constructor.

void	initializeModel ()
	Initialize the model before its first use.

bool	initializeStepImpl ()
	default implementation of initializeStepImpl (do nothing and return true)

void	finalizeStepImpl ()
	default implementation of finalizeStepImpl (do nothing)

void	setNbSample (int nbSample)
	Set the number of sample of the model (needed by kernel models)

Protected Member Functions inherited from STK::IRecursiveTemplate< Derived >
	IRecursiveTemplate ()
	constructor.

	~IRecursiveTemplate ()
	destructor.

Protected Attributes inherited from STK::IMixtureDensity< Derived >
Parameters	param_
	parameters of the derived mixture model.

Detailed Description

template<class Array>
class STK::Gamma_aj_bk< Array >

Gamma_aj_bk is a mixture model of the following form.

$f(\mathbf{x}_i|\theta) = \sum_{k=1}^K p_k \prod_{j=1}^p\left(\frac{x_i^j}{b_{k}}\right)^{a_{j}-1} \frac{e^{-x_i^j/b_{k}}}{b_{k} \, \Gamma(a_{j})}, \quad x_i^j>0, \quad i=1,\ldots,n.$

Definition at line 73 of file STK_Gamma_aj_bk.h.

Member Typedef Documentation

◆ Base

template<class Array >

typedef GammaBase< Gamma_aj_bk<Array> > STK::Gamma_aj_bk< Array >::Base

Definition at line 76 of file STK_Gamma_aj_bk.h.

Constructor & Destructor Documentation

◆ Gamma_aj_bk() [1/2]

template<class Array >

STK::Gamma_aj_bk< Array >::Gamma_aj_bk ( int nbCluster )

inline

default constructor

Parameters

nbCluster number of cluster in the model

Definition at line 86 of file STK_Gamma_aj_bk.h.

86: Base(nbCluster) {}

STK::Gamma_aj_bk::Base

GammaBase< Gamma_aj_bk< Array > > Base

Definition STK_Gamma_aj_bk.h:76

STK::IMixtureDensity::nbCluster

int nbCluster() const

Definition STK_IMixtureDensity.h:124

◆ Gamma_aj_bk() [2/2]

template<class Array >

STK::Gamma_aj_bk< Array >::Gamma_aj_bk ( Gamma_aj_bk< Array > const & model )

inline

copy constructor

Parameters

model The model to copy

Definition at line 90 of file STK_Gamma_aj_bk.h.

90: Base(model) {}

◆ ~Gamma_aj_bk()

template<class Array >

STK::Gamma_aj_bk< Array >::~Gamma_aj_bk ( )

inline

destructor

Definition at line 92 of file STK_Gamma_aj_bk.h.

92{}

Member Function Documentation

◆ computeNbFreeParameters()

template<class Array >

int STK::Gamma_aj_bk< Array >::computeNbFreeParameters ( ) const

inline

Returns: the number of free parameters of the model

Definition at line 102 of file STK_Gamma_aj_bk.h.

103 { return(this->nbCluster()+p_data()->sizeCols());}

STK::GammaBase< Gamma_aj_bk< Array > >::p_data

Array const *const & p_data() const

Definition STK_IMixtureDensity.h:131

References STK::IMixtureDensity< Derived >::nbCluster(), and STK::GammaBase< Gamma_aj_bk< Array > >::p_data().

◆ randomInit()

template<class Array >

void STK::Gamma_aj_bk< Array >::randomInit	(	CArrayXX const *const &	p_tik,
		CPointX const *const &	p_tk
	)

Initialize randomly the parameters of the Gamma mixture.

The shape will be selected randomly using an exponential of parameter mean^2/variance and the scale will be selected randomly using an exponential of parameter variance/mean.

Definition at line 111 of file STK_Gamma_aj_bk.h.

{
  // compute moments
  this->moments(p_tik);
  // simulate aj
  for (int j=p_data()->beginCols(); j < p_data()->endCols(); ++j)
  {
    Real value= 0.;
    for (int k= p_tik->beginCols(); k < p_tik->endCols(); ++k)
    {
      Real mean = meanjk(j,k), variance = variancejk(j,k);
      value += p_tk->elt(k) * mean*mean/variance;
    }
    param_.shape_[j] = Law::Exponential::rand(value/(this->nbSample()));
  }
  // simulates bk
  for (int k= p_tik->beginCols(); k < p_tik->endCols(); ++k)
  { param_.scale_[k] = Law::Exponential::rand((this->variancek(k)/this->meank(k)));}
#ifdef STK_MIXTURE_VERY_VERBOSE
  stk_cout << _T(" Gamma_aj_bk<Array>::randomInit done\n");
#endif
}

References _T, STK::mean(), STK::Law::Exponential::rand(), and stk_cout.

◆ run()

template<class Array >

bool STK::Gamma_aj_bk< Array >::run	(	CArrayXX const *const &	p_tik,
		CPointX const *const &	p_tk
	)

Compute the run( CArrayXX const* const& p_tik, CPointX const* const& p_tk) .

Definition at line 136 of file STK_Gamma_aj_bk.h.

{
  bool flag = true;
  if (!this->moments(p_tik)) { flag = false;}
  // start estimations of the ajk and bj
  Real qvalue = this->qValue(p_tik, p_tk);
  // enter iterative algorithm
  int iter;
  for(iter = 0; iter<MAXITER; ++iter)
  {
    // compute aj
    for (int j=p_data()->beginCols(); j<p_data()->endCols(); ++j)
    {
      // moment estimate and oldest value
      Real y = 0, x0 = 0;
      for (int k= p_tik->beginCols(); k < p_tik->endCols(); ++k)
      {
        Real mean = meanjk(j,k), variance = variancejk(j,k);
        y  += p_tk->elt(k) * (param_.meanLog_[k][j] - std::log(param_.scale_[k]));
        x0 += p_tk->elt(k) * mean*mean/variance;
      }
      y /= this->nbSample();
      x0/= this->nbSample();
      Real x1 = param_.shape_[j];
      if ((x0 <=0.) || !Arithmetic<Real>::isFinite(x0))
      { x0 = 1; flag = false;}
      // compute shape
      hidden::invPsi f(y);
      Real a = x0; // use moment estimate
      try
      {
        a = Algo::findZero(f, x0, x1, 1e-08);
      }
      catch (...)
      {
    #ifdef STK_MIXTURE_DEBUG
          stk_cout << "ML estimation failed in Gamma_aj_bk::run( CArrayXX const* const& p_tik, CPointX const* const& p_tk) \n";
          stk_cout << "x0 =" << x0 << _T("\n";);
          stk_cout << "f(x0) =" << f(x0) << _T("\n";);
          stk_cout << "x1 =" << x1 << _T("\n";);
          stk_cout << "f(x1) =" << f(x1) << _T("\n";);
    #endif
          a = x0; // use moment estimate
          flag = false;
      }
      if (!Arithmetic<Real>::isFinite(a))
      {
#ifdef STK_MIXTURE_DEBUG
        stk_cout << _T("ML estimation failed in Gamma_aj_bk::run( CArrayXX const* const& p_tik, CPointX const* const& p_tk) \n");
        stk_cout << "x0 =" << x0 << _T("\n";);
        stk_cout << "f(x0) =" << f(x0) << _T("\n";);
        stk_cout << "x1 =" << x1 << _T("\n";);
        stk_cout << "f(x1) =" << f(x1) << _T("\n";);
#endif
        a = 1.;
        flag = false;
      }
      param_.shape_[j] = a;
      // compute bk
      Real sum = param_.shape_.sum();
      for (int k= p_tik->beginCols(); k < p_tik->endCols(); ++k)
      { // update bk
        param_.scale_[k] = param_.mean_[k].sum()/sum;
      }
    }
  // check convergence
    Real value = this->qValue(p_tik, p_tk);
#ifdef STK_MIXTURE_VERBOSE
  if (value < qvalue)
  {
    stk_cout << _T("In Gamma_aj_bk::run( CArrayXX const* const& p_tik, CPointX const* const& p_tk) : run( CArrayXX const* const& p_tik, CPointX const* const& p_tk)  diverge\n");
    stk_cout << _T("New value =") << value << _T(", qvalue =") << qvalue << _T("\n");
  }
#endif
    if ((value - qvalue) < TOL) break;
    qvalue = value;
  }
#ifdef STK_MIXTURE_VERBOSE
  if (iter == MAXITER)
  {
    stk_cout << _T("In Gamma_aj_bk::run( CArrayXX const* const& p_tik, CPointX const* const& p_tk) : run( CArrayXX const* const& p_tik, CPointX const* const& p_tk)  did not converge\n");
    stk_cout << _T("qvalue =") << qvalue << _T("\n");
  }
#endif
  return flag;
}

References _T, STK::Algo::findZero(), MAXITER, STK::mean(), stk_cout, STK::sum(), and TOL.

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

STK_Gamma_aj_bk.h

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Base

Constructor & Destructor Documentation

◆ Gamma_aj_bk() [1/2]

◆ Gamma_aj_bk() [2/2]

◆ ~Gamma_aj_bk()

Member Function Documentation

◆ computeNbFreeParameters()

◆ randomInit()

◆ run()