root/library/bdm/stat/merger.h @ 384

/*!
  \file
  \brief Mergers for combination of pdfs
  \author Vaclav Smidl.

  -----------------------------------
  BDM++ - C++ library for Bayesian Decision Making under Uncertainty

  Using IT++ for numerical operations
  -----------------------------------
*/

#ifndef MERGER_H
#define MERGER_H


#include "../estim/mixtures.h"

namespace bdm
{
using std::string;

//!Merging methods
enum MERGER_METHOD {ARITHMETIC = 1, GEOMETRIC = 2, LOGNORMAL = 3};

/*!
@brief Base class for general combination of pdfs on discrete support

Mixtures of Gaussian densities are used internally. Switching to other densities should be trivial.

The merged pdfs are expected to be of the form:
 \f[ f(x_i|y_i),  i=1..n \f]
where the resulting merger is a density on \f$ \cup [x_i,y_i] \f$ .
Note that all variables will be joined.

As a result of this feature, each source must be extended to common support
\f[ f(z_i|y_i,x_i) f(x_i|y_i) f(y_i)  i=1..n \f]
where \f$ z_i \f$ accumulate variables that were not in the original source.
These extensions are calculated on-the-fly.

However, these operations can not be performed in general. Hence, this class merges only sources on common support, \f$ y_i={}, z_i={}, \forall i \f$.
For merging of more general cases, use offsprings merger_mix and merger_grid.
*/

class merger_base : public compositepdf, public epdf
{
        protected:
                //! Data link for each mpdf in mpdfs
                Array<datalink_m2e*> dls;
                //! Array of rvs that are not modelled by mpdfs at all, \f$ z_i \f$
                Array<RV> rvzs;
                //! Data Links for extension \f$ f(z_i|x_i,y_i) \f$
                Array<datalink_m2e*> zdls;
                //! number of support points
                int Npoints;
                //! number of sources
                int Nsources;

                //! switch of the methoh used for merging
                MERGER_METHOD METHOD;
                //!Prior on the log-normal merging model
                double beta;

                //! Projection to empirical density (could also be piece-wise linear)
                eEmp eSmp;

                //! debug or not debug
                bool DBG;

                //! debugging file
                it_file* dbg_file;
        public:
                //! \name Constructors
                //! @{

                //!Empty constructor
                merger_base () : compositepdf() {DBG=false;dbg_file=NULL;};
                //!Constructor from sources
                merger_base (const Array<mpdf*> &S) {set_sources (S);};
                //! Function setting the main internal structures 
                void set_sources (const Array<mpdf*> &Sources) {
                        compositepdf::set_elements (Sources);
                        //set sizes
                        dls.set_size (Sources.length());
                        rvzs.set_size (Sources.length());
                        zdls.set_size (Sources.length());

                        rv = getrv (/* checkoverlap = */ false);
                        RV rvc; setrvc (rv, rvc);  // Extend rv by rvc!
                        // join rv and rvc - see descriprion
                        rv.add (rvc);
                        // get dimension
                        dim = rv._dsize();

                        // create links between sources and common rv
                        RV xytmp;
                        for (int i = 0;i < mpdfs.length();i++) {
                                //Establich connection between mpdfs and merger
                                dls (i) = new datalink_m2e;
                                dls (i)->set_connection (mpdfs (i)->_rv(), mpdfs (i)->_rvc(), rv);

                                // find out what is missing in each mpdf
                                xytmp = mpdfs (i)->_rv();
                                xytmp.add (mpdfs (i)->_rvc());
                                // z_i = common_rv-xy
                                rvzs (i) = rv.subt (xytmp);
                                //establish connection between extension (z_i|x,y)s and common rv
                                zdls (i) = new datalink_m2e; zdls (i)->set_connection (rvzs (i), xytmp, rv) ;
                        };
                }
                //! set debug file
                void set_debug_file (const string fname) { 
                        if (DBG) delete dbg_file; 
                        dbg_file = new it_file (fname); 
                        if (dbg_file) DBG = true;
                }
                //! Set internal parameters used in approximation
                void set_method (MERGER_METHOD MTH, double beta0=0.0) {
                        METHOD = MTH; 
                        beta = beta0;
                }
                //! Set support points from a pdf by drawing N samples
                void set_support(const epdf &overall, int N){
                        it_assert_debug ( rv.equal ( overall._rv() ),"Incompatible parameter overall!" );
                        eSmp.set_statistics(&overall,N);
                        Npoints=N;
                }
                
                //! Destructor
                virtual ~merger_base() {
                        for (int i = 0; i < Nsources; i++) {
                                delete dls (i);
                                delete zdls (i);
                        }
                        if (DBG) delete dbg_file;
                };
                //!@}
                
                //! \name Mathematical operations
                //!@{
                
                //!Merge given sources in given points
                void merge () {
                        if (eSmp._w().length() ==0) {it_error("Empty support points use set_support" );}
                        //check if sources overlap:
                        bool OK = true;
                        for (int i = 0;i < mpdfs.length(); i++) {
                                OK &= (rvzs (i)._dsize() == 0); // z_i is empty
                                OK &= (mpdfs (i)->_rvc()._dsize() == 0); // y_i is empty
                        }

                        if (OK) {
                                mat lW = zeros (mpdfs.length(), eSmp._w().length());

                                vec emptyvec (0);
                                for (int i = 0; i < mpdfs.length(); i++) {
                                        for (int j = 0; j < eSmp._w().length(); j++) {
                                                lW (i, j) = mpdfs (i)->evallogcond (eSmp._samples() (j), emptyvec);
                                        }
                                }

                                vec wtmp = exp (merge_points (lW));
                                //renormalize
                                eSmp._w() = wtmp / sum (wtmp);
                        } else {
                                it_error("Sources are not compatible - use merger_mix");
                        }
                        ;
                };


                //! Merge log-likelihood values in points using method specified by parameter METHOD
                vec merge_points (mat &lW);
                
                
                //! sample from merged density
//! weight w is a
                vec mean() const {
                        const Vec<double> &w = eSmp._w();
                        const Array<vec> &S = eSmp._samples();
                        vec tmp = zeros (dim);
                        for (int i = 0; i < Npoints; i++) {
                                tmp += w (i) * S (i);
                        }
                        return tmp;
                }
                mat covariance() const {
                        const vec &w = eSmp._w();
                        const Array<vec> &S = eSmp._samples();

                        vec mea = mean();

                        cout << sum (w) << "," << w*w << endl;

                        mat Tmp = zeros (dim, dim);
                        for (int i = 0; i < Npoints; i++) {
                                Tmp += w (i) * outer_product (S (i), S (i));
                        }
                        return Tmp -outer_product (mea, mea);
                }
                vec variance() const {
                        const vec &w = eSmp._w();
                        const Array<vec> &S = eSmp._samples();

                        vec tmp = zeros (dim);
                        for (int i = 0; i < Nsources; i++) {
                                tmp += w (i) * pow (S (i), 2);
                        }
                        return tmp -pow (mean(), 2);
                }
                //!@}

                //! \name Access to attributes
                //! @{

                //! Access function
                eEmp& _Smp() {return eSmp;}
                
                //!@}
};

class merger_mix : public merger_base
{
        protected:
                //!Internal mixture of EF models
                MixEF Mix;
                //!Number of components in a mixture
                int Ncoms;
                //! coefficient of resampling
                double effss_coef;

        public:
                //!\name Constructors
                //!@{
                merger_mix () {};
                merger_mix (const Array<mpdf*> &S) {set_sources(S);};
                //! Set sources and prepare all internal structures
                void set_sources (const Array<mpdf*> &S) {
                        merger_base::set_sources(S);
                        Nsources = S.length();
                }
                //! Set internal parameters used in approximation
                void set_parameters (int Ncoms0=10, double effss_coef0 = 0.5) {
                        Ncoms = Ncoms0;
                        effss_coef = effss_coef0;
                }
                //!@}
                
                //! \name Mathematical operations
                //!@{
                
                //!Merge values using mixture approximation
                void merge ();

                //! sample from the approximating mixture
                vec sample () const { return Mix.posterior().sample();}
                //! loglikelihood computed on mixture models
                double evallog (const vec &dt) const {
                        vec dtf = ones (dt.length() + 1);
                        dtf.set_subvector (0, dt);
                        return Mix.logpred (dtf);
                }
                //!@}

                //!\name Access functions
                //!@{
//! Access function
                MixEF& _Mix() {return Mix;}
                //! Access function
                emix* proposal() {emix* tmp = Mix.epredictor(); tmp->set_rv (rv); return tmp;}
        //! @}
                
};

}

#endif // MER_H