root/library/bdm/estim/arx.cpp @ 1038

#include "arx.h"
namespace bdm {

void ARX::bayes_weighted ( const vec &yt, const vec &cond, const double w ) {
        bdm_assert_debug ( yt.length() == dimy, "BM::bayes yt is of size "+num2str(yt.length())+" expected dimension is "+num2str(dimy) );
        bdm_assert_debug ( cond.length() == rgrlen , "BM::bayes cond is of size "+num2str(cond.length())+" expected dimension is "+num2str(rgrlen) );
        
        BMEF::bayes_weighted(yt,cond,w); //potential discount scheduling
        
        double lnc;
        //cache
        ldmat &V = est._V();
        double &nu = est._nu();

        dyad.set_subvector ( 0, yt );
        if (cond.length()>0)
                dyad.set_subvector ( dimy, cond );
        // possible "1" is there from the beginning

        if ( frg < 1.0 ) {
                est.pow ( frg ); // multiply V and nu


                //stabilize
                ldmat V0 = alter_est._V(); //$ copy
                double &nu0 = alter_est._nu();

                V0 *= ( 1 - frg );
                V += V0; //stabilization
                nu += ( 1 - frg ) * nu0;

                // recompute loglikelihood of new "prior"
                if ( evalll ) {
                        last_lognc = est.lognc();
                }
        }
        V.opupdt ( dyad, w );
        nu += w;

        // log(sqrt(2*pi)) = 0.91893853320467
        if ( evalll ) {
                lnc = est.lognc();
                ll = lnc - last_lognc - 0.91893853320467;
                last_lognc = lnc;
        }
}

double ARX::logpred ( const vec &yt, const vec &cond ) const {
        egiw pred ( est );
        ldmat &V = pred._V();
        double &nu = pred._nu();

        double lll;
        vec dyad_p = dyad;
        dyad_p.set_subvector ( 0, yt );
        dyad_p.set_subvector(dimy,cond);
        
        if ( frg < 1.0 ) {
                pred.pow ( frg );
                lll = pred.lognc();
        } else//should be save: last_lognc is changed only by bayes;
                if ( evalll ) {
                        lll = last_lognc;
                } else {
                        lll = pred.lognc();
                }

        V.opupdt ( dyad_p, 1.0 );
        nu += 1.0;
        // log(sqrt(2*pi)) = 0.91893853320467
        return pred.lognc() - lll - 0.91893853320467;
}

void ARX::flatten ( const BMEF* B , double weight =1.0) {
        const ARX* A = dynamic_cast<const ARX*> ( B );
        // nu should be equal to B.nu
        est.pow ( A->posterior()._nu() / posterior()._nu() *weight);
        if ( evalll ) {
                last_lognc = est.lognc();
        }
}

ARX* ARX::_copy ( ) const {
        ARX* Tmp = new ARX ( *this );
        return Tmp;
}

void ARX::set_statistics ( const BMEF* B0 ) {
        const ARX* A0 = dynamic_cast<const ARX*> ( B0 );

        bdm_assert_debug ( dimension() == A0->dimension(), "Statistics of different dimensions" );
        set_statistics ( A0->dimensiony(), A0->posterior()._V(), A0->posterior()._nu() );
}

enorm<ldmat>* ARX::epredictor ( const vec &cond ) const {
        bdm_assert_debug ( cond.length() == rgrlen , "ARX::epredictor cond is of size "+num2str(cond.length())+" expected dimension is "+num2str(rgrlen) );
        
        mat mu ( dimy, posterior()._V().rows() - dimy );
        mat R ( dimy, dimy );

        vec ext_rgr;
        if (have_constant){
                ext_rgr = concat(cond,vec_1(1.0));
        } else {
                ext_rgr = cond;
        }
        
        enorm<ldmat>* tmp;
        tmp = new enorm<ldmat> ( );
        //TODO: too hackish
        if ( yrv._dsize() > 0 ) {
        }

        est.mean_mat ( mu, R ); //mu =
        //correction for student-t  -- TODO check if correct!!
        //R*=nu/(nu-2);
        if (mu.cols()>0) {// nonempty egiw
                mat p_mu = mu.T() * ext_rgr;    //the result is one column
                tmp->set_parameters ( p_mu.get_col ( 0 ), ldmat ( R ) );
        } else {
                tmp->set_parameters ( zeros( R.rows() ), ldmat ( R ) );
        }
        if (dimy==yrv._dsize())
                tmp->set_rv(yrv);
        return tmp;
}

mlstudent* ARX::predictor_student ( ) const {
        const ldmat &V = posterior()._V();

        mat mu ( dimy, V.rows() - dimy );
        mat R ( dimy, dimy );
        mlstudent* tmp;
        tmp = new mlstudent ( );

        est.mean_mat ( mu, R ); //
        mu = mu.T();

        int end = V._L().rows() - 1;
        ldmat Lam ( V._L() ( dimy, end, dimy, end ), V._D() ( dimy, end ) );  //exp val of R


        if ( have_constant ) { // no constant term
                //Assume the constant term is the last one:
                if ( mu.cols() > 1 ) {
                        tmp->set_parameters ( mu.get_cols ( 0, mu.cols() - 2 ), mu.get_col ( mu.cols() - 1 ), ldmat ( R ), Lam );
                } else {
                        tmp->set_parameters ( mat ( dimy, dimc ), mu.get_col ( mu.cols() - 1 ), ldmat ( R ), Lam );
                }
        } else {
                // no constant term
                tmp->set_parameters ( mu, zeros ( dimy ), ldmat ( R ), Lam );
        }
        return tmp;
}



/*! \brief Return the best structure
@param Eg a copy of GiW density that is being examined
@param Eg0 a copy of prior GiW density before estimation
@param Egll likelihood of the current Eg
@param indices current indices
\return best likelihood in the structure below the given one
*/
double egiw_bestbelow ( egiw Eg, egiw Eg0, double Egll, ivec &indices ) { //parameter Eg is a copy!
        ldmat Vo = Eg._V(); //copy
        ldmat Vo0 = Eg._V(); //copy
        ldmat& Vp = Eg._V(); // pointer into Eg
        ldmat& Vp0 = Eg._V(); // pointer into Eg
        int end = Vp.rows() - 1;
        int i;
        mat Li;
        mat Li0;
        double maxll = Egll;
        double tmpll = Egll;
        double belll = Egll;

        ivec tmpindices;
        ivec maxindices = indices;


        cout << "bb:(" << indices << ") ll=" << Egll << endl;

        //try to remove only one rv
        for ( i = 0; i < end; i++ ) {
                //copy original
                Li = Vo._L();
                Li0 = Vo0._L();
                //remove stuff
                Li.del_col ( i + 1 );
                Li0.del_col ( i + 1 );
                Vp.ldform ( Li, Vo._D() );
                Vp0.ldform ( Li0, Vo0._D() );
                tmpll = Eg.lognc() - Eg0.lognc(); // likelihood is difference of norm. coefs.

                cout << "i=(" << i << ") ll=" << tmpll << endl;

                //
                if ( tmpll > Egll ) { //increase of the likelihood
                        tmpindices = indices;
                        tmpindices.del ( i );
                        //search for a better match in this substructure
                        belll = egiw_bestbelow ( Eg, Eg0, tmpll, tmpindices );
                        if ( belll > maxll ) { //better match found
                                maxll = belll;
                                maxindices = tmpindices;
                        }
                }
        }
        indices = maxindices;
        return maxll;
}

ivec ARX::structure_est ( const egiw &est0 ) {
        ivec ind = linspace ( 1, est.dimension() - 1 );
        egiw_bestbelow ( est, est0, est.lognc() - est0.lognc(), ind );
        return ind;
}



ivec ARX::structure_est_LT ( const egiw &est0 ) {
        //some stuff with beliefs etc.
        ivec belief = vec_1 ( 2 );        // default belief
        int nbest = 1;           // nbest: how many regressors are returned
        int nrep = 5;         // nrep: number of random repetions of structure estimation
        double lambda   = 0.9;
        int k = 2;
        
        Array<str_aux> o2;
        
        ivec ind = bdm::straux1(est._V(),est._nu(), est0._V(), est0._nu(), belief, nbest, nrep, lambda, k, o2);
        
        return ind;
}

void ARX::from_setting ( const Setting &set ) {
        BMEF::from_setting(set);
        
        UI::get (rgr, set, "rgr", UI::compulsory );
        
        dimy = yrv._dsize();
        bdm_assert(dimy>0,"ARX::yrv should not be empty");
        rgrlen = rgr._dsize();

        int constant;
        if ( !UI::get ( constant, set, "constant", UI::optional ) ) {
                have_constant = true;
        } else {
                have_constant = constant > 0;
        }
        dimc = rgrlen;
        rvc = rgr;

        //init
        shared_ptr<egiw> pri = UI::build<egiw> ( set, "prior", UI::optional );
        if (pri){
                set_prior(pri.get());
        } else {
                shared_ptr<egiw> post = UI::build<egiw> ( set, "posterior", UI::optional );
                set_prior(post.get());
        }
                
        
        shared_ptr<egiw> alt = UI::build<egiw> ( set, "alternative", UI::optional );
        if ( alt ) {
                bdm_assert ( alt->_dimx() == dimy, "alternative is not compatible" );
                bdm_assert ( alt->_V().rows() == dimy + rgrlen + int(have_constant==true), "alternative is not compatible" );
                alter_est.set_parameters ( alt->_dimx(), alt->_V(), alt->_nu() );
                alter_est.validate();
        } 
        // frg handled by BMEF

}

void ARX::set_prior(const epdf *pri){
        const egiw * eg=dynamic_cast<const egiw*>(pri);
        if ( eg ) {
                bdm_assert ( eg->_dimx() == dimy, "prior is not compatible" );
                bdm_assert ( eg->_V().rows() == dimy + rgrlen + int(have_constant==true), "prior is not compatible" );
                est.set_parameters ( eg->_dimx(), eg->_V(), eg->_nu() );
                est.validate();
        } else {
                est.set_parameters ( dimy, zeros ( dimy + rgrlen +int(have_constant==true)) );
                set_prior_default ( est );
        }
        //check alternative
        if (alter_est.dimension()!=dimension()){
                alter_est = est;
        }
}

void ARXpartialforg::bayes ( const vec &val, const vec &cond ) {
    #define LOG2  0.69314718055995
    vec frg = cond.right(cond.length() - rgrlen);
    vec cond_rgr = cond.left(rgrlen);       // regression vector

    int dimV = est._V().cols();
    int nparams = dimV - 1;                 // number of parameters
    int nalternatives = 1 << nparams;    // number of alternatives

    // Permutation matrix
    mat perm_matrix = ones(nalternatives, nparams);
    int i, j, period, idx_from, idx_to, start, end;
    for(i = 0; i < nparams; i++) {
                idx_from = 1 << i;
                period   = ( idx_from << 1 );
        idx_to   = period - 1;
                j = 0;
        start = idx_from;
        end = idx_to;
                while ( start < nalternatives ) {
            perm_matrix.set_submatrix(start, end, i, i, 0);
            j++;
            start = idx_from + period * j;
            end = idx_to + period * j;
        }
    }

    // Array of egiws for approximation
    Array<egiw*> egiw_array(nalternatives + 1);
    // No. of conditioning rows in LD
    int nalternatives_cond, position;

    for(int i = 0; i < nalternatives; i++) {
        // vector defining alternatives
        vec vec_alt = perm_matrix.get_row(i);

        // full alternative or filtered
        if( sum(vec_alt) == vec_alt.length() )  {
            egiw_array(i) = &alter_est;
            continue;
        } else if( sum(vec_alt) == 0 ) {
            egiw_array(i) = &est;
            continue;
        }

        nalternatives_cond = (int) sum(vec_alt) + 1;
        ivec vec_perm(0);                   // permutation vector

        for(int j = 0; j < nparams; j++) {
            position = dimV - j - 2;
            if ( vec_alt(position) == 0 ) {
                vec_perm.ins(j, position + 1);
            }
            else {
                vec_perm.ins(0, position + 1);
            }
        }
        vec_perm.ins(0, 0);

        ldmat filt (est._V(), vec_perm);
        ldmat alt (alter_est._V(), vec_perm);

        mat tmpL(dimV, dimV);
        tmpL.set_rows( 0, alt._L().get_rows(0, nalternatives_cond - 1) );
        tmpL.set_rows( nalternatives_cond, filt._L().get_rows(nalternatives_cond, nparams) );

        vec tmpD(dimV);
        tmpD.set_subvector( 0, alt._D()(0, nalternatives_cond - 1) );
        tmpD.set_subvector( nalternatives_cond, filt._D()(nalternatives_cond, nparams) );

        ldmat tmpLD (tmpL, tmpD);

        vec_perm = sort_index(vec_perm);
        ldmat newLD (tmpLD, vec_perm);

        egiw_array(i) = new egiw(1, newLD, alter_est._nu());
    }

    // Approximation
    double sumVecCommon;                // frequently used term
    vec vecNu(nalternatives);           // vector of nus of components
    vec vecD(nalternatives);            // vector of LS reminders 
    vec vecCommon(nalternatives);       // vector of common parts
    mat matVecsTheta;                           // matrix whose rows are theta vects.

    for (i = 0; i < nalternatives; i++) {
        vecNu.shift_left( egiw_array(i)->_nu() );
        vecD.shift_left( egiw_array(i)->_V()._D()(0) );
        matVecsTheta.append_row( egiw_array(i)->est_theta()  );
    }

    vecCommon = elem_mult ( frg, elem_div(vecNu, vecD) );
    sumVecCommon = sum(vecCommon);

    // approximation of est. regr. coefficients
    vec aprEstTheta(nparams);  aprEstTheta.zeros();
    for (i = 0; i < nalternatives; i++) {
        aprEstTheta +=  matVecsTheta.get_row(i) * vecCommon(i);
    }
    aprEstTheta /= sumVecCommon;
    
    // approximation of degr. of freedom
    double aprNu;
    double A = log( sumVecCommon );             // Term 'A' in equation
    for ( int i = 0; i < nalternatives; i++ ) {
        A += frg(i) * ( log( vecD(i) ) - psi( 0.5 * vecNu(i) ) );
    }
    aprNu = ( 1 + sqrt(1 + 4 * (A - LOG2)/3 ) ) / ( 2 * (A - LOG2) );

    // approximation of LS reminder D(0,0)
    double aprD = aprNu / sumVecCommon;

    // Aproximation of covariance of LS est.
    mat aprC = zeros(nparams, nparams);
    for ( int i = 0; i < nalternatives; i++ ) {
        aprC += egiw_array(i)->est_theta_cov().to_mat() * frg(i); 
        vec tmp = ( matVecsTheta.get_row(i) - aprEstTheta );
        aprC += vecCommon(i) * outer_product( tmp, tmp);
    }

    // Construct GiW pdf
    ldmat aprCinv ( inv(aprC) );
    vec D = concat( aprD, aprCinv._D() );
    mat L = eye(dimV);
    L.set_submatrix(1, 0, aprCinv._L() * aprEstTheta);
    L.set_submatrix(1, 1, aprCinv._L());
    ldmat aprLD (L, D);
    est = egiw(1, aprLD, aprNu);

        if ( evalll ) {
                last_lognc = est.lognc();
        }
                
    // update
    ARX::bayes ( val, cond_rgr );
}

}