[97] | 1 | /*! |
---|
| 2 | \file |
---|
| 3 | \brief Bayesian Filtering for generalized autoregressive (ARX) model |
---|
| 4 | \author Vaclav Smidl. |
---|
| 5 | |
---|
| 6 | ----------------------------------- |
---|
| 7 | BDM++ - C++ library for Bayesian Decision Making under Uncertainty |
---|
| 8 | |
---|
| 9 | Using IT++ for numerical operations |
---|
| 10 | ----------------------------------- |
---|
| 11 | */ |
---|
| 12 | |
---|
| 13 | #ifndef AR_H |
---|
| 14 | #define AR_H |
---|
| 15 | |
---|
[384] | 16 | #include "../math/functions.h" |
---|
| 17 | #include "../stat/exp_family.h" |
---|
| 18 | #include "../base/user_info.h" |
---|
[585] | 19 | //#include "../estim/kalman.h" |
---|
| 20 | #include "arx_straux.h" |
---|
[97] | 21 | |
---|
[270] | 22 | namespace bdm { |
---|
[97] | 23 | |
---|
| 24 | /*! |
---|
| 25 | * \brief Linear Autoregressive model with Gaussian noise |
---|
| 26 | |
---|
| 27 | Regression of the following kind: |
---|
| 28 | \f[ |
---|
| 29 | y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t |
---|
| 30 | \f] |
---|
| 31 | where unknown parameters \c rv are \f$[\theta r]\f$, regression vector \f$\psi=\psi(y_{1:t},u_{1:t})\f$ is a known function of past outputs and exogeneous variables \f$u_t\f$. Distrubances \f$e_t\f$ are supposed to be normally distributed: |
---|
| 32 | \f[ |
---|
| 33 | e_t \sim \mathcal{N}(0,1). |
---|
| 34 | \f] |
---|
| 35 | |
---|
[271] | 36 | See \ref tut_arx for mathematical treatment. |
---|
| 37 | |
---|
| 38 | The easiest way how to use the class is: |
---|
| 39 | \include arx_simple.cpp |
---|
| 40 | |
---|
[384] | 41 | \todo sort out constant terms - bayes should accept vec without additional 1s |
---|
[97] | 42 | */ |
---|
[170] | 43 | class ARX: public BMEF { |
---|
[97] | 44 | protected: |
---|
[625] | 45 | //! switch if constant is modelled or not |
---|
| 46 | bool have_constant; |
---|
[679] | 47 | //! vector of dyadic update |
---|
| 48 | vec dyad; |
---|
[964] | 49 | //! length of the regressor |
---|
| 50 | int rgrlen; |
---|
[679] | 51 | //! posterior density |
---|
| 52 | egiw est; |
---|
[639] | 53 | //! Alternative estimate of parameters, used in stabilized forgetting, see [Kulhavy] |
---|
| 54 | egiw alter_est; |
---|
[97] | 55 | public: |
---|
[270] | 56 | //! \name Constructors |
---|
| 57 | //!@{ |
---|
[964] | 58 | ARX ( const double frg0 = 1.0 ) : BMEF ( frg0 ), have_constant ( true ), dyad(), rgrlen(),est(), alter_est() {}; |
---|
| 59 | ARX ( const ARX &A0 ) : BMEF ( A0 ), have_constant ( A0.have_constant ), dyad ( A0.dyad ),rgrlen(A0.rgrlen), est ( A0.est ), alter_est ( A0.alter_est ) { }; |
---|
[766] | 60 | |
---|
| 61 | ARX* _copy() const; |
---|
| 62 | |
---|
[796] | 63 | void set_frg ( double frg0 ) { |
---|
[477] | 64 | frg = frg0; |
---|
| 65 | } |
---|
[649] | 66 | void set_constant ( bool const0 ) { |
---|
[737] | 67 | have_constant = const0; |
---|
[649] | 68 | } |
---|
[679] | 69 | void set_statistics ( int dimy0, const ldmat V0, double nu0 = -1.0 ) { |
---|
| 70 | est.set_parameters ( dimy0, V0, nu0 ); |
---|
[878] | 71 | est.validate(); |
---|
[477] | 72 | last_lognc = est.lognc(); |
---|
[679] | 73 | dimy = dimy0; |
---|
[477] | 74 | } |
---|
[270] | 75 | //!@} |
---|
[170] | 76 | |
---|
[145] | 77 | //! Set sufficient statistics |
---|
[170] | 78 | void set_statistics ( const BMEF* BM0 ); |
---|
[625] | 79 | |
---|
[270] | 80 | //!\name Mathematical operations |
---|
| 81 | //!@{ |
---|
| 82 | |
---|
| 83 | //! Weighted Bayes \f$ dt = [y_t psi_t] \f$. |
---|
[737] | 84 | void bayes_weighted ( const vec &yt, const vec &cond = empty_vec, const double w = 1.0 ); |
---|
| 85 | void bayes ( const vec &yt, const vec &cond = empty_vec ) { |
---|
| 86 | bayes_weighted ( yt, cond, 1.0 ); |
---|
[477] | 87 | }; |
---|
[679] | 88 | double logpred ( const vec &yt ) const; |
---|
[738] | 89 | void flatten ( const BMEF* B ); |
---|
[262] | 90 | //! Conditioned version of the predictor |
---|
[270] | 91 | enorm<ldmat>* epredictor ( const vec &rgr ) const; |
---|
| 92 | //! Predictor for empty regressor |
---|
[738] | 93 | enorm<ldmat>* epredictor() const; |
---|
[262] | 94 | //! conditional version of the predictor |
---|
[723] | 95 | template<class sq_T> |
---|
| 96 | shared_ptr<mlnorm<sq_T> > ml_predictor() const; |
---|
[737] | 97 | //! fast version of predicto |
---|
[723] | 98 | template<class sq_T> |
---|
[737] | 99 | void ml_predictor_update ( mlnorm<sq_T> &pred ) const; |
---|
[270] | 100 | mlstudent* predictor_student() const; |
---|
[896] | 101 | //! Brute force structure estimation.\return indices of accepted regressors. |
---|
[170] | 102 | ivec structure_est ( egiw Eg0 ); |
---|
[896] | 103 | //! Smarter structure estimation by Ludvik Tesar.\return indices of accepted regressors. |
---|
[577] | 104 | ivec structure_est_LT ( egiw Eg0 ); |
---|
[270] | 105 | //!@} |
---|
| 106 | |
---|
| 107 | //!\name Access attributes |
---|
| 108 | //!@{ |
---|
[737] | 109 | //! return correctly typed posterior (covariant return) |
---|
| 110 | const egiw& posterior() const { |
---|
[477] | 111 | return est; |
---|
| 112 | } |
---|
[270] | 113 | //!@} |
---|
| 114 | |
---|
[357] | 115 | /*! UI for ARX estimator |
---|
| 116 | |
---|
| 117 | \code |
---|
[625] | 118 | class = 'ARX'; |
---|
[964] | 119 | yrv = RV({names_of_dt} ) // description of output variables |
---|
[625] | 120 | rgr = RV({names_of_regressors}, [-1,-2]} // description of regressor variables |
---|
[631] | 121 | constant = 1; // 0/1 switch if the constant term is modelled or not |
---|
[357] | 122 | |
---|
[625] | 123 | --- optional --- |
---|
[665] | 124 | prior = {class='egiw',...}; // Prior density, when given default is used instead |
---|
| 125 | alternative = {class='egiw',...}; // Alternative density in stabilized estimation, when not given prior is used |
---|
[737] | 126 | |
---|
[625] | 127 | frg = 1.0; // forgetting, default frg=1.0 |
---|
| 128 | |
---|
[964] | 129 | rv = RV({names_of_parameters}} // description of parametetr names |
---|
| 130 | // default: [""] |
---|
[357] | 131 | \endcode |
---|
| 132 | */ |
---|
[477] | 133 | void from_setting ( const Setting &set ); |
---|
[357] | 134 | |
---|
[625] | 135 | void validate() { |
---|
[850] | 136 | BMEF::validate(); |
---|
[964] | 137 | est.validate(); |
---|
[679] | 138 | //if dimc not set set it from V |
---|
[737] | 139 | if ( dimc == 0 ) { |
---|
| 140 | dimc = posterior()._V().rows() - dimy - int ( have_constant == true ); |
---|
[679] | 141 | } |
---|
[737] | 142 | |
---|
| 143 | if ( have_constant ) { |
---|
| 144 | dyad = ones ( dimy + dimc + 1 ); |
---|
| 145 | } else { |
---|
| 146 | dyad = zeros ( dimy + dimc ); |
---|
[679] | 147 | } |
---|
[737] | 148 | |
---|
[625] | 149 | } |
---|
[737] | 150 | //! function sets prior and alternative density |
---|
[973] | 151 | void set_prior ( const epdf *prior ); |
---|
[665] | 152 | //! build default prior and alternative when all values are set |
---|
[737] | 153 | void set_prior_default ( egiw &prior ) { |
---|
| 154 | //assume |
---|
| 155 | vec dV0 ( prior._V().rows() ); |
---|
| 156 | dV0.set_subvector ( 0, prior._dimx() - 1, 1.0 ); |
---|
[810] | 157 | if (dV0.length()>prior._dimx()) |
---|
| 158 | dV0.set_subvector ( prior._dimx(), dV0.length() - 1, 1e-5 ); |
---|
[878] | 159 | |
---|
[737] | 160 | prior.set_parameters ( prior._dimx(), ldmat ( dV0 ) ); |
---|
[878] | 161 | prior.validate(); |
---|
[665] | 162 | } |
---|
[746] | 163 | |
---|
| 164 | void to_setting ( Setting &set ) const |
---|
| 165 | { |
---|
[796] | 166 | BMEF::to_setting( set ); // takes care of rv, yrv, rvc |
---|
| 167 | int constant = have_constant ? 1 : 0; |
---|
| 168 | UI::save(constant, set, "constant"); |
---|
| 169 | UI::save(&est, set, "prior"); |
---|
| 170 | UI::save(&alter_est, set, "alternative"); |
---|
| 171 | |
---|
| 172 | |
---|
[746] | 173 | } |
---|
[97] | 174 | }; |
---|
[477] | 175 | UIREGISTER ( ARX ); |
---|
[529] | 176 | SHAREDPTR ( ARX ); |
---|
[357] | 177 | |
---|
[639] | 178 | /*! ARX model conditined by knowledge of the forgetting factor |
---|
| 179 | \f[ f(\theta| d_1 \ldots d_t , \phi_t) \f] |
---|
[700] | 180 | |
---|
| 181 | The symbol \f$ \phi \f$ is assumed to be the last of the conditioning variables. |
---|
[639] | 182 | */ |
---|
[737] | 183 | class ARXfrg : public ARX { |
---|
| 184 | public: |
---|
| 185 | ARXfrg() : ARX() {}; |
---|
| 186 | //! copy constructor |
---|
| 187 | ARXfrg ( const ARXfrg &A0 ) : ARX ( A0 ) {}; |
---|
[766] | 188 | virtual ARXfrg* _copy() const { |
---|
[737] | 189 | ARXfrg *A = new ARXfrg ( *this ); |
---|
| 190 | return A; |
---|
| 191 | } |
---|
[700] | 192 | |
---|
[737] | 193 | void bayes ( const vec &val, const vec &cond ) { |
---|
[964] | 194 | int arx_cond_size=rgrlen -int(have_constant==true); |
---|
| 195 | bdm_assert_debug(cond.size()>arx_cond_size, "ARXfrg: Insufficient conditioning, frg not given."); |
---|
| 196 | frg = cond ( arx_cond_size ); // the first part after rgrlen |
---|
| 197 | ARX::bayes ( val, cond.left(arx_cond_size) ); |
---|
[639] | 198 | } |
---|
[700] | 199 | void validate() { |
---|
| 200 | ARX::validate(); |
---|
[737] | 201 | rvc.add ( RV ( "{phi }", vec_1 ( 1 ) ) ); |
---|
| 202 | dimc += 1; |
---|
[700] | 203 | } |
---|
[639] | 204 | }; |
---|
[737] | 205 | UIREGISTER ( ARXfrg ); |
---|
[723] | 206 | |
---|
| 207 | |
---|
| 208 | //////////////////// |
---|
| 209 | template<class sq_T> |
---|
| 210 | shared_ptr< mlnorm<sq_T> > ARX::ml_predictor ( ) const { |
---|
| 211 | shared_ptr< mlnorm<sq_T> > tmp = new mlnorm<sq_T> ( ); |
---|
[737] | 212 | tmp->set_rv ( yrv ); |
---|
| 213 | tmp->set_rvc ( _rvc() ); |
---|
| 214 | |
---|
| 215 | ml_predictor_update ( *tmp ); |
---|
[723] | 216 | tmp->validate(); |
---|
| 217 | return tmp; |
---|
| 218 | } |
---|
| 219 | |
---|
| 220 | template<class sq_T> |
---|
[737] | 221 | void ARX::ml_predictor_update ( mlnorm<sq_T> &pred ) const { |
---|
[723] | 222 | mat mu ( dimy, posterior()._V().rows() - dimy ); |
---|
| 223 | mat R ( dimy, dimy ); |
---|
[737] | 224 | |
---|
[723] | 225 | est.mean_mat ( mu, R ); //mu = |
---|
| 226 | mu = mu.T(); |
---|
| 227 | //correction for student-t -- TODO check if correct!! |
---|
[737] | 228 | |
---|
| 229 | if ( have_constant ) { // constant term |
---|
[723] | 230 | //Assume the constant term is the last one: |
---|
| 231 | pred.set_parameters ( mu.get_cols ( 0, mu.cols() - 2 ), mu.get_col ( mu.cols() - 1 ), sq_T ( R ) ); |
---|
| 232 | } else { |
---|
[737] | 233 | pred.set_parameters ( mu, zeros ( dimy ), sq_T ( R ) ); |
---|
[723] | 234 | } |
---|
| 235 | } |
---|
| 236 | |
---|
[639] | 237 | }; |
---|
[97] | 238 | #endif // AR_H |
---|
| 239 | |
---|