1 | /*! |
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2 | \file |
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3 | \brief Bayesian Filtering for generalized autoregressive (ARX) model |
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4 | \author Vaclav Smidl. |
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5 | |
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6 | ----------------------------------- |
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7 | BDM++ - C++ library for Bayesian Decision Making under Uncertainty |
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8 | |
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9 | Using IT++ for numerical operations |
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10 | ----------------------------------- |
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11 | */ |
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12 | |
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13 | #ifndef AR_H |
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14 | #define AR_H |
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15 | |
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16 | #include "../math/functions.h" |
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17 | #include "../stat/exp_family.h" |
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18 | #include "../base/user_info.h" |
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19 | //#include "../estim/kalman.h" |
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20 | #include "arx_straux.h" |
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21 | |
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22 | namespace bdm { |
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23 | |
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24 | /*! |
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25 | * \brief Linear Autoregressive model with Gaussian noise |
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26 | |
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27 | Regression of the following kind: |
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28 | \f[ |
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29 | y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t |
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30 | \f] |
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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: |
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32 | \f[ |
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33 | e_t \sim \mathcal{N}(0,1). |
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34 | \f] |
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35 | |
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36 | See \ref tut_arx for mathematical treatment. |
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37 | |
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38 | The easiest way how to use the class is: |
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39 | \include arx_simple.cpp |
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40 | |
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41 | \todo sort out constant terms - bayes should accept vec without additional 1s |
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42 | */ |
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43 | class ARX: public BMEF { |
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44 | protected: |
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45 | //! switch if constant is modelled or not |
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46 | bool have_constant; |
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47 | //! vector of dyadic update |
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48 | vec dyad; |
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49 | //! RV of regressor |
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50 | RV rgr; |
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51 | //! length of the regressor (without optional constant) |
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52 | int rgrlen; |
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53 | //! posterior density |
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54 | egiw est; |
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55 | //! Alternative estimate of parameters, used in stabilized forgetting, see [Kulhavy] |
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56 | egiw alter_est; |
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57 | public: |
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58 | //! \name Constructors |
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59 | //!@{ |
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60 | ARX ( const double frg0 = 1.0 ) : BMEF ( frg0 ), have_constant ( true ), dyad(), rgrlen(),est(), alter_est() {}; |
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61 | 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 ) { }; |
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62 | |
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63 | ARX* _copy() const; |
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64 | |
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65 | void set_frg ( double frg0 ) { |
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66 | frg = frg0; |
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67 | } |
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68 | void set_constant ( bool const0 ) { |
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69 | have_constant = const0; |
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70 | } |
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71 | void set_statistics ( int dimy0, const ldmat V0, double nu0 = -1.0 ) { |
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72 | est.set_parameters ( dimy0, V0, nu0 ); |
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73 | est.validate(); |
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74 | last_lognc = est.lognc(); |
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75 | dimy = dimy0; |
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76 | } |
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77 | //!@} |
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78 | |
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79 | //! Set sufficient statistics |
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80 | void set_statistics ( const BMEF* BM0 ); |
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81 | |
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82 | //!\name Mathematical operations |
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83 | //!@{ |
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84 | |
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85 | //! Weighted Bayes \f$ dt = [y_t psi_t] \f$. |
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86 | void bayes_weighted ( const vec &yt, const vec &cond = empty_vec, const double w = 1.0 ); |
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87 | void bayes ( const vec &yt, const vec &cond = empty_vec ) { |
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88 | bayes_weighted ( yt, cond, 1.0 ); |
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89 | }; |
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90 | double logpred ( const vec &yt, const vec &cond ) const; |
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91 | void flatten ( const BMEF* B , double weight ); |
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92 | //! Conditioned version of the predictor |
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93 | enorm<ldmat>* epredictor ( const vec &rgr ) const; |
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94 | //! conditional version of the predictor |
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95 | template<class sq_T> |
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96 | shared_ptr<mlnorm<sq_T> > ml_predictor() const; |
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97 | //! fast version of predicto |
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98 | template<class sq_T> |
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99 | void ml_predictor_update ( mlnorm<sq_T> &pred ) const; |
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100 | mlstudent* predictor_student() const; |
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101 | //! Brute force structure estimation.\return indices of accepted regressors. |
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102 | ivec structure_est ( const egiw &Eg0 ); |
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103 | //! Smarter structure estimation by Ludvik Tesar.\return indices of accepted regressors. |
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104 | ivec structure_est_LT ( const egiw &Eg0 ); |
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105 | //! reduce structure to the given ivec of matrix V |
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106 | void reduce_structure(ivec &inds_in_V){ |
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107 | ldmat V = posterior()._V(); |
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108 | if (max(inds_in_V)>=V.rows()) {bdm_error("Incompatible structure");} |
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109 | |
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110 | ldmat newV(V,inds_in_V); |
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111 | est.set_parameters(dimy,newV, posterior()._nu()); |
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112 | |
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113 | if (have_constant){ |
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114 | ivec rgr_elem= find(inds_in_V<(V.rows()-1)); // < -- find non-constant |
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115 | rgr = rgr.subselect(rgr_elem); |
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116 | rgrlen = rgr_elem.length(); |
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117 | } else{ |
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118 | rgr = rgr.subselect(inds_in_V); |
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119 | } |
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120 | validate(); |
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121 | } |
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122 | //!@} |
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123 | |
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124 | //!\name Access attributes |
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125 | //!@{ |
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126 | //! return correctly typed posterior (covariant return) |
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127 | const egiw& posterior() const { |
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128 | return est; |
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129 | } |
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130 | //!@} |
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131 | |
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132 | /*! UI for ARX estimator |
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133 | |
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134 | \code |
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135 | class = 'ARX'; |
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136 | yrv = RV({names_of_dt} ) // description of output variables |
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137 | rgr = RV({names_of_regressors}, [-1,-2]} // description of regressor variables |
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138 | constant = 1; // 0/1 switch if the constant term is modelled or not |
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139 | |
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140 | --- optional --- |
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141 | prior = {class='egiw',...}; // Prior density, when given default is used instead |
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142 | alternative = {class='egiw',...}; // Alternative density in stabilized estimation, when not given prior is used |
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143 | |
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144 | frg = 1.0; // forgetting, default frg=1.0 |
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145 | |
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146 | rv = RV({names_of_parameters}} // description of parametetr names |
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147 | // default: [""] |
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148 | \endcode |
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149 | */ |
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150 | void from_setting ( const Setting &set ); |
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151 | |
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152 | void validate() { |
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153 | BMEF::validate(); |
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154 | est.validate(); |
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155 | |
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156 | // When statistics is defined, it has priority |
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157 | if(posterior()._dimx()>0) {//statistics is assigned |
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158 | dimy = posterior()._dimx(); |
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159 | rgrlen=posterior()._V().rows() - dimy - int ( have_constant == true ); |
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160 | dimc = rgrlen; |
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161 | } else{ // statistics is not assigned - build it from dimy and rgrlen |
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162 | bdm_assert(dimy>0,"No way to validate egiw: empty statistics and empty dimy"); |
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163 | est.set_parameters(dimy, zeros(dimy+rgrlen+int(have_constant==true))); |
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164 | set_prior_default(est); |
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165 | } |
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166 | if (alter_est.dimension()==0) alter_est=est; |
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167 | |
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168 | dyad = ones ( est._V().rows() ); |
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169 | } |
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170 | //! function sets prior and alternative density |
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171 | void set_prior ( const epdf *prior ); |
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172 | //! build default prior and alternative when all values are set |
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173 | void set_prior_default ( egiw &prior ) { |
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174 | //assume |
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175 | vec dV0 ( prior._V().rows() ); |
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176 | dV0.set_subvector ( 0, prior._dimx() - 1, 1.0 ); |
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177 | if (dV0.length()>prior._dimx()) |
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178 | dV0.set_subvector ( prior._dimx(), dV0.length() - 1, 1e-5 ); |
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179 | |
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180 | prior.set_parameters ( prior._dimx(), ldmat ( dV0 ) ); |
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181 | prior.validate(); |
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182 | } |
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183 | |
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184 | void to_setting ( Setting &set ) const |
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185 | { |
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186 | BMEF::to_setting( set ); // takes care of rv, yrv, rvc |
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187 | UI::save(rgr, set, "rgr"); |
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188 | int constant = have_constant ? 1 : 0; |
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189 | UI::save(constant, set, "constant"); |
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190 | UI::save(&alter_est, set, "alternative"); |
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191 | UI::save(&posterior(), set, "posterior"); |
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192 | |
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193 | } |
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194 | //! access function |
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195 | RV & _rgr() {return rgr;} |
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196 | bool _have_constant() {return have_constant;} |
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197 | int _rgrlen() {return rgrlen;} |
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198 | }; |
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199 | UIREGISTER ( ARX ); |
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200 | SHAREDPTR ( ARX ); |
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201 | |
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202 | /*! ARX model conditined by knowledge of the forgetting factor |
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203 | \f[ f(\theta| d_1 \ldots d_t , \phi_t) \f] |
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204 | |
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205 | The symbol \f$ \phi \f$ is assumed to be the last of the conditioning variables. |
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206 | */ |
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207 | class ARXfrg : public ARX { |
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208 | public: |
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209 | ARXfrg() : ARX() {}; |
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210 | //! copy constructor |
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211 | ARXfrg ( const ARXfrg &A0 ) : ARX ( A0 ) {}; |
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212 | virtual ARXfrg* _copy() const { |
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213 | ARXfrg *A = new ARXfrg ( *this ); |
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214 | return A; |
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215 | } |
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216 | |
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217 | void bayes ( const vec &val, const vec &cond ) { |
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218 | bdm_assert_debug(cond.size()>rgrlen, "ARXfrg: Insufficient conditioning, frg not given."); |
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219 | frg = cond ( rgrlen); // the first part after rgrlen |
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220 | ARX::bayes ( val, cond.left(rgrlen) ); |
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221 | } |
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222 | void validate() { |
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223 | ARX::validate(); |
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224 | rvc.add ( RV ( "{phi }", vec_1 ( 1 ) ) ); |
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225 | dimc += 1; |
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226 | } |
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227 | }; |
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228 | UIREGISTER ( ARXfrg ); |
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229 | |
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230 | |
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231 | /*! |
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232 | * \brief ARX with partial forgetting |
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233 | |
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234 | Implements partial forgetting when <tt>bayes(const vec &yt, const vec &cond=empty_vec)</tt> is called, where \c cond is a vector <em>(regressor', forg.factor')</em>. |
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235 | |
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236 | Note, that the weights have the same order as hypotheses, following this scheme: |
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237 | \li 0 means that the parameter doesn't change, |
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238 | \li 1 means that the parameter varies. |
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239 | |
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240 | The combinations of parameters are described binary: |
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241 | \f[ |
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242 | 0, 0, 0\ldots \\ |
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243 | 1, 0, 0\ldots \\ |
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244 | 0, 1, 0\ldots \\ |
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245 | 1, 1, 0\ldots \\ |
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246 | \ldots |
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247 | \f] |
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248 | where each n-th column has altering 1's and 0's in n-tuples, n = 0,...,number of params. Hence, the first forg. factor relates to the situation when no parameter changes, the second one when the first parameter changes etc. |
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249 | |
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250 | See ARX class for more information about ARX. |
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251 | */ |
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252 | class ARXpartialforg : public ARX { |
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253 | public: |
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254 | ARXpartialforg() : ARX(1.0) {}; |
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255 | //! copy constructor |
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256 | ARXpartialforg ( const ARXpartialforg &A0 ) : ARX ( A0 ) {}; |
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257 | virtual ARXpartialforg* _copy() const { |
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258 | ARXpartialforg *A = new ARXpartialforg ( *this ); |
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259 | return A; |
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260 | } |
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261 | |
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262 | void bayes ( const vec &val, const vec &cond ); |
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263 | void validate() { |
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264 | ARX::validate(); |
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265 | int philen = pow(2, est._V().cols() - 1); |
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266 | rvc.add ( RV ( "{phi }", vec_1(philen) ) ); // pocet 2^parametru |
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267 | dimc += philen; |
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268 | } |
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269 | }; |
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270 | UIREGISTER ( ARXpartialforg ); |
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271 | |
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272 | |
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273 | //////////////////// |
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274 | template<class sq_T> |
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275 | shared_ptr< mlnorm<sq_T> > ARX::ml_predictor ( ) const { |
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276 | shared_ptr< mlnorm<sq_T> > tmp = new mlnorm<sq_T> ( ); |
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277 | tmp->set_rv ( yrv ); |
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278 | tmp->set_rvc ( _rvc() ); |
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279 | |
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280 | ml_predictor_update ( *tmp ); |
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281 | tmp->validate(); |
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282 | return tmp; |
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283 | } |
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284 | |
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285 | template<class sq_T> |
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286 | void ARX::ml_predictor_update ( mlnorm<sq_T> &pred ) const { |
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287 | mat mu ( dimy, posterior()._V().rows() - dimy ); |
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288 | mat R ( dimy, dimy ); |
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289 | |
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290 | est.mean_mat ( mu, R ); //mu = |
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291 | mu = mu.T(); |
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292 | //correction for student-t -- TODO check if correct!! |
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293 | |
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294 | if ( have_constant ) { // constant term |
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295 | //Assume the constant term is the last one: |
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296 | pred.set_parameters ( mu.get_cols ( 0, mu.cols() - 2 ), mu.get_col ( mu.cols() - 1 ), sq_T ( R ) ); |
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297 | } else { |
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298 | pred.set_parameters ( mu, zeros ( dimy ), sq_T ( R ) ); |
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299 | } |
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300 | } |
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301 | |
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302 | }; |
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303 | #endif // AR_H |
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304 | |
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