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 | |
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20 | namespace bdm { |
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21 | |
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22 | /*! |
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23 | * \brief Linear Autoregressive model with Gaussian noise |
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24 | |
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25 | Regression of the following kind: |
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26 | \f[ |
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27 | y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t |
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28 | \f] |
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29 | 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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30 | \f[ |
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31 | e_t \sim \mathcal{N}(0,1). |
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32 | \f] |
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33 | |
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34 | See \ref tut_arx for mathematical treatment. |
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35 | |
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36 | The easiest way how to use the class is: |
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37 | \include arx_simple.cpp |
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38 | |
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39 | \todo sort out constant terms - bayes should accept vec without additional 1s |
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40 | */ |
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41 | class ARX: public BMEF { |
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42 | protected: |
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43 | //!size of output variable (needed in regressors) |
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44 | int dimx; |
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45 | //!description of modelled data \f$ y_t \f$ in the likelihood function |
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46 | //! Do NOT access directly, only via \c get_yrv(). |
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47 | RV _yrv; |
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48 | //! Posterior estimate of \f$\theta,r\f$ in the form of Normal-inverse Wishart density |
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49 | egiw est; |
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50 | //! cached value of est.V |
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51 | ldmat &V; |
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52 | //! cached value of est.nu |
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53 | double ν |
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54 | public: |
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55 | //! \name Constructors |
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56 | //!@{ |
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57 | ARX ( const double frg0 = 1.0 ) : BMEF ( frg0 ), est (), V ( est._V() ), nu ( est._nu() ) {}; |
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58 | ARX ( const ARX &A0 ) : BMEF (), est (), V ( est._V() ), nu ( est._nu() ) { |
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59 | set_statistics ( A0.dimx, A0.V, A0.nu ); |
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60 | set_parameters ( A0.frg ); |
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61 | }; |
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62 | ARX* _copy_() const; |
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63 | void set_parameters ( double frg0 ) { |
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64 | frg = frg0; |
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65 | } |
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66 | void set_statistics ( int dimx0, const ldmat V0, double nu0 = -1.0 ) { |
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67 | est.set_parameters ( dimx0, V0, nu0 ); |
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68 | last_lognc = est.lognc(); |
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69 | dimx = dimx0; |
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70 | } |
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71 | //!@} |
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72 | |
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73 | // //! Set parameters given by moments, \c mu (mean of theta), \c R (mean of R) and \c C (variance of theta) |
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74 | // void set_parameters ( const vec &mu, const mat &R, const mat &C, double dfm){}; |
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75 | //! Set sufficient statistics |
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76 | void set_statistics ( const BMEF* BM0 ); |
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77 | // //! Returns sufficient statistics |
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78 | // void get_parameters ( mat &V0, double &nu0 ) {V0=est._V().to_mat(); nu0=est._nu();} |
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79 | //!\name Mathematical operations |
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80 | //!@{ |
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81 | |
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82 | //! Weighted Bayes \f$ dt = [y_t psi_t] \f$. |
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83 | void bayes ( const vec &dt, const double w ); |
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84 | void bayes ( const vec &dt ) { |
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85 | bayes ( dt, 1.0 ); |
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86 | }; |
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87 | double logpred ( const vec &dt ) const; |
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88 | void flatten ( const BMEF* B ) { |
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89 | const ARX* A = dynamic_cast<const ARX*> ( B ); |
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90 | // nu should be equal to B.nu |
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91 | est.pow ( A->nu / nu ); |
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92 | if ( evalll ) { |
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93 | last_lognc = est.lognc(); |
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94 | } |
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95 | } |
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96 | //! Conditioned version of the predictor |
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97 | enorm<ldmat>* epredictor ( const vec &rgr ) const; |
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98 | //! Predictor for empty regressor |
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99 | enorm<ldmat>* epredictor() const { |
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100 | it_assert_debug ( dimx == V.rows() - 1, "Regressor is not only 1" ); |
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101 | return epredictor ( vec_1 ( 1.0 ) ); |
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102 | } |
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103 | //! conditional version of the predictor |
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104 | mlnorm<ldmat>* predictor() const; |
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105 | mlstudent* predictor_student() const; |
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106 | //! Brute force structure estimation.\return indeces of accepted regressors. |
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107 | ivec structure_est ( egiw Eg0 ); |
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108 | //!@} |
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109 | |
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110 | //!\name Access attributes |
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111 | //!@{ |
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112 | const egiw* _e() const { |
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113 | return &est ; |
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114 | }; |
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115 | const egiw& posterior() const { |
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116 | return est; |
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117 | } |
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118 | //!@} |
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119 | |
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120 | //!\name Connection |
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121 | //!@{ |
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122 | void set_drv ( const RV &drv0 ) { |
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123 | drv = drv0; |
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124 | } |
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125 | RV& get_yrv() { |
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126 | //if yrv is not ready create it |
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127 | if ( _yrv._dsize() != dimx ) { |
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128 | int i = 0; |
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129 | while ( _yrv._dsize() < dimx ) { |
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130 | _yrv.add ( drv ( vec_1 ( i ) ) ); |
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131 | i++; |
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132 | } |
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133 | } |
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134 | //yrv should be ready by now |
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135 | it_assert_debug ( _yrv._dsize() == dimx, "incompatible drv" ); |
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136 | return _yrv; |
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137 | } |
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138 | //!@} |
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139 | |
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140 | // TODO dokumentace - aktualizovat |
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141 | /*! UI for ARX estimator |
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142 | |
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143 | The ARX is constructed from a structure with fields: |
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144 | \code |
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145 | estimator = { |
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146 | type = "ARX"; |
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147 | y = {type="rv", ...} // description of output variables |
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148 | rgr = {type="rv", ...} // description of regressor variables |
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149 | constant = true; // boolean switch if the constant term is modelled or not |
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150 | |
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151 | //optional fields |
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152 | dV0 = [1e-3, 1e-5, 1e-5, 1e-5]; |
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153 | // default: 1e-3 for y, 1e-5 for rgr |
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154 | nu0 = 6; // default: rgrlen + 2 |
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155 | frg = 1.0; // forgetting, default frg=1.0 |
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156 | }; |
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157 | \endcode |
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158 | |
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159 | The estimator will assign names of the posterior in the form ["theta_i" and "r_i"] |
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160 | */ |
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161 | void from_setting ( const Setting &set ); |
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162 | |
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163 | }; |
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164 | |
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165 | UIREGISTER ( ARX ); |
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166 | SHAREDPTR ( ARX ); |
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167 | |
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168 | } |
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169 | |
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170 | #endif // AR_H |
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171 | |
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