[8] | 1 | /*! |
---|
| 2 | \file |
---|
| 3 | \brief Probability distributions for Exponential Family models. |
---|
| 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 EF_H |
---|
| 14 | #define EF_H |
---|
| 15 | |
---|
[262] | 16 | |
---|
[461] | 17 | #include "../shared_ptr.h" |
---|
[384] | 18 | #include "../base/bdmbase.h" |
---|
[262] | 19 | #include "../math/chmat.h" |
---|
[8] | 20 | |
---|
[737] | 21 | namespace bdm { |
---|
[8] | 22 | |
---|
[32] | 23 | |
---|
| 24 | //! Global Uniform_RNG |
---|
[488] | 25 | extern Uniform_RNG UniRNG; |
---|
[33] | 26 | //! Global Normal_RNG |
---|
[488] | 27 | extern Normal_RNG NorRNG; |
---|
[33] | 28 | //! Global Gamma_RNG |
---|
[488] | 29 | extern Gamma_RNG GamRNG; |
---|
[32] | 30 | |
---|
[488] | 31 | /*! |
---|
| 32 | * \brief General conjugate exponential family posterior density. |
---|
[8] | 33 | |
---|
[488] | 34 | * More?... |
---|
| 35 | */ |
---|
[28] | 36 | |
---|
[737] | 37 | class eEF : public epdf { |
---|
| 38 | public: |
---|
[32] | 39 | // eEF() :epdf() {}; |
---|
[737] | 40 | //! default constructor |
---|
| 41 | eEF () : epdf () {}; |
---|
| 42 | //! logarithm of the normalizing constant, \f$\mathcal{I}\f$ |
---|
| 43 | virtual double lognc() const = 0; |
---|
[565] | 44 | |
---|
[737] | 45 | //!Evaluate normalized log-probability |
---|
| 46 | virtual double evallog_nn ( const vec &val ) const { |
---|
| 47 | bdm_error ( "Not implemented" ); |
---|
| 48 | return 0.0; |
---|
| 49 | } |
---|
[565] | 50 | |
---|
[737] | 51 | //!Evaluate normalized log-probability |
---|
| 52 | virtual double evallog ( const vec &val ) const { |
---|
| 53 | double tmp; |
---|
| 54 | tmp = evallog_nn ( val ) - lognc(); |
---|
| 55 | return tmp; |
---|
| 56 | } |
---|
| 57 | //!Evaluate normalized log-probability for many samples |
---|
| 58 | virtual vec evallog_mat ( const mat &Val ) const { |
---|
| 59 | vec x ( Val.cols() ); |
---|
| 60 | for ( int i = 0; i < Val.cols(); i++ ) { |
---|
| 61 | x ( i ) = evallog_nn ( Val.get_col ( i ) ) ; |
---|
[488] | 62 | } |
---|
[737] | 63 | return x - lognc(); |
---|
| 64 | } |
---|
| 65 | //!Evaluate normalized log-probability for many samples |
---|
| 66 | virtual vec evallog_mat ( const Array<vec> &Val ) const { |
---|
| 67 | vec x ( Val.length() ); |
---|
| 68 | for ( int i = 0; i < Val.length(); i++ ) { |
---|
| 69 | x ( i ) = evallog_nn ( Val ( i ) ) ; |
---|
[488] | 70 | } |
---|
[737] | 71 | return x - lognc(); |
---|
| 72 | } |
---|
[565] | 73 | |
---|
[737] | 74 | //!Power of the density, used e.g. to flatten the density |
---|
| 75 | virtual void pow ( double p ) { |
---|
| 76 | bdm_error ( "Not implemented" ); |
---|
| 77 | } |
---|
[488] | 78 | }; |
---|
[8] | 79 | |
---|
[33] | 80 | |
---|
[170] | 81 | //! Estimator for Exponential family |
---|
[737] | 82 | class BMEF : public BM { |
---|
| 83 | protected: |
---|
| 84 | //! forgetting factor |
---|
| 85 | double frg; |
---|
| 86 | //! cached value of lognc() in the previous step (used in evaluation of \c ll ) |
---|
| 87 | double last_lognc; |
---|
| 88 | public: |
---|
| 89 | //! Default constructor (=empty constructor) |
---|
| 90 | BMEF ( double frg0 = 1.0 ) : BM (), frg ( frg0 ) {} |
---|
| 91 | //! Copy constructor |
---|
| 92 | BMEF ( const BMEF &B ) : BM ( B ), frg ( B.frg ), last_lognc ( B.last_lognc ) {} |
---|
| 93 | //!get statistics from another model |
---|
| 94 | virtual void set_statistics ( const BMEF* BM0 ) { |
---|
| 95 | bdm_error ( "Not implemented" ); |
---|
| 96 | } |
---|
[565] | 97 | |
---|
[737] | 98 | //! Weighted update of sufficient statistics (Bayes rule) |
---|
| 99 | virtual void bayes_weighted ( const vec &data, const vec &cond = empty_vec, const double w = 1.0 ) {}; |
---|
| 100 | //original Bayes |
---|
| 101 | void bayes ( const vec &yt, const vec &cond = empty_vec ); |
---|
[565] | 102 | |
---|
[737] | 103 | //!Flatten the posterior according to the given BMEF (of the same type!) |
---|
| 104 | virtual void flatten ( const BMEF * B ) { |
---|
| 105 | bdm_error ( "Not implemented" ); |
---|
| 106 | } |
---|
[198] | 107 | |
---|
[737] | 108 | BMEF* _copy_ () const { |
---|
| 109 | bdm_error ( "function _copy_ not implemented for this BM" ); |
---|
| 110 | return NULL; |
---|
| 111 | } |
---|
[746] | 112 | |
---|
| 113 | void to_setting ( Setting &set ) const |
---|
| 114 | { |
---|
| 115 | BM::to_setting( set ); |
---|
| 116 | // TODO DOPLNIT? CHYBI FROM_SETTING PRO INSPIRACI |
---|
| 117 | } |
---|
[488] | 118 | }; |
---|
[170] | 119 | |
---|
[504] | 120 | template<class sq_T, template <typename> class TEpdf> |
---|
[488] | 121 | class mlnorm; |
---|
[178] | 122 | |
---|
[488] | 123 | /*! |
---|
| 124 | * \brief Gaussian density with positive definite (decomposed) covariance matrix. |
---|
[8] | 125 | |
---|
[488] | 126 | * More?... |
---|
| 127 | */ |
---|
| 128 | template<class sq_T> |
---|
[737] | 129 | class enorm : public eEF { |
---|
| 130 | protected: |
---|
| 131 | //! mean value |
---|
| 132 | vec mu; |
---|
| 133 | //! Covariance matrix in decomposed form |
---|
| 134 | sq_T R; |
---|
| 135 | public: |
---|
| 136 | //!\name Constructors |
---|
| 137 | //!@{ |
---|
[270] | 138 | |
---|
[737] | 139 | enorm () : eEF (), mu (), R () {}; |
---|
| 140 | enorm ( const vec &mu, const sq_T &R ) { |
---|
| 141 | set_parameters ( mu, R ); |
---|
| 142 | } |
---|
| 143 | void set_parameters ( const vec &mu, const sq_T &R ); |
---|
| 144 | /*! Create Normal density |
---|
| 145 | \f[ f(rv) = N(\mu, R) \f] |
---|
| 146 | from structure |
---|
| 147 | \code |
---|
| 148 | class = 'enorm<ldmat>', (OR) 'enorm<chmat>', (OR) 'enorm<fsqmat>'; |
---|
| 149 | mu = []; // mean value |
---|
| 150 | R = []; // variance, square matrix of appropriate dimension |
---|
| 151 | \endcode |
---|
| 152 | */ |
---|
| 153 | void from_setting ( const Setting &root ); |
---|
| 154 | void validate() { |
---|
| 155 | bdm_assert ( mu.length() == R.rows(), "mu and R parameters do not match" ); |
---|
| 156 | dim = mu.length(); |
---|
| 157 | } |
---|
| 158 | //!@} |
---|
[270] | 159 | |
---|
[737] | 160 | //! \name Mathematical operations |
---|
| 161 | //!@{ |
---|
[270] | 162 | |
---|
[737] | 163 | //! dupdate in exponential form (not really handy) |
---|
| 164 | void dupdate ( mat &v, double nu = 1.0 ); |
---|
[28] | 165 | |
---|
[737] | 166 | vec sample() const; |
---|
[450] | 167 | |
---|
[737] | 168 | double evallog_nn ( const vec &val ) const; |
---|
| 169 | double lognc () const; |
---|
| 170 | vec mean() const { |
---|
| 171 | return mu; |
---|
| 172 | } |
---|
| 173 | vec variance() const { |
---|
| 174 | return diag ( R.to_mat() ); |
---|
| 175 | } |
---|
[299] | 176 | // mlnorm<sq_T>* condition ( const RV &rvn ) const ; <=========== fails to cmpile. Why? |
---|
[737] | 177 | shared_ptr<pdf> condition ( const RV &rvn ) const; |
---|
[504] | 178 | |
---|
[737] | 179 | // target not typed to mlnorm<sq_T, enorm<sq_T> > & |
---|
| 180 | // because that doesn't compile (perhaps because we |
---|
| 181 | // haven't finished defining enorm yet), but the type |
---|
| 182 | // is required |
---|
| 183 | void condition ( const RV &rvn, pdf &target ) const; |
---|
[504] | 184 | |
---|
[737] | 185 | shared_ptr<epdf> marginal ( const RV &rvn ) const; |
---|
| 186 | void marginal ( const RV &rvn, enorm<sq_T> &target ) const; |
---|
| 187 | //!@} |
---|
[270] | 188 | |
---|
[737] | 189 | //! \name Access to attributes |
---|
| 190 | //!@{ |
---|
[270] | 191 | |
---|
[737] | 192 | vec& _mu() { |
---|
| 193 | return mu; |
---|
| 194 | } |
---|
| 195 | const vec& _mu() const { |
---|
| 196 | return mu; |
---|
| 197 | } |
---|
| 198 | void set_mu ( const vec mu0 ) { |
---|
| 199 | mu = mu0; |
---|
| 200 | } |
---|
| 201 | sq_T& _R() { |
---|
| 202 | return R; |
---|
| 203 | } |
---|
| 204 | const sq_T& _R() const { |
---|
| 205 | return R; |
---|
| 206 | } |
---|
| 207 | //!@} |
---|
[28] | 208 | |
---|
[488] | 209 | }; |
---|
[737] | 210 | UIREGISTER2 ( enorm, chmat ); |
---|
[529] | 211 | SHAREDPTR2 ( enorm, chmat ); |
---|
[737] | 212 | UIREGISTER2 ( enorm, ldmat ); |
---|
[529] | 213 | SHAREDPTR2 ( enorm, ldmat ); |
---|
[737] | 214 | UIREGISTER2 ( enorm, fsqmat ); |
---|
[529] | 215 | SHAREDPTR2 ( enorm, fsqmat ); |
---|
[8] | 216 | |
---|
[388] | 217 | |
---|
[488] | 218 | /*! |
---|
| 219 | * \brief Gauss-inverse-Wishart density stored in LD form |
---|
[96] | 220 | |
---|
[488] | 221 | * For \f$p\f$-variate densities, given rv.count() should be \f$p\times\f$ V.rows(). |
---|
| 222 | * |
---|
| 223 | */ |
---|
[737] | 224 | class egiw : public eEF { |
---|
| 225 | protected: |
---|
| 226 | //! Extended information matrix of sufficient statistics |
---|
| 227 | ldmat V; |
---|
| 228 | //! Number of data records (degrees of freedom) of sufficient statistics |
---|
| 229 | double nu; |
---|
| 230 | //! Dimension of the output |
---|
| 231 | int dimx; |
---|
| 232 | //! Dimension of the regressor |
---|
| 233 | int nPsi; |
---|
| 234 | public: |
---|
| 235 | //!\name Constructors |
---|
| 236 | //!@{ |
---|
| 237 | egiw() : eEF() {}; |
---|
| 238 | egiw ( int dimx0, ldmat V0, double nu0 = -1.0 ) : eEF() { |
---|
| 239 | set_parameters ( dimx0, V0, nu0 ); |
---|
| 240 | }; |
---|
[270] | 241 | |
---|
[737] | 242 | void set_parameters ( int dimx0, ldmat V0, double nu0 = -1.0 ); |
---|
| 243 | //!@} |
---|
[96] | 244 | |
---|
[737] | 245 | vec sample() const; |
---|
| 246 | mat sample_mat ( int n ) const; |
---|
| 247 | vec mean() const; |
---|
| 248 | vec variance() const; |
---|
| 249 | void sample_mat ( mat &Mi, chmat &Ri ) const; |
---|
[330] | 250 | |
---|
[737] | 251 | void factorize ( mat &M, ldmat &Vz, ldmat &Lam ) const; |
---|
| 252 | //! LS estimate of \f$\theta\f$ |
---|
| 253 | vec est_theta() const; |
---|
[330] | 254 | |
---|
[737] | 255 | //! Covariance of the LS estimate |
---|
| 256 | ldmat est_theta_cov() const; |
---|
[96] | 257 | |
---|
[737] | 258 | //! expected values of the linear coefficient and the covariance matrix are written to \c M and \c R , respectively |
---|
| 259 | void mean_mat ( mat &M, mat&R ) const; |
---|
| 260 | //! In this instance, val= [theta, r]. For multivariate instances, it is stored columnwise val = [theta_1 theta_2 ... r_1 r_2 ] |
---|
| 261 | double evallog_nn ( const vec &val ) const; |
---|
| 262 | double lognc () const; |
---|
| 263 | void pow ( double p ) { |
---|
| 264 | V *= p; |
---|
| 265 | nu *= p; |
---|
| 266 | }; |
---|
[270] | 267 | |
---|
[737] | 268 | //! \name Access attributes |
---|
| 269 | //!@{ |
---|
| 270 | |
---|
| 271 | ldmat& _V() { |
---|
| 272 | return V; |
---|
| 273 | } |
---|
| 274 | const ldmat& _V() const { |
---|
| 275 | return V; |
---|
| 276 | } |
---|
| 277 | double& _nu() { |
---|
| 278 | return nu; |
---|
| 279 | } |
---|
| 280 | const double& _nu() const { |
---|
| 281 | return nu; |
---|
| 282 | } |
---|
| 283 | const int & _dimx() const { |
---|
| 284 | return dimx; |
---|
| 285 | } |
---|
| 286 | |
---|
| 287 | /*! Create Gauss-inverse-Wishart density |
---|
| 288 | \f[ f(rv) = GiW(V,\nu) \f] |
---|
| 289 | from structure |
---|
| 290 | \code |
---|
| 291 | class = 'egiw'; |
---|
| 292 | V = []; // square matrix |
---|
| 293 | dV = []; // vector of diagonal of V (when V not given) |
---|
| 294 | nu = []; // scalar \nu ((almost) degrees of freedom) |
---|
| 295 | // when missing, it will be computed to obtain proper pdf |
---|
| 296 | dimx = []; // dimension of the wishart part |
---|
| 297 | rv = RV({'name'}) // description of RV |
---|
| 298 | rvc = RV({'name'}) // description of RV in condition |
---|
| 299 | \endcode |
---|
| 300 | */ |
---|
| 301 | |
---|
| 302 | void from_setting ( const Setting &set ) { |
---|
| 303 | epdf::from_setting ( set ); |
---|
| 304 | UI::get ( dimx, set, "dimx", UI::compulsory ); |
---|
| 305 | if ( !UI::get ( nu, set, "nu", UI::optional ) ) { |
---|
| 306 | nu = -1; |
---|
[488] | 307 | } |
---|
[737] | 308 | mat V; |
---|
| 309 | if ( !UI::get ( V, set, "V", UI::optional ) ) { |
---|
| 310 | vec dV; |
---|
| 311 | UI::get ( dV, set, "dV", UI::compulsory ); |
---|
| 312 | set_parameters ( dimx, ldmat ( dV ), nu ); |
---|
| 313 | |
---|
| 314 | } else { |
---|
| 315 | set_parameters ( dimx, V, nu ); |
---|
[665] | 316 | } |
---|
[737] | 317 | } |
---|
| 318 | |
---|
| 319 | void to_setting ( Setting& set ) const { |
---|
| 320 | epdf::to_setting ( set ); |
---|
| 321 | string s ( "egiw" ); |
---|
| 322 | UI::save ( s, set, "class" ); |
---|
| 323 | UI::save ( dimx, set, "dimx" ); |
---|
| 324 | UI::save ( V.to_mat(), set, "V" ); |
---|
| 325 | UI::save ( nu, set, "nu" ); |
---|
| 326 | }; |
---|
| 327 | |
---|
| 328 | void validate() { |
---|
| 329 | // check sizes, rvs etc. |
---|
| 330 | } |
---|
[739] | 331 | void log_register ( bdm::logger& L, const string& prefix ); |
---|
[737] | 332 | |
---|
[739] | 333 | void log_write() const; |
---|
[737] | 334 | //!@} |
---|
[488] | 335 | }; |
---|
[529] | 336 | UIREGISTER ( egiw ); |
---|
| 337 | SHAREDPTR ( egiw ); |
---|
[96] | 338 | |
---|
[488] | 339 | /*! \brief Dirichlet posterior density |
---|
[173] | 340 | |
---|
[488] | 341 | Continuous Dirichlet density of \f$n\f$-dimensional variable \f$x\f$ |
---|
| 342 | \f[ |
---|
| 343 | f(x|\beta) = \frac{\Gamma[\gamma]}{\prod_{i=1}^{n}\Gamma(\beta_i)} \prod_{i=1}^{n}x_i^{\beta_i-1} |
---|
| 344 | \f] |
---|
| 345 | where \f$\gamma=\sum_i \beta_i\f$. |
---|
| 346 | */ |
---|
[737] | 347 | class eDirich: public eEF { |
---|
| 348 | protected: |
---|
| 349 | //!sufficient statistics |
---|
| 350 | vec beta; |
---|
| 351 | public: |
---|
| 352 | //!\name Constructors |
---|
| 353 | //!@{ |
---|
[270] | 354 | |
---|
[737] | 355 | eDirich () : eEF () {}; |
---|
| 356 | eDirich ( const eDirich &D0 ) : eEF () { |
---|
| 357 | set_parameters ( D0.beta ); |
---|
| 358 | }; |
---|
| 359 | eDirich ( const vec &beta0 ) { |
---|
| 360 | set_parameters ( beta0 ); |
---|
| 361 | }; |
---|
| 362 | void set_parameters ( const vec &beta0 ) { |
---|
| 363 | beta = beta0; |
---|
| 364 | dim = beta.length(); |
---|
| 365 | } |
---|
| 366 | //!@} |
---|
[270] | 367 | |
---|
[737] | 368 | //! using sampling procedure from wikipedia |
---|
| 369 | vec sample() const { |
---|
| 370 | vec y ( beta.length() ); |
---|
| 371 | for ( int i = 0; i < beta.length(); i++ ) { |
---|
| 372 | GamRNG.setup ( beta ( i ), 1 ); |
---|
| 373 | #pragma omp critical |
---|
| 374 | y ( i ) = GamRNG(); |
---|
[565] | 375 | } |
---|
[737] | 376 | return y / sum ( y ); |
---|
| 377 | } |
---|
[565] | 378 | |
---|
[737] | 379 | vec mean() const { |
---|
| 380 | return beta / sum ( beta ); |
---|
| 381 | }; |
---|
| 382 | vec variance() const { |
---|
| 383 | double gamma = sum ( beta ); |
---|
| 384 | return elem_mult ( beta, ( gamma - beta ) ) / ( gamma*gamma* ( gamma + 1 ) ); |
---|
| 385 | } |
---|
| 386 | //! In this instance, val is ... |
---|
| 387 | double evallog_nn ( const vec &val ) const { |
---|
| 388 | double tmp; |
---|
| 389 | tmp = ( beta - 1 ) * log ( val ); |
---|
| 390 | return tmp; |
---|
| 391 | } |
---|
[565] | 392 | |
---|
[737] | 393 | double lognc () const { |
---|
| 394 | double tmp; |
---|
| 395 | double gam = sum ( beta ); |
---|
| 396 | double lgb = 0.0; |
---|
| 397 | for ( int i = 0; i < beta.length(); i++ ) { |
---|
| 398 | lgb += lgamma ( beta ( i ) ); |
---|
[565] | 399 | } |
---|
[737] | 400 | tmp = lgb - lgamma ( gam ); |
---|
| 401 | return tmp; |
---|
| 402 | } |
---|
[565] | 403 | |
---|
[737] | 404 | //!access function |
---|
| 405 | vec& _beta() { |
---|
| 406 | return beta; |
---|
| 407 | } |
---|
| 408 | /*! configuration structure |
---|
| 409 | \code |
---|
| 410 | class = 'eDirich'; |
---|
| 411 | beta = []; //parametr beta |
---|
| 412 | \endcode |
---|
| 413 | */ |
---|
| 414 | void from_setting ( const Setting &set ) { |
---|
| 415 | epdf::from_setting ( set ); |
---|
| 416 | UI::get ( beta, set, "beta", UI::compulsory ); |
---|
| 417 | validate(); |
---|
| 418 | } |
---|
| 419 | void validate() { |
---|
| 420 | //check rv |
---|
| 421 | dim = beta.length(); |
---|
| 422 | } |
---|
[746] | 423 | |
---|
| 424 | void to_setting ( Setting &set ) const |
---|
| 425 | { |
---|
| 426 | eEF::to_setting( set ); |
---|
| 427 | UI::save( beta, set, "beta" ); |
---|
| 428 | } |
---|
[488] | 429 | }; |
---|
[737] | 430 | UIREGISTER ( eDirich ); |
---|
[96] | 431 | |
---|
[637] | 432 | /*! Random Walk on Dirichlet |
---|
[737] | 433 | Using simple assignment |
---|
[637] | 434 | \f[ \beta = rvc / k + \beta_c \f] |
---|
| 435 | hence, mean value = rvc, variance = (k+1)*mean*mean; |
---|
[737] | 436 | |
---|
[637] | 437 | The greater k is, the greater is the variance of the random walk; |
---|
[737] | 438 | |
---|
[637] | 439 | \f$ \beta_c \f$ is used as regularizing element to avoid corner cases, i.e. when one element of rvc is zero. |
---|
| 440 | By default is it set to 0.1; |
---|
| 441 | */ |
---|
| 442 | |
---|
[693] | 443 | class mDirich: public pdf_internal<eDirich> { |
---|
[737] | 444 | protected: |
---|
| 445 | //! constant \f$ k \f$ of the random walk |
---|
| 446 | double k; |
---|
| 447 | //! cache of beta_i |
---|
| 448 | vec &_beta; |
---|
| 449 | //! stabilizing coefficient \f$ \beta_c \f$ |
---|
| 450 | vec betac; |
---|
| 451 | public: |
---|
| 452 | mDirich() : pdf_internal<eDirich>(), _beta ( iepdf._beta() ) {}; |
---|
| 453 | void condition ( const vec &val ) { |
---|
| 454 | _beta = val / k + betac; |
---|
| 455 | }; |
---|
| 456 | /*! Create Dirichlet random walk |
---|
| 457 | \f[ f(rv|rvc) = Di(rvc*k) \f] |
---|
| 458 | from structure |
---|
| 459 | \code |
---|
| 460 | class = 'mDirich'; |
---|
| 461 | k = 1; // multiplicative constant k |
---|
| 462 | --- optional --- |
---|
| 463 | rv = RV({'name'},size) // description of RV |
---|
| 464 | beta0 = []; // initial value of beta |
---|
| 465 | betac = []; // initial value of beta |
---|
| 466 | \endcode |
---|
| 467 | */ |
---|
| 468 | void from_setting ( const Setting &set ) { |
---|
| 469 | pdf::from_setting ( set ); // reads rv and rvc |
---|
| 470 | if ( _rv()._dsize() > 0 ) { |
---|
| 471 | rvc = _rv().copy_t ( -1 ); |
---|
[637] | 472 | } |
---|
[737] | 473 | vec beta0; |
---|
| 474 | if ( !UI::get ( beta0, set, "beta0", UI::optional ) ) { |
---|
| 475 | beta0 = ones ( _rv()._dsize() ); |
---|
| 476 | } |
---|
| 477 | if ( !UI::get ( betac, set, "betac", UI::optional ) ) { |
---|
| 478 | betac = 0.1 * ones ( _rv()._dsize() ); |
---|
| 479 | } |
---|
| 480 | _beta = beta0; |
---|
| 481 | |
---|
| 482 | UI::get ( k, set, "k", UI::compulsory ); |
---|
| 483 | validate(); |
---|
| 484 | } |
---|
| 485 | void validate() { |
---|
| 486 | pdf_internal<eDirich>::validate(); |
---|
| 487 | bdm_assert ( _beta.length() == betac.length(), "beta0 and betac are not compatible" ); |
---|
| 488 | if ( _rv()._dsize() > 0 ) { |
---|
| 489 | bdm_assert ( ( _rv()._dsize() == dimension() ) , "Size of rv does not match with beta" ); |
---|
| 490 | } |
---|
| 491 | dimc = _beta.length(); |
---|
| 492 | }; |
---|
[637] | 493 | }; |
---|
[737] | 494 | UIREGISTER ( mDirich ); |
---|
[637] | 495 | |
---|
[181] | 496 | //! \brief Estimator for Multinomial density |
---|
[737] | 497 | class multiBM : public BMEF { |
---|
| 498 | protected: |
---|
| 499 | //! Conjugate prior and posterior |
---|
| 500 | eDirich est; |
---|
| 501 | //! Pointer inside est to sufficient statistics |
---|
| 502 | vec β |
---|
| 503 | public: |
---|
| 504 | //!Default constructor |
---|
| 505 | multiBM () : BMEF (), est (), beta ( est._beta() ) { |
---|
| 506 | if ( beta.length() > 0 ) { |
---|
| 507 | last_lognc = est.lognc(); |
---|
| 508 | } else { |
---|
| 509 | last_lognc = 0.0; |
---|
[488] | 510 | } |
---|
[737] | 511 | } |
---|
| 512 | //!Copy constructor |
---|
| 513 | multiBM ( const multiBM &B ) : BMEF ( B ), est ( B.est ), beta ( est._beta() ) {} |
---|
| 514 | //! Sets sufficient statistics to match that of givefrom mB0 |
---|
| 515 | void set_statistics ( const BM* mB0 ) { |
---|
| 516 | const multiBM* mB = dynamic_cast<const multiBM*> ( mB0 ); |
---|
| 517 | beta = mB->beta; |
---|
| 518 | } |
---|
[739] | 519 | void bayes ( const vec &yt, const vec &cond = empty_vec ); |
---|
[176] | 520 | |
---|
[739] | 521 | double logpred ( const vec &yt ) const; |
---|
[170] | 522 | |
---|
[739] | 523 | void flatten ( const BMEF* B ); |
---|
| 524 | |
---|
[737] | 525 | //! return correctly typed posterior (covariant return) |
---|
| 526 | const eDirich& posterior() const { |
---|
| 527 | return est; |
---|
| 528 | }; |
---|
| 529 | //! constructor function |
---|
| 530 | void set_parameters ( const vec &beta0 ) { |
---|
| 531 | est.set_parameters ( beta0 ); |
---|
[741] | 532 | est.validate(); |
---|
[737] | 533 | if ( evalll ) { |
---|
| 534 | last_lognc = est.lognc(); |
---|
[488] | 535 | } |
---|
[737] | 536 | } |
---|
[746] | 537 | |
---|
[737] | 538 | void to_setting ( Setting &set ) const { |
---|
| 539 | BMEF::to_setting ( set ); |
---|
[746] | 540 | UI::save( &est, set, "prior" ); |
---|
[737] | 541 | } |
---|
[488] | 542 | }; |
---|
[746] | 543 | UIREGISTER( multiBM ); |
---|
[170] | 544 | |
---|
[488] | 545 | /*! |
---|
| 546 | \brief Gamma posterior density |
---|
[32] | 547 | |
---|
[488] | 548 | Multivariate Gamma density as product of independent univariate densities. |
---|
| 549 | \f[ |
---|
| 550 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
---|
| 551 | \f] |
---|
| 552 | */ |
---|
[32] | 553 | |
---|
[737] | 554 | class egamma : public eEF { |
---|
| 555 | protected: |
---|
| 556 | //! Vector \f$\alpha\f$ |
---|
| 557 | vec alpha; |
---|
| 558 | //! Vector \f$\beta\f$ |
---|
| 559 | vec beta; |
---|
| 560 | public : |
---|
| 561 | //! \name Constructors |
---|
| 562 | //!@{ |
---|
| 563 | egamma () : eEF (), alpha ( 0 ), beta ( 0 ) {}; |
---|
| 564 | egamma ( const vec &a, const vec &b ) { |
---|
| 565 | set_parameters ( a, b ); |
---|
| 566 | }; |
---|
| 567 | void set_parameters ( const vec &a, const vec &b ) { |
---|
| 568 | alpha = a, beta = b; |
---|
| 569 | dim = alpha.length(); |
---|
| 570 | }; |
---|
| 571 | //!@} |
---|
[270] | 572 | |
---|
[737] | 573 | vec sample() const; |
---|
| 574 | double evallog ( const vec &val ) const; |
---|
| 575 | double lognc () const; |
---|
| 576 | //! Returns pointer to internal alpha. Potentially dengerous: use with care! |
---|
| 577 | vec& _alpha() { |
---|
| 578 | return alpha; |
---|
| 579 | } |
---|
| 580 | //! Returns pointer to internal beta. Potentially dengerous: use with care! |
---|
| 581 | vec& _beta() { |
---|
| 582 | return beta; |
---|
| 583 | } |
---|
| 584 | vec mean() const { |
---|
| 585 | return elem_div ( alpha, beta ); |
---|
| 586 | } |
---|
| 587 | vec variance() const { |
---|
| 588 | return elem_div ( alpha, elem_mult ( beta, beta ) ); |
---|
| 589 | } |
---|
[225] | 590 | |
---|
[737] | 591 | /*! Create Gamma density |
---|
| 592 | \f[ f(rv|rvc) = \Gamma(\alpha, \beta) \f] |
---|
| 593 | from structure |
---|
| 594 | \code |
---|
| 595 | class = 'egamma'; |
---|
| 596 | alpha = [...]; // vector of alpha |
---|
| 597 | beta = [...]; // vector of beta |
---|
| 598 | rv = RV({'name'}) // description of RV |
---|
| 599 | \endcode |
---|
| 600 | */ |
---|
| 601 | void from_setting ( const Setting &set ) { |
---|
| 602 | epdf::from_setting ( set ); // reads rv |
---|
| 603 | UI::get ( alpha, set, "alpha", UI::compulsory ); |
---|
| 604 | UI::get ( beta, set, "beta", UI::compulsory ); |
---|
| 605 | validate(); |
---|
| 606 | } |
---|
| 607 | void validate() { |
---|
| 608 | bdm_assert ( alpha.length() == beta.length(), "parameters do not match" ); |
---|
| 609 | dim = alpha.length(); |
---|
| 610 | } |
---|
[488] | 611 | }; |
---|
[737] | 612 | UIREGISTER ( egamma ); |
---|
[529] | 613 | SHAREDPTR ( egamma ); |
---|
| 614 | |
---|
[488] | 615 | /*! |
---|
| 616 | \brief Inverse-Gamma posterior density |
---|
[225] | 617 | |
---|
[488] | 618 | Multivariate inverse-Gamma density as product of independent univariate densities. |
---|
| 619 | \f[ |
---|
| 620 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
---|
| 621 | \f] |
---|
[283] | 622 | |
---|
[488] | 623 | Vector \f$\beta\f$ has different meaning (in fact it is 1/beta as used in definition of iG) |
---|
[225] | 624 | |
---|
[488] | 625 | Inverse Gamma can be converted to Gamma using \f[ |
---|
| 626 | x\sim iG(a,b) => 1/x\sim G(a,1/b) |
---|
| 627 | \f] |
---|
| 628 | This relation is used in sampling. |
---|
| 629 | */ |
---|
[270] | 630 | |
---|
[737] | 631 | class eigamma : public egamma { |
---|
| 632 | protected: |
---|
| 633 | public : |
---|
| 634 | //! \name Constructors |
---|
| 635 | //! All constructors are inherited |
---|
| 636 | //!@{ |
---|
| 637 | //!@} |
---|
[32] | 638 | |
---|
[737] | 639 | vec sample() const { |
---|
| 640 | return 1.0 / egamma::sample(); |
---|
| 641 | }; |
---|
| 642 | //! Returns poiter to alpha and beta. Potentially dangerous: use with care! |
---|
| 643 | vec mean() const { |
---|
| 644 | return elem_div ( beta, alpha - 1 ); |
---|
| 645 | } |
---|
| 646 | vec variance() const { |
---|
| 647 | vec mea = mean(); |
---|
| 648 | return elem_div ( elem_mult ( mea, mea ), alpha - 2 ); |
---|
| 649 | } |
---|
[488] | 650 | }; |
---|
| 651 | /* |
---|
| 652 | //! Weighted mixture of epdfs with external owned components. |
---|
| 653 | class emix : public epdf { |
---|
| 654 | protected: |
---|
| 655 | int n; |
---|
| 656 | vec &w; |
---|
| 657 | Array<epdf*> Coms; |
---|
| 658 | public: |
---|
| 659 | //! Default constructor |
---|
| 660 | emix ( const RV &rv, vec &w0): epdf(rv), n(w0.length()), w(w0), Coms(n) {}; |
---|
| 661 | void set_parameters( int &i, double wi, epdf* ep){w(i)=wi;Coms(i)=ep;} |
---|
| 662 | vec mean(){vec pom; for(int i=0;i<n;i++){pom+=Coms(i)->mean()*w(i);} return pom;}; |
---|
| 663 | }; |
---|
| 664 | */ |
---|
| 665 | |
---|
[32] | 666 | //! Uniform distributed density on a rectangular support |
---|
| 667 | |
---|
[737] | 668 | class euni: public epdf { |
---|
| 669 | protected: |
---|
[32] | 670 | //! lower bound on support |
---|
[737] | 671 | vec low; |
---|
[32] | 672 | //! upper bound on support |
---|
[737] | 673 | vec high; |
---|
[32] | 674 | //! internal |
---|
[737] | 675 | vec distance; |
---|
[32] | 676 | //! normalizing coefficients |
---|
[737] | 677 | double nk; |
---|
[33] | 678 | //! cache of log( \c nk ) |
---|
[737] | 679 | double lnk; |
---|
| 680 | public: |
---|
| 681 | //! \name Constructors |
---|
| 682 | //!@{ |
---|
| 683 | euni () : epdf () {} |
---|
| 684 | euni ( const vec &low0, const vec &high0 ) { |
---|
| 685 | set_parameters ( low0, high0 ); |
---|
| 686 | } |
---|
| 687 | void set_parameters ( const vec &low0, const vec &high0 ) { |
---|
| 688 | distance = high0 - low0; |
---|
| 689 | low = low0; |
---|
| 690 | high = high0; |
---|
| 691 | nk = prod ( 1.0 / distance ); |
---|
| 692 | lnk = log ( nk ); |
---|
| 693 | dim = low.length(); |
---|
| 694 | } |
---|
| 695 | //!@} |
---|
[270] | 696 | |
---|
[737] | 697 | double evallog ( const vec &val ) const { |
---|
| 698 | if ( any ( val < low ) && any ( val > high ) ) { |
---|
| 699 | return -inf; |
---|
| 700 | } else return lnk; |
---|
| 701 | } |
---|
| 702 | vec sample() const { |
---|
| 703 | vec smp ( dim ); |
---|
[270] | 704 | #pragma omp critical |
---|
[737] | 705 | UniRNG.sample_vector ( dim , smp ); |
---|
| 706 | return low + elem_mult ( distance, smp ); |
---|
| 707 | } |
---|
| 708 | //! set values of \c low and \c high |
---|
| 709 | vec mean() const { |
---|
| 710 | return ( high - low ) / 2.0; |
---|
| 711 | } |
---|
| 712 | vec variance() const { |
---|
| 713 | return ( pow ( high, 2 ) + pow ( low, 2 ) + elem_mult ( high, low ) ) / 3.0; |
---|
| 714 | } |
---|
| 715 | /*! Create Uniform density |
---|
| 716 | \f[ f(rv) = U(low,high) \f] |
---|
| 717 | from structure |
---|
| 718 | \code |
---|
| 719 | class = 'euni' |
---|
| 720 | high = [...]; // vector of upper bounds |
---|
| 721 | low = [...]; // vector of lower bounds |
---|
| 722 | rv = RV({'name'}); // description of RV |
---|
| 723 | \endcode |
---|
| 724 | */ |
---|
| 725 | void from_setting ( const Setting &set ) { |
---|
| 726 | epdf::from_setting ( set ); // reads rv and rvc |
---|
[471] | 727 | |
---|
[737] | 728 | UI::get ( high, set, "high", UI::compulsory ); |
---|
| 729 | UI::get ( low, set, "low", UI::compulsory ); |
---|
| 730 | set_parameters ( low, high ); |
---|
| 731 | validate(); |
---|
| 732 | } |
---|
| 733 | void validate() { |
---|
| 734 | bdm_assert ( high.length() == low.length(), "Incompatible high and low vectors" ); |
---|
| 735 | dim = high.length(); |
---|
| 736 | bdm_assert ( min ( distance ) > 0.0, "bad support" ); |
---|
| 737 | } |
---|
[488] | 738 | }; |
---|
[737] | 739 | UIREGISTER ( euni ); |
---|
[32] | 740 | |
---|
[665] | 741 | //! Uniform density with conditional mean value |
---|
[737] | 742 | class mguni : public pdf_internal<euni> { |
---|
[665] | 743 | //! function of the mean value |
---|
| 744 | shared_ptr<fnc> mean; |
---|
| 745 | //! distance from mean to both sides |
---|
| 746 | vec delta; |
---|
[737] | 747 | public: |
---|
| 748 | void condition ( const vec &cond ) { |
---|
| 749 | vec mea = mean->eval ( cond ); |
---|
| 750 | iepdf.set_parameters ( mea - delta, mea + delta ); |
---|
| 751 | } |
---|
| 752 | //! load from |
---|
| 753 | void from_setting ( const Setting &set ) { |
---|
| 754 | pdf::from_setting ( set ); //reads rv and rvc |
---|
| 755 | UI::get ( delta, set, "delta", UI::compulsory ); |
---|
| 756 | mean = UI::build<fnc> ( set, "mean", UI::compulsory ); |
---|
| 757 | |
---|
| 758 | iepdf.set_parameters ( -delta, delta ); |
---|
| 759 | dimc = mean->dimensionc(); |
---|
| 760 | validate(); |
---|
| 761 | } |
---|
[665] | 762 | }; |
---|
[737] | 763 | UIREGISTER ( mguni ); |
---|
[488] | 764 | /*! |
---|
| 765 | \brief Normal distributed linear function with linear function of mean value; |
---|
[32] | 766 | |
---|
[536] | 767 | Mean value \f$ \mu=A*\mbox{rvc}+\mu_0 \f$. |
---|
[488] | 768 | */ |
---|
| 769 | template < class sq_T, template <typename> class TEpdf = enorm > |
---|
[737] | 770 | class mlnorm : public pdf_internal< TEpdf<sq_T> > { |
---|
| 771 | protected: |
---|
| 772 | //! Internal epdf that arise by conditioning on \c rvc |
---|
| 773 | mat A; |
---|
| 774 | //! Constant additive term |
---|
| 775 | vec mu_const; |
---|
[487] | 776 | // vec& _mu; //cached epdf.mu; !!!!!! WHY NOT? |
---|
[737] | 777 | public: |
---|
| 778 | //! \name Constructors |
---|
| 779 | //!@{ |
---|
| 780 | mlnorm() : pdf_internal< TEpdf<sq_T> >() {}; |
---|
| 781 | mlnorm ( const mat &A, const vec &mu0, const sq_T &R ) : pdf_internal< TEpdf<sq_T> >() { |
---|
| 782 | set_parameters ( A, mu0, R ); |
---|
| 783 | } |
---|
[461] | 784 | |
---|
[737] | 785 | //! Set \c A and \c R |
---|
| 786 | void set_parameters ( const mat &A0, const vec &mu0, const sq_T &R0 ) { |
---|
| 787 | this->iepdf.set_parameters ( zeros ( A0.rows() ), R0 ); |
---|
| 788 | A = A0; |
---|
| 789 | mu_const = mu0; |
---|
| 790 | this->dimc = A0.cols(); |
---|
| 791 | } |
---|
| 792 | //!@} |
---|
| 793 | //! Set value of \c rvc . Result of this operation is stored in \c epdf use function \c _ep to access it. |
---|
| 794 | void condition ( const vec &cond ) { |
---|
| 795 | this->iepdf._mu() = A * cond + mu_const; |
---|
[487] | 796 | //R is already assigned; |
---|
[737] | 797 | } |
---|
[198] | 798 | |
---|
[737] | 799 | //!access function |
---|
| 800 | const vec& _mu_const() const { |
---|
| 801 | return mu_const; |
---|
| 802 | } |
---|
| 803 | //!access function |
---|
| 804 | const mat& _A() const { |
---|
| 805 | return A; |
---|
| 806 | } |
---|
| 807 | //!access function |
---|
| 808 | mat _R() const { |
---|
| 809 | return this->iepdf._R().to_mat(); |
---|
| 810 | } |
---|
| 811 | //!access function |
---|
| 812 | sq_T __R() const { |
---|
| 813 | return this->iepdf._R(); |
---|
| 814 | } |
---|
[8] | 815 | |
---|
[737] | 816 | //! Debug stream |
---|
| 817 | template<typename sq_M> |
---|
| 818 | friend std::ostream &operator<< ( std::ostream &os, mlnorm<sq_M, enorm> &ml ); |
---|
[488] | 819 | |
---|
[737] | 820 | /*! Create Normal density with linear function of mean value |
---|
| 821 | \f[ f(rv|rvc) = N(A*rvc+const, R) \f] |
---|
| 822 | from structure |
---|
| 823 | \code |
---|
| 824 | class = 'mlnorm<ldmat>', (OR) 'mlnorm<chmat>', (OR) 'mlnorm<fsqmat>'; |
---|
| 825 | A = []; // matrix or vector of appropriate dimension |
---|
| 826 | const = []; // vector of constant term |
---|
| 827 | R = []; // square matrix of appropriate dimension |
---|
| 828 | \endcode |
---|
| 829 | */ |
---|
| 830 | void from_setting ( const Setting &set ) { |
---|
| 831 | pdf::from_setting ( set ); |
---|
| 832 | |
---|
| 833 | UI::get ( A, set, "A", UI::compulsory ); |
---|
| 834 | UI::get ( mu_const, set, "const", UI::compulsory ); |
---|
| 835 | mat R0; |
---|
| 836 | UI::get ( R0, set, "R", UI::compulsory ); |
---|
| 837 | set_parameters ( A, mu_const, R0 ); |
---|
| 838 | validate(); |
---|
| 839 | }; |
---|
| 840 | void validate() { |
---|
| 841 | pdf_internal<TEpdf<sq_T> >::validate(); |
---|
| 842 | bdm_assert ( A.rows() == mu_const.length(), "mlnorm: A vs. mu mismatch" ); |
---|
| 843 | bdm_assert ( A.rows() == _R().rows(), "mlnorm: A vs. R mismatch" ); |
---|
| 844 | |
---|
| 845 | } |
---|
[488] | 846 | }; |
---|
[737] | 847 | UIREGISTER2 ( mlnorm, ldmat ); |
---|
[529] | 848 | SHAREDPTR2 ( mlnorm, ldmat ); |
---|
[737] | 849 | UIREGISTER2 ( mlnorm, fsqmat ); |
---|
[529] | 850 | SHAREDPTR2 ( mlnorm, fsqmat ); |
---|
[737] | 851 | UIREGISTER2 ( mlnorm, chmat ); |
---|
[529] | 852 | SHAREDPTR2 ( mlnorm, chmat ); |
---|
[488] | 853 | |
---|
[693] | 854 | //! pdf with general function for mean value |
---|
[488] | 855 | template<class sq_T> |
---|
[737] | 856 | class mgnorm : public pdf_internal< enorm< sq_T > > { |
---|
| 857 | private: |
---|
[487] | 858 | // vec μ WHY NOT? |
---|
[737] | 859 | shared_ptr<fnc> g; |
---|
[527] | 860 | |
---|
[737] | 861 | public: |
---|
| 862 | //!default constructor |
---|
| 863 | mgnorm() : pdf_internal<enorm<sq_T> >() { } |
---|
| 864 | //!set mean function |
---|
| 865 | inline void set_parameters ( const shared_ptr<fnc> &g0, const sq_T &R0 ); |
---|
| 866 | inline void condition ( const vec &cond ); |
---|
[357] | 867 | |
---|
| 868 | |
---|
[737] | 869 | /*! Create Normal density with given function of mean value |
---|
| 870 | \f[ f(rv|rvc) = N( g(rvc), R) \f] |
---|
| 871 | from structure |
---|
| 872 | \code |
---|
| 873 | class = 'mgnorm'; |
---|
| 874 | g.class = 'fnc'; // function for mean value evolution |
---|
| 875 | g._fields_of_fnc = ...; |
---|
[357] | 876 | |
---|
[737] | 877 | R = [1, 0; // covariance matrix |
---|
| 878 | 0, 1]; |
---|
| 879 | --OR -- |
---|
| 880 | dR = [1, 1]; // diagonal of cavariance matrix |
---|
[357] | 881 | |
---|
[737] | 882 | rv = RV({'name'}) // description of RV |
---|
| 883 | rvc = RV({'name'}) // description of RV in condition |
---|
| 884 | \endcode |
---|
| 885 | */ |
---|
[357] | 886 | |
---|
[737] | 887 | void from_setting ( const Setting &set ) { |
---|
| 888 | pdf::from_setting ( set ); |
---|
| 889 | shared_ptr<fnc> g = UI::build<fnc> ( set, "g", UI::compulsory ); |
---|
[357] | 890 | |
---|
[737] | 891 | mat R; |
---|
| 892 | vec dR; |
---|
| 893 | if ( UI::get ( dR, set, "dR" ) ) |
---|
| 894 | R = diag ( dR ); |
---|
| 895 | else |
---|
| 896 | UI::get ( R, set, "R", UI::compulsory ); |
---|
[280] | 897 | |
---|
[737] | 898 | set_parameters ( g, R ); |
---|
| 899 | validate(); |
---|
| 900 | } |
---|
| 901 | void validate() { |
---|
| 902 | bdm_assert ( g->dimension() == this->dimension(), "incompatible function" ); |
---|
| 903 | } |
---|
[488] | 904 | }; |
---|
[357] | 905 | |
---|
[737] | 906 | UIREGISTER2 ( mgnorm, chmat ); |
---|
[529] | 907 | SHAREDPTR2 ( mgnorm, chmat ); |
---|
[357] | 908 | |
---|
[262] | 909 | |
---|
[488] | 910 | /*! (Approximate) Student t density with linear function of mean value |
---|
[262] | 911 | |
---|
[488] | 912 | The internal epdf of this class is of the type of a Gaussian (enorm). |
---|
| 913 | However, each conditioning is trying to assure the best possible approximation by taking into account the zeta function. See [] for reference. |
---|
[270] | 914 | |
---|
[488] | 915 | Perhaps a moment-matching technique? |
---|
| 916 | */ |
---|
[737] | 917 | class mlstudent : public mlnorm<ldmat, enorm> { |
---|
| 918 | protected: |
---|
| 919 | //! Variable \f$ \Lambda \f$ from theory |
---|
| 920 | ldmat Lambda; |
---|
| 921 | //! Reference to variable \f$ R \f$ |
---|
| 922 | ldmat &_R; |
---|
| 923 | //! Variable \f$ R_e \f$ |
---|
| 924 | ldmat Re; |
---|
| 925 | public: |
---|
| 926 | mlstudent () : mlnorm<ldmat, enorm> (), |
---|
| 927 | Lambda (), _R ( iepdf._R() ) {} |
---|
| 928 | //! constructor function |
---|
| 929 | void set_parameters ( const mat &A0, const vec &mu0, const ldmat &R0, const ldmat& Lambda0 ) { |
---|
| 930 | iepdf.set_parameters ( mu0, R0 );// was Lambda, why? |
---|
| 931 | A = A0; |
---|
| 932 | mu_const = mu0; |
---|
| 933 | Re = R0; |
---|
| 934 | Lambda = Lambda0; |
---|
| 935 | } |
---|
[294] | 936 | |
---|
[739] | 937 | void condition ( const vec &cond ); |
---|
| 938 | |
---|
[737] | 939 | void validate() { |
---|
| 940 | bdm_assert ( A.rows() == mu_const.length(), "mlstudent: A vs. mu mismatch" ); |
---|
| 941 | bdm_assert ( _R.rows() == A.rows(), "mlstudent: A vs. R mismatch" ); |
---|
| 942 | |
---|
| 943 | } |
---|
[488] | 944 | }; |
---|
| 945 | /*! |
---|
| 946 | \brief Gamma random walk |
---|
[198] | 947 | |
---|
[488] | 948 | Mean value, \f$\mu\f$, of this density is given by \c rvc . |
---|
| 949 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
| 950 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
[32] | 951 | |
---|
[488] | 952 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
| 953 | */ |
---|
[737] | 954 | class mgamma : public pdf_internal<egamma> { |
---|
| 955 | protected: |
---|
[461] | 956 | |
---|
[737] | 957 | //! Constant \f$k\f$ |
---|
| 958 | double k; |
---|
[461] | 959 | |
---|
[737] | 960 | //! cache of iepdf.beta |
---|
| 961 | vec &_beta; |
---|
[32] | 962 | |
---|
[737] | 963 | public: |
---|
| 964 | //! Constructor |
---|
| 965 | mgamma() : pdf_internal<egamma>(), k ( 0 ), |
---|
| 966 | _beta ( iepdf._beta() ) { |
---|
| 967 | } |
---|
[461] | 968 | |
---|
[737] | 969 | //! Set value of \c k |
---|
| 970 | void set_parameters ( double k, const vec &beta0 ); |
---|
[461] | 971 | |
---|
[737] | 972 | void condition ( const vec &val ) { |
---|
| 973 | _beta = k / val; |
---|
| 974 | }; |
---|
| 975 | /*! Create Gamma density with conditional mean value |
---|
| 976 | \f[ f(rv|rvc) = \Gamma(k, k/rvc) \f] |
---|
| 977 | from structure |
---|
| 978 | \code |
---|
| 979 | class = 'mgamma'; |
---|
| 980 | beta = [...]; // vector of initial alpha |
---|
| 981 | k = 1.1; // multiplicative constant k |
---|
| 982 | rv = RV({'name'}) // description of RV |
---|
| 983 | rvc = RV({'name'}) // description of RV in condition |
---|
| 984 | \endcode |
---|
| 985 | */ |
---|
| 986 | void from_setting ( const Setting &set ) { |
---|
| 987 | pdf::from_setting ( set ); // reads rv and rvc |
---|
| 988 | vec betatmp; // ugly but necessary |
---|
| 989 | UI::get ( betatmp, set, "beta", UI::compulsory ); |
---|
| 990 | UI::get ( k, set, "k", UI::compulsory ); |
---|
| 991 | set_parameters ( k, betatmp ); |
---|
| 992 | validate(); |
---|
| 993 | } |
---|
| 994 | void validate() { |
---|
| 995 | pdf_internal<egamma>::validate(); |
---|
| 996 | |
---|
| 997 | dim = _beta.length(); |
---|
| 998 | dimc = _beta.length(); |
---|
| 999 | } |
---|
[488] | 1000 | }; |
---|
[737] | 1001 | UIREGISTER ( mgamma ); |
---|
| 1002 | SHAREDPTR ( mgamma ); |
---|
[32] | 1003 | |
---|
[488] | 1004 | /*! |
---|
| 1005 | \brief Inverse-Gamma random walk |
---|
[225] | 1006 | |
---|
[488] | 1007 | Mean value, \f$ \mu \f$, of this density is given by \c rvc . |
---|
| 1008 | Standard deviation of the random walk is proportional to one \f$ k \f$-th the mean. |
---|
| 1009 | This is achieved by setting \f$ \alpha=\mu/k^2+2 \f$ and \f$ \beta=\mu(\alpha-1)\f$. |
---|
[461] | 1010 | |
---|
[488] | 1011 | The standard deviation of the walk is then: \f$ \mu/\sqrt(k)\f$. |
---|
| 1012 | */ |
---|
[737] | 1013 | class migamma : public pdf_internal<eigamma> { |
---|
| 1014 | protected: |
---|
| 1015 | //! Constant \f$k\f$ |
---|
| 1016 | double k; |
---|
[461] | 1017 | |
---|
[737] | 1018 | //! cache of iepdf.alpha |
---|
| 1019 | vec &_alpha; |
---|
[225] | 1020 | |
---|
[737] | 1021 | //! cache of iepdf.beta |
---|
| 1022 | vec &_beta; |
---|
[461] | 1023 | |
---|
[737] | 1024 | public: |
---|
| 1025 | //! \name Constructors |
---|
| 1026 | //!@{ |
---|
| 1027 | migamma() : pdf_internal<eigamma>(), |
---|
| 1028 | k ( 0 ), |
---|
| 1029 | _alpha ( iepdf._alpha() ), |
---|
| 1030 | _beta ( iepdf._beta() ) { |
---|
| 1031 | } |
---|
[225] | 1032 | |
---|
[737] | 1033 | migamma ( const migamma &m ) : pdf_internal<eigamma>(), |
---|
| 1034 | k ( 0 ), |
---|
| 1035 | _alpha ( iepdf._alpha() ), |
---|
| 1036 | _beta ( iepdf._beta() ) { |
---|
| 1037 | } |
---|
| 1038 | //!@} |
---|
[225] | 1039 | |
---|
[737] | 1040 | //! Set value of \c k |
---|
| 1041 | void set_parameters ( int len, double k0 ) { |
---|
| 1042 | k = k0; |
---|
| 1043 | iepdf.set_parameters ( ( 1.0 / ( k*k ) + 2.0 ) *ones ( len ) /*alpha*/, ones ( len ) /*beta*/ ); |
---|
| 1044 | dimc = dimension(); |
---|
| 1045 | }; |
---|
| 1046 | void condition ( const vec &val ) { |
---|
| 1047 | _beta = elem_mult ( val, ( _alpha - 1.0 ) ); |
---|
| 1048 | }; |
---|
[488] | 1049 | }; |
---|
[357] | 1050 | |
---|
[60] | 1051 | |
---|
[488] | 1052 | /*! |
---|
| 1053 | \brief Gamma random walk around a fixed point |
---|
[60] | 1054 | |
---|
[488] | 1055 | Mean value, \f$\mu\f$, of this density is given by a geometric combination of \c rvc and given fixed point, \f$p\f$. \f$l\f$ is the coefficient of the geometric combimation |
---|
| 1056 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
---|
[60] | 1057 | |
---|
[488] | 1058 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
| 1059 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
[294] | 1060 | |
---|
[488] | 1061 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
| 1062 | */ |
---|
[737] | 1063 | class mgamma_fix : public mgamma { |
---|
| 1064 | protected: |
---|
| 1065 | //! parameter l |
---|
| 1066 | double l; |
---|
| 1067 | //! reference vector |
---|
| 1068 | vec refl; |
---|
| 1069 | public: |
---|
| 1070 | //! Constructor |
---|
| 1071 | mgamma_fix () : mgamma (), refl () {}; |
---|
| 1072 | //! Set value of \c k |
---|
| 1073 | void set_parameters ( double k0 , vec ref0, double l0 ) { |
---|
| 1074 | mgamma::set_parameters ( k0, ref0 ); |
---|
| 1075 | refl = pow ( ref0, 1.0 - l0 ); |
---|
| 1076 | l = l0; |
---|
| 1077 | dimc = dimension(); |
---|
| 1078 | }; |
---|
[60] | 1079 | |
---|
[737] | 1080 | void condition ( const vec &val ) { |
---|
| 1081 | vec mean = elem_mult ( refl, pow ( val, l ) ); |
---|
| 1082 | _beta = k / mean; |
---|
| 1083 | }; |
---|
[488] | 1084 | }; |
---|
[60] | 1085 | |
---|
[225] | 1086 | |
---|
[488] | 1087 | /*! |
---|
| 1088 | \brief Inverse-Gamma random walk around a fixed point |
---|
[225] | 1089 | |
---|
[488] | 1090 | Mean value, \f$\mu\f$, of this density is given by a geometric combination of \c rvc and given fixed point, \f$p\f$. \f$l\f$ is the coefficient of the geometric combimation |
---|
| 1091 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
---|
[225] | 1092 | |
---|
[488] | 1093 | ==== Check == vv = |
---|
| 1094 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
| 1095 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
[225] | 1096 | |
---|
[488] | 1097 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
| 1098 | */ |
---|
[737] | 1099 | class migamma_ref : public migamma { |
---|
| 1100 | protected: |
---|
| 1101 | //! parameter l |
---|
| 1102 | double l; |
---|
| 1103 | //! reference vector |
---|
| 1104 | vec refl; |
---|
| 1105 | public: |
---|
| 1106 | //! Constructor |
---|
| 1107 | migamma_ref () : migamma (), refl () {}; |
---|
| 1108 | //! Set value of \c k |
---|
| 1109 | void set_parameters ( double k0 , vec ref0, double l0 ) { |
---|
| 1110 | migamma::set_parameters ( ref0.length(), k0 ); |
---|
| 1111 | refl = pow ( ref0, 1.0 - l0 ); |
---|
| 1112 | l = l0; |
---|
| 1113 | dimc = dimension(); |
---|
| 1114 | }; |
---|
[357] | 1115 | |
---|
[737] | 1116 | void condition ( const vec &val ) { |
---|
| 1117 | vec mean = elem_mult ( refl, pow ( val, l ) ); |
---|
| 1118 | migamma::condition ( mean ); |
---|
| 1119 | }; |
---|
[357] | 1120 | |
---|
| 1121 | |
---|
[737] | 1122 | /*! Create inverse-Gamma density with conditional mean value |
---|
| 1123 | \f[ f(rv|rvc) = i\Gamma(k, k/(rvc^l \circ ref^{(1-l)}) \f] |
---|
| 1124 | from structure |
---|
| 1125 | \code |
---|
| 1126 | class = 'migamma_ref'; |
---|
| 1127 | ref = [1e-5; 1e-5; 1e-2 1e-3]; // reference vector |
---|
| 1128 | l = 0.999; // constant l |
---|
| 1129 | k = 0.1; // constant k |
---|
| 1130 | rv = RV({'name'}) // description of RV |
---|
| 1131 | rvc = RV({'name'}) // description of RV in condition |
---|
| 1132 | \endcode |
---|
| 1133 | */ |
---|
| 1134 | void from_setting ( const Setting &set ); |
---|
[225] | 1135 | |
---|
[737] | 1136 | // TODO dodelat void to_setting( Setting &set ) const; |
---|
[488] | 1137 | }; |
---|
[357] | 1138 | |
---|
| 1139 | |
---|
[737] | 1140 | UIREGISTER ( migamma_ref ); |
---|
| 1141 | SHAREDPTR ( migamma_ref ); |
---|
[294] | 1142 | |
---|
[488] | 1143 | /*! Log-Normal probability density |
---|
| 1144 | only allow diagonal covariances! |
---|
[294] | 1145 | |
---|
[488] | 1146 | Density of the form \f$ \log(x)\sim \mathcal{N}(\mu,\sigma^2) \f$ , i.e. |
---|
| 1147 | \f[ |
---|
| 1148 | x \sim \frac{1}{x\sigma\sqrt{2\pi}}\exp{-\frac{1}{2\sigma^2}(\log(x)-\mu)} |
---|
| 1149 | \f] |
---|
[294] | 1150 | |
---|
[621] | 1151 | Function from_setting loads mu and R in the same way as it does for enorm<>! |
---|
[488] | 1152 | */ |
---|
[737] | 1153 | class elognorm: public enorm<ldmat> { |
---|
| 1154 | public: |
---|
| 1155 | vec sample() const { |
---|
| 1156 | return exp ( enorm<ldmat>::sample() ); |
---|
| 1157 | }; |
---|
| 1158 | vec mean() const { |
---|
| 1159 | vec var = enorm<ldmat>::variance(); |
---|
| 1160 | return exp ( mu - 0.5*var ); |
---|
| 1161 | }; |
---|
[285] | 1162 | |
---|
[488] | 1163 | }; |
---|
[285] | 1164 | |
---|
[488] | 1165 | /*! |
---|
| 1166 | \brief Log-Normal random walk |
---|
[285] | 1167 | |
---|
[488] | 1168 | Mean value, \f$\mu\f$, is... |
---|
[285] | 1169 | |
---|
[488] | 1170 | */ |
---|
[737] | 1171 | class mlognorm : public pdf_internal<elognorm> { |
---|
| 1172 | protected: |
---|
| 1173 | //! parameter 1/2*sigma^2 |
---|
| 1174 | double sig2; |
---|
[461] | 1175 | |
---|
[737] | 1176 | //! access |
---|
| 1177 | vec μ |
---|
| 1178 | public: |
---|
| 1179 | //! Constructor |
---|
| 1180 | mlognorm() : pdf_internal<elognorm>(), |
---|
| 1181 | sig2 ( 0 ), |
---|
| 1182 | mu ( iepdf._mu() ) { |
---|
| 1183 | } |
---|
[285] | 1184 | |
---|
[737] | 1185 | //! Set value of \c k |
---|
| 1186 | void set_parameters ( int size, double k ) { |
---|
| 1187 | sig2 = 0.5 * log ( k * k + 1 ); |
---|
| 1188 | iepdf.set_parameters ( zeros ( size ), 2*sig2*eye ( size ) ); |
---|
[285] | 1189 | |
---|
[737] | 1190 | dimc = size; |
---|
| 1191 | }; |
---|
[357] | 1192 | |
---|
[737] | 1193 | void condition ( const vec &val ) { |
---|
| 1194 | mu = log ( val ) - sig2;//elem_mult ( refl,pow ( val,l ) ); |
---|
| 1195 | }; |
---|
[357] | 1196 | |
---|
[737] | 1197 | /*! Create logNormal random Walk |
---|
| 1198 | \f[ f(rv|rvc) = log\mathcal{N}( \log(rvc)-0.5\log(k^2+1), k I) \f] |
---|
| 1199 | from structure |
---|
| 1200 | \code |
---|
| 1201 | class = 'mlognorm'; |
---|
| 1202 | k = 0.1; // "variance" k |
---|
| 1203 | mu0 = 0.1; // Initial value of mean |
---|
| 1204 | rv = RV({'name'}) // description of RV |
---|
| 1205 | rvc = RV({'name'}) // description of RV in condition |
---|
| 1206 | \endcode |
---|
| 1207 | */ |
---|
| 1208 | void from_setting ( const Setting &set ); |
---|
[357] | 1209 | |
---|
[737] | 1210 | // TODO dodelat void to_setting( Setting &set ) const; |
---|
[285] | 1211 | |
---|
[488] | 1212 | }; |
---|
[294] | 1213 | |
---|
[737] | 1214 | UIREGISTER ( mlognorm ); |
---|
| 1215 | SHAREDPTR ( mlognorm ); |
---|
[294] | 1216 | |
---|
[488] | 1217 | /*! inverse Wishart density defined on Choleski decomposition |
---|
| 1218 | |
---|
| 1219 | */ |
---|
[737] | 1220 | class eWishartCh : public epdf { |
---|
| 1221 | protected: |
---|
| 1222 | //! Upper-Triagle of Choleski decomposition of \f$ \Psi \f$ |
---|
| 1223 | chmat Y; |
---|
| 1224 | //! dimension of matrix \f$ \Psi \f$ |
---|
| 1225 | int p; |
---|
| 1226 | //! degrees of freedom \f$ \nu \f$ |
---|
| 1227 | double delta; |
---|
| 1228 | public: |
---|
| 1229 | //! Set internal structures |
---|
| 1230 | void set_parameters ( const mat &Y0, const double delta0 ) { |
---|
| 1231 | Y = chmat ( Y0 ); |
---|
| 1232 | delta = delta0; |
---|
| 1233 | p = Y.rows(); |
---|
| 1234 | dim = p * p; |
---|
| 1235 | } |
---|
| 1236 | //! Set internal structures |
---|
| 1237 | void set_parameters ( const chmat &Y0, const double delta0 ) { |
---|
| 1238 | Y = Y0; |
---|
| 1239 | delta = delta0; |
---|
| 1240 | p = Y.rows(); |
---|
| 1241 | dim = p * p; |
---|
| 1242 | } |
---|
| 1243 | //! Sample matrix argument |
---|
| 1244 | mat sample_mat() const { |
---|
| 1245 | mat X = zeros ( p, p ); |
---|
[488] | 1246 | |
---|
[737] | 1247 | //sample diagonal |
---|
| 1248 | for ( int i = 0; i < p; i++ ) { |
---|
| 1249 | GamRNG.setup ( 0.5* ( delta - i ) , 0.5 ); // no +1 !! index if from 0 |
---|
[294] | 1250 | #pragma omp critical |
---|
[737] | 1251 | X ( i, i ) = sqrt ( GamRNG() ); |
---|
| 1252 | } |
---|
| 1253 | //do the rest |
---|
| 1254 | for ( int i = 0; i < p; i++ ) { |
---|
| 1255 | for ( int j = i + 1; j < p; j++ ) { |
---|
[294] | 1256 | #pragma omp critical |
---|
[737] | 1257 | X ( i, j ) = NorRNG.sample(); |
---|
[294] | 1258 | } |
---|
[488] | 1259 | } |
---|
[737] | 1260 | return X*Y._Ch();// return upper triangular part of the decomposition |
---|
| 1261 | } |
---|
| 1262 | vec sample () const { |
---|
| 1263 | return vec ( sample_mat()._data(), p*p ); |
---|
| 1264 | } |
---|
| 1265 | //! fast access function y0 will be copied into Y.Ch. |
---|
| 1266 | void setY ( const mat &Ch0 ) { |
---|
| 1267 | copy_vector ( dim, Ch0._data(), Y._Ch()._data() ); |
---|
| 1268 | } |
---|
| 1269 | //! fast access function y0 will be copied into Y.Ch. |
---|
| 1270 | void _setY ( const vec &ch0 ) { |
---|
| 1271 | copy_vector ( dim, ch0._data(), Y._Ch()._data() ); |
---|
| 1272 | } |
---|
| 1273 | //! access function |
---|
| 1274 | const chmat& getY() const { |
---|
| 1275 | return Y; |
---|
| 1276 | } |
---|
[488] | 1277 | }; |
---|
[294] | 1278 | |
---|
[536] | 1279 | //! Inverse Wishart on Choleski decomposition |
---|
| 1280 | /*! Being computed by conversion from `standard' Wishart |
---|
| 1281 | */ |
---|
[737] | 1282 | class eiWishartCh: public epdf { |
---|
| 1283 | protected: |
---|
| 1284 | //! Internal instance of Wishart density |
---|
| 1285 | eWishartCh W; |
---|
| 1286 | //! size of Ch |
---|
| 1287 | int p; |
---|
| 1288 | //! parameter delta |
---|
| 1289 | double delta; |
---|
| 1290 | public: |
---|
| 1291 | //! constructor function |
---|
| 1292 | void set_parameters ( const mat &Y0, const double delta0 ) { |
---|
| 1293 | delta = delta0; |
---|
| 1294 | W.set_parameters ( inv ( Y0 ), delta0 ); |
---|
| 1295 | p = Y0.rows(); |
---|
| 1296 | } |
---|
[750] | 1297 | |
---|
| 1298 | virtual void validate (){ |
---|
| 1299 | dim = W.dimension(); |
---|
| 1300 | } |
---|
| 1301 | |
---|
| 1302 | |
---|
[737] | 1303 | vec sample() const { |
---|
| 1304 | mat iCh; |
---|
| 1305 | iCh = inv ( W.sample_mat() ); |
---|
| 1306 | return vec ( iCh._data(), dim ); |
---|
| 1307 | } |
---|
| 1308 | //! access function |
---|
| 1309 | void _setY ( const vec &y0 ) { |
---|
| 1310 | mat Ch ( p, p ); |
---|
| 1311 | mat iCh ( p, p ); |
---|
| 1312 | copy_vector ( dim, y0._data(), Ch._data() ); |
---|
[488] | 1313 | |
---|
[737] | 1314 | iCh = inv ( Ch ); |
---|
| 1315 | W.setY ( iCh ); |
---|
| 1316 | } |
---|
| 1317 | virtual double evallog ( const vec &val ) const { |
---|
| 1318 | chmat X ( p ); |
---|
| 1319 | const chmat& Y = W.getY(); |
---|
[488] | 1320 | |
---|
[737] | 1321 | copy_vector ( p*p, val._data(), X._Ch()._data() ); |
---|
| 1322 | chmat iX ( p ); |
---|
| 1323 | X.inv ( iX ); |
---|
| 1324 | // compute |
---|
[294] | 1325 | // \frac{ |\Psi|^{m/2}|X|^{-(m+p+1)/2}e^{-tr(\Psi X^{-1})/2} }{ 2^{mp/2}\Gamma_p(m/2)}, |
---|
[737] | 1326 | mat M = Y.to_mat() * iX.to_mat(); |
---|
[285] | 1327 | |
---|
[737] | 1328 | double log1 = 0.5 * p * ( 2 * Y.logdet() ) - 0.5 * ( delta + p + 1 ) * ( 2 * X.logdet() ) - 0.5 * trace ( M ); |
---|
| 1329 | //Fixme! Multivariate gamma omitted!! it is ok for sampling, but not otherwise!! |
---|
[461] | 1330 | |
---|
[737] | 1331 | /* if (0) { |
---|
| 1332 | mat XX=X.to_mat(); |
---|
| 1333 | mat YY=Y.to_mat(); |
---|
[461] | 1334 | |
---|
[737] | 1335 | double log2 = 0.5*p*log(det(YY))-0.5*(delta+p+1)*log(det(XX))-0.5*trace(YY*inv(XX)); |
---|
| 1336 | cout << log1 << "," << log2 << endl; |
---|
| 1337 | }*/ |
---|
| 1338 | return log1; |
---|
| 1339 | }; |
---|
[285] | 1340 | |
---|
[488] | 1341 | }; |
---|
| 1342 | |
---|
[536] | 1343 | //! Random Walk on inverse Wishart |
---|
[737] | 1344 | class rwiWishartCh : public pdf_internal<eiWishartCh> { |
---|
| 1345 | protected: |
---|
| 1346 | //!square root of \f$ \nu-p-1 \f$ - needed for computation of \f$ \Psi \f$ from conditions |
---|
| 1347 | double sqd; |
---|
| 1348 | //!reference point for diagonal |
---|
| 1349 | vec refl; |
---|
| 1350 | //! power of the reference |
---|
| 1351 | double l; |
---|
| 1352 | //! dimension |
---|
| 1353 | int p; |
---|
[488] | 1354 | |
---|
[737] | 1355 | public: |
---|
| 1356 | rwiWishartCh() : sqd ( 0 ), l ( 0 ), p ( 0 ) {} |
---|
| 1357 | //! constructor function |
---|
| 1358 | void set_parameters ( int p0, double k, vec ref0, double l0 ) { |
---|
| 1359 | p = p0; |
---|
| 1360 | double delta = 2 / ( k * k ) + p + 3; |
---|
| 1361 | sqd = sqrt ( delta - p - 1 ); |
---|
| 1362 | l = l0; |
---|
| 1363 | refl = pow ( ref0, 1 - l ); |
---|
[488] | 1364 | |
---|
[737] | 1365 | iepdf.set_parameters ( eye ( p ), delta ); |
---|
| 1366 | dimc = iepdf.dimension(); |
---|
| 1367 | } |
---|
| 1368 | void condition ( const vec &c ) { |
---|
| 1369 | vec z = c; |
---|
| 1370 | int ri = 0; |
---|
| 1371 | for ( int i = 0; i < p*p; i += ( p + 1 ) ) {//trace diagonal element |
---|
| 1372 | z ( i ) = pow ( z ( i ), l ) * refl ( ri ); |
---|
| 1373 | ri++; |
---|
[488] | 1374 | } |
---|
[285] | 1375 | |
---|
[737] | 1376 | iepdf._setY ( sqd*z ); |
---|
| 1377 | } |
---|
[488] | 1378 | }; |
---|
| 1379 | |
---|
[32] | 1380 | //! Switch between various resampling methods. |
---|
[488] | 1381 | enum RESAMPLING_METHOD { MULTINOMIAL = 0, STRATIFIED = 1, SYSTEMATIC = 3 }; |
---|
| 1382 | /*! |
---|
| 1383 | \brief Weighted empirical density |
---|
[32] | 1384 | |
---|
[488] | 1385 | Used e.g. in particle filters. |
---|
| 1386 | */ |
---|
[737] | 1387 | class eEmp: public epdf { |
---|
| 1388 | protected : |
---|
| 1389 | //! Number of particles |
---|
| 1390 | int n; |
---|
| 1391 | //! Sample weights \f$w\f$ |
---|
| 1392 | vec w; |
---|
| 1393 | //! Samples \f$x^{(i)}, i=1..n\f$ |
---|
| 1394 | Array<vec> samples; |
---|
| 1395 | public: |
---|
| 1396 | //! \name Constructors |
---|
| 1397 | //!@{ |
---|
| 1398 | eEmp () : epdf (), w (), samples () {}; |
---|
| 1399 | //! copy constructor |
---|
| 1400 | eEmp ( const eEmp &e ) : epdf ( e ), w ( e.w ), samples ( e.samples ) {}; |
---|
| 1401 | //!@} |
---|
[280] | 1402 | |
---|
[737] | 1403 | //! Set samples and weights |
---|
| 1404 | void set_statistics ( const vec &w0, const epdf &pdf0 ); |
---|
| 1405 | //! Set samples and weights |
---|
| 1406 | void set_statistics ( const epdf &pdf0 , int n ) { |
---|
| 1407 | set_statistics ( ones ( n ) / n, pdf0 ); |
---|
| 1408 | }; |
---|
| 1409 | //! Set sample |
---|
| 1410 | void set_samples ( const epdf* pdf0 ); |
---|
| 1411 | //! Set sample |
---|
| 1412 | void set_parameters ( int n0, bool copy = true ) { |
---|
| 1413 | n = n0; |
---|
| 1414 | w.set_size ( n0, copy ); |
---|
| 1415 | samples.set_size ( n0, copy ); |
---|
| 1416 | }; |
---|
| 1417 | //! Set samples |
---|
| 1418 | void set_parameters ( const Array<vec> &Av ) { |
---|
| 1419 | n = Av.size(); |
---|
| 1420 | w = 1 / n * ones ( n ); |
---|
| 1421 | samples = Av; |
---|
| 1422 | }; |
---|
[750] | 1423 | virtual void validate (){ |
---|
| 1424 | bdm_assert ( n > 0, "Empty samples" ); |
---|
| 1425 | epdf::validate ( samples ( 0 ).length() ); |
---|
| 1426 | } |
---|
[737] | 1427 | //! Potentially dangerous, use with care. |
---|
| 1428 | vec& _w() { |
---|
| 1429 | return w; |
---|
| 1430 | }; |
---|
| 1431 | //! Potentially dangerous, use with care. |
---|
| 1432 | const vec& _w() const { |
---|
| 1433 | return w; |
---|
| 1434 | }; |
---|
| 1435 | //! access function |
---|
| 1436 | Array<vec>& _samples() { |
---|
| 1437 | return samples; |
---|
| 1438 | }; |
---|
| 1439 | //! access function |
---|
| 1440 | const vec& _sample ( int i ) const { |
---|
| 1441 | return samples ( i ); |
---|
| 1442 | }; |
---|
| 1443 | //! access function |
---|
| 1444 | const Array<vec>& _samples() const { |
---|
| 1445 | return samples; |
---|
| 1446 | }; |
---|
| 1447 | //! Function performs resampling, i.e. removal of low-weight samples and duplication of high-weight samples such that the new samples represent the same density. |
---|
| 1448 | //! The vector with indeces of new samples is returned in variable \c index. |
---|
| 1449 | void resample ( ivec &index, RESAMPLING_METHOD method = SYSTEMATIC ); |
---|
[565] | 1450 | |
---|
[737] | 1451 | //! Resampling without returning index of new particles. |
---|
| 1452 | void resample ( RESAMPLING_METHOD method = SYSTEMATIC ) { |
---|
| 1453 | ivec ind; |
---|
| 1454 | resample ( ind, method ); |
---|
| 1455 | }; |
---|
[565] | 1456 | |
---|
[737] | 1457 | //! inherited operation : NOT implemented |
---|
| 1458 | vec sample() const { |
---|
| 1459 | bdm_error ( "Not implemented" ); |
---|
| 1460 | return vec(); |
---|
| 1461 | } |
---|
[565] | 1462 | |
---|
[737] | 1463 | //! inherited operation : NOT implemented |
---|
| 1464 | double evallog ( const vec &val ) const { |
---|
| 1465 | bdm_error ( "Not implemented" ); |
---|
| 1466 | return 0.0; |
---|
| 1467 | } |
---|
| 1468 | |
---|
| 1469 | vec mean() const { |
---|
| 1470 | vec pom = zeros ( dim ); |
---|
| 1471 | for ( int i = 0; i < n; i++ ) { |
---|
| 1472 | pom += samples ( i ) * w ( i ); |
---|
[488] | 1473 | } |
---|
[737] | 1474 | return pom; |
---|
| 1475 | } |
---|
| 1476 | vec variance() const { |
---|
| 1477 | vec pom = zeros ( dim ); |
---|
| 1478 | for ( int i = 0; i < n; i++ ) { |
---|
| 1479 | pom += pow ( samples ( i ), 2 ) * w ( i ); |
---|
[488] | 1480 | } |
---|
[737] | 1481 | return pom - pow ( mean(), 2 ); |
---|
| 1482 | } |
---|
| 1483 | //! For this class, qbounds are minimum and maximum value of the population! |
---|
[739] | 1484 | void qbounds ( vec &lb, vec &ub, double perc = 0.95 ) const; |
---|
[488] | 1485 | }; |
---|
[32] | 1486 | |
---|
| 1487 | |
---|
[8] | 1488 | //////////////////////// |
---|
| 1489 | |
---|
[488] | 1490 | template<class sq_T> |
---|
[737] | 1491 | void enorm<sq_T>::set_parameters ( const vec &mu0, const sq_T &R0 ) { |
---|
[28] | 1492 | //Fixme test dimensions of mu0 and R0; |
---|
[488] | 1493 | mu = mu0; |
---|
| 1494 | R = R0; |
---|
| 1495 | validate(); |
---|
| 1496 | }; |
---|
[8] | 1497 | |
---|
[488] | 1498 | template<class sq_T> |
---|
[737] | 1499 | void enorm<sq_T>::from_setting ( const Setting &set ) { |
---|
| 1500 | epdf::from_setting ( set ); //reads rv |
---|
[384] | 1501 | |
---|
[737] | 1502 | UI::get ( mu, set, "mu", UI::compulsory ); |
---|
[488] | 1503 | mat Rtmp;// necessary for conversion |
---|
[737] | 1504 | UI::get ( Rtmp, set, "R", UI::compulsory ); |
---|
[488] | 1505 | R = Rtmp; // conversion |
---|
| 1506 | validate(); |
---|
| 1507 | } |
---|
[8] | 1508 | |
---|
[488] | 1509 | template<class sq_T> |
---|
[737] | 1510 | void enorm<sq_T>::dupdate ( mat &v, double nu ) { |
---|
[488] | 1511 | // |
---|
| 1512 | }; |
---|
| 1513 | |
---|
[178] | 1514 | // template<class sq_T> |
---|
| 1515 | // void enorm<sq_T>::tupdate ( double phi, mat &vbar, double nubar ) { |
---|
| 1516 | // // |
---|
| 1517 | // }; |
---|
[8] | 1518 | |
---|
[488] | 1519 | template<class sq_T> |
---|
[737] | 1520 | vec enorm<sq_T>::sample() const { |
---|
| 1521 | vec x ( dim ); |
---|
[270] | 1522 | #pragma omp critical |
---|
[737] | 1523 | NorRNG.sample_vector ( dim, x ); |
---|
| 1524 | vec smp = R.sqrt_mult ( x ); |
---|
[12] | 1525 | |
---|
[488] | 1526 | smp += mu; |
---|
| 1527 | return smp; |
---|
| 1528 | }; |
---|
[8] | 1529 | |
---|
[214] | 1530 | // template<class sq_T> |
---|
| 1531 | // double enorm<sq_T>::eval ( const vec &val ) const { |
---|
| 1532 | // double pdfl,e; |
---|
| 1533 | // pdfl = evallog ( val ); |
---|
| 1534 | // e = exp ( pdfl ); |
---|
| 1535 | // return e; |
---|
| 1536 | // }; |
---|
[8] | 1537 | |
---|
[488] | 1538 | template<class sq_T> |
---|
[737] | 1539 | double enorm<sq_T>::evallog_nn ( const vec &val ) const { |
---|
[488] | 1540 | // 1.83787706640935 = log(2pi) |
---|
[737] | 1541 | double tmp = -0.5 * ( R.invqform ( mu - val ) );// - lognc(); |
---|
[488] | 1542 | return tmp; |
---|
| 1543 | }; |
---|
[28] | 1544 | |
---|
[488] | 1545 | template<class sq_T> |
---|
[737] | 1546 | inline double enorm<sq_T>::lognc () const { |
---|
[488] | 1547 | // 1.83787706640935 = log(2pi) |
---|
[737] | 1548 | double tmp = 0.5 * ( R.cols() * 1.83787706640935 + R.logdet() ); |
---|
[488] | 1549 | return tmp; |
---|
| 1550 | }; |
---|
[28] | 1551 | |
---|
[8] | 1552 | |
---|
[192] | 1553 | // template<class sq_T> |
---|
| 1554 | // vec mlnorm<sq_T>::samplecond (const vec &cond, double &lik ) { |
---|
| 1555 | // this->condition ( cond ); |
---|
| 1556 | // vec smp = epdf.sample(); |
---|
| 1557 | // lik = epdf.eval ( smp ); |
---|
| 1558 | // return smp; |
---|
| 1559 | // } |
---|
[8] | 1560 | |
---|
[192] | 1561 | // template<class sq_T> |
---|
| 1562 | // mat mlnorm<sq_T>::samplecond (const vec &cond, vec &lik, int n ) { |
---|
| 1563 | // int i; |
---|
| 1564 | // int dim = rv.count(); |
---|
| 1565 | // mat Smp ( dim,n ); |
---|
| 1566 | // vec smp ( dim ); |
---|
| 1567 | // this->condition ( cond ); |
---|
[198] | 1568 | // |
---|
[192] | 1569 | // for ( i=0; i<n; i++ ) { |
---|
| 1570 | // smp = epdf.sample(); |
---|
| 1571 | // lik ( i ) = epdf.eval ( smp ); |
---|
| 1572 | // Smp.set_col ( i ,smp ); |
---|
| 1573 | // } |
---|
[198] | 1574 | // |
---|
[192] | 1575 | // return Smp; |
---|
| 1576 | // } |
---|
[28] | 1577 | |
---|
[8] | 1578 | |
---|
[488] | 1579 | template<class sq_T> |
---|
[737] | 1580 | shared_ptr<epdf> enorm<sq_T>::marginal ( const RV &rvn ) const { |
---|
[504] | 1581 | enorm<sq_T> *tmp = new enorm<sq_T> (); |
---|
[737] | 1582 | shared_ptr<epdf> narrow ( tmp ); |
---|
[504] | 1583 | marginal ( rvn, *tmp ); |
---|
| 1584 | return narrow; |
---|
| 1585 | } |
---|
| 1586 | |
---|
| 1587 | template<class sq_T> |
---|
[737] | 1588 | void enorm<sq_T>::marginal ( const RV &rvn, enorm<sq_T> &target ) const { |
---|
| 1589 | bdm_assert ( isnamed(), "rv description is not assigned" ); |
---|
| 1590 | ivec irvn = rvn.dataind ( rv ); |
---|
[178] | 1591 | |
---|
[737] | 1592 | sq_T Rn ( R, irvn ); // select rows and columns of R |
---|
[280] | 1593 | |
---|
[504] | 1594 | target.set_rv ( rvn ); |
---|
[737] | 1595 | target.set_parameters ( mu ( irvn ), Rn ); |
---|
[488] | 1596 | } |
---|
[178] | 1597 | |
---|
[488] | 1598 | template<class sq_T> |
---|
[737] | 1599 | shared_ptr<pdf> enorm<sq_T>::condition ( const RV &rvn ) const { |
---|
[504] | 1600 | mlnorm<sq_T> *tmp = new mlnorm<sq_T> (); |
---|
[737] | 1601 | shared_ptr<pdf> narrow ( tmp ); |
---|
[504] | 1602 | condition ( rvn, *tmp ); |
---|
| 1603 | return narrow; |
---|
| 1604 | } |
---|
[178] | 1605 | |
---|
[504] | 1606 | template<class sq_T> |
---|
[737] | 1607 | void enorm<sq_T>::condition ( const RV &rvn, pdf &target ) const { |
---|
[504] | 1608 | typedef mlnorm<sq_T> TMlnorm; |
---|
| 1609 | |
---|
[737] | 1610 | bdm_assert ( isnamed(), "rvs are not assigned" ); |
---|
| 1611 | TMlnorm &uptarget = dynamic_cast<TMlnorm &> ( target ); |
---|
[270] | 1612 | |
---|
[737] | 1613 | RV rvc = rv.subt ( rvn ); |
---|
| 1614 | bdm_assert ( ( rvc._dsize() + rvn._dsize() == rv._dsize() ), "wrong rvn" ); |
---|
[488] | 1615 | //Permutation vector of the new R |
---|
[737] | 1616 | ivec irvn = rvn.dataind ( rv ); |
---|
| 1617 | ivec irvc = rvc.dataind ( rv ); |
---|
| 1618 | ivec perm = concat ( irvn , irvc ); |
---|
| 1619 | sq_T Rn ( R, perm ); |
---|
[178] | 1620 | |
---|
[488] | 1621 | //fixme - could this be done in general for all sq_T? |
---|
| 1622 | mat S = Rn.to_mat(); |
---|
| 1623 | //fixme |
---|
| 1624 | int n = rvn._dsize() - 1; |
---|
| 1625 | int end = R.rows() - 1; |
---|
[737] | 1626 | mat S11 = S.get ( 0, n, 0, n ); |
---|
| 1627 | mat S12 = S.get ( 0, n , rvn._dsize(), end ); |
---|
| 1628 | mat S22 = S.get ( rvn._dsize(), end, rvn._dsize(), end ); |
---|
[178] | 1629 | |
---|
[737] | 1630 | vec mu1 = mu ( irvn ); |
---|
| 1631 | vec mu2 = mu ( irvc ); |
---|
| 1632 | mat A = S12 * inv ( S22 ); |
---|
| 1633 | sq_T R_n ( S11 - A *S12.T() ); |
---|
[178] | 1634 | |
---|
[737] | 1635 | uptarget.set_rv ( rvn ); |
---|
| 1636 | uptarget.set_rvc ( rvc ); |
---|
| 1637 | uptarget.set_parameters ( A, mu1 - A*mu2, R_n ); |
---|
[488] | 1638 | } |
---|
[178] | 1639 | |
---|
[488] | 1640 | //// |
---|
| 1641 | /////// |
---|
| 1642 | template<class sq_T> |
---|
[737] | 1643 | void mgnorm<sq_T >::set_parameters ( const shared_ptr<fnc> &g0, const sq_T &R0 ) { |
---|
[527] | 1644 | g = g0; |
---|
[737] | 1645 | this->iepdf.set_parameters ( zeros ( g->dimension() ), R0 ); |
---|
[527] | 1646 | } |
---|
| 1647 | |
---|
[488] | 1648 | template<class sq_T> |
---|
[737] | 1649 | void mgnorm<sq_T >::condition ( const vec &cond ) { |
---|
| 1650 | this->iepdf._mu() = g->eval ( cond ); |
---|
| 1651 | }; |
---|
[28] | 1652 | |
---|
[536] | 1653 | //! \todo unify this stuff with to_string() |
---|
[488] | 1654 | template<class sq_T> |
---|
[737] | 1655 | std::ostream &operator<< ( std::ostream &os, mlnorm<sq_T> &ml ) { |
---|
[488] | 1656 | os << "A:" << ml.A << endl; |
---|
| 1657 | os << "mu:" << ml.mu_const << endl; |
---|
| 1658 | os << "R:" << ml._R() << endl; |
---|
| 1659 | return os; |
---|
| 1660 | }; |
---|
[28] | 1661 | |
---|
[254] | 1662 | } |
---|
[8] | 1663 | #endif //EF_H |
---|