| 43 | | <div class="dynheader"> |
| 44 | | Collaboration diagram for bdm::MixEF:</div> |
| 45 | | <div class="dynsection"> |
| 46 | | <p><center><img src="classbdm_1_1MixEF__coll__graph.png" border="0" usemap="#bdm_1_1MixEF__coll__map" alt="Collaboration graph"></center> |
| 47 | | <map name="bdm_1_1MixEF__coll__map"> |
| 48 | | <area shape="rect" href="classbdm_1_1BMEF.html" title="Estimator for Exponential family." alt="" coords="5,385,99,412"><area shape="rect" href="classbdm_1_1multiBM.html" title="Estimator for Multinomial density." alt="" coords="108,481,217,508"><area shape="rect" href="classbdm_1_1BM.html" title="Bayesian Model of a system, i.e. all uncertainty is modeled by probabilities." alt="" coords="13,199,91,225"><area shape="rect" href="classbdm_1_1bdmroot.html" title="Root class of BDM objects." alt="" coords="64,7,176,33"><area shape="rect" href="classbdm_1_1RV.html" title="Class representing variables, most often random variables." alt="" coords="83,87,157,113"><area shape="rect" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="139,199,224,225"><area shape="rect" href="classbdm_1_1eDirich.html" title="Dirichlet posterior density." alt="" coords="123,385,224,412"><area shape="rect" href="classbdm_1_1eEF.html" title="General conjugate exponential family posterior density." alt="" coords="136,279,216,305"><area shape="rect" href="classbdm_1_1eprod.html" title="Product of independent epdfs. For dependent pdfs, use mprod." alt="" coords="212,332,308,359"></map> |
| 49 | | <center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div> |
| 50 | | |
| 51 | | <p> |
| 52 | | <a href="classbdm_1_1MixEF-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0"> |
| | 40 | |
| | 41 | <p> |
| | 42 | <a href="classbdm_1_1MixEF-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2> |
| | 43 | Mixture of Exponential Family Densities. |
| | 44 | <p> |
| | 45 | An approximate estimation method for models with latent discrete variable, such as mixture models of the following kind: <p class="formulaDsp"> |
| | 46 | <img class="formulaDsp" alt="\[ f(y_t|\psi_t, \Theta) = \sum_{i=1}^{n} w_i f(y_t|\psi_t, \theta_i) \]" src="form_66.png"> |
| | 47 | <p> |
| | 48 | where <img class="formulaInl" alt="$\psi$" src="form_67.png"> is a known function of past outputs, <img class="formulaInl" alt="$w=[w_1,\ldots,w_n]$" src="form_68.png"> are component weights, and component parameters <img class="formulaInl" alt="$\theta_i$" src="form_69.png"> are assumed to be mutually independent. <img class="formulaInl" alt="$\Theta$" src="form_70.png"> is an aggregation af all component parameters and weights, i.e. <img class="formulaInl" alt="$\Theta = [\theta_1,\ldots,\theta_n,w]$" src="form_71.png">.<p> |
| | 49 | The characteristic feature of this model is that if the exact values of the latent variable were known, estimation of the parameters can be handled by a single model. For example, for the case of mixture models, posterior density for each component parameters would be a BayesianModel from Exponential Family.<p> |
| | 50 | This class uses EM-style type algorithms for estimation of its parameters. Under this simplification, the posterior density is a product of exponential family members, hence under EM-style approximate estimation this class itself belongs to the exponential family.<p> |
| | 51 | TODO: Extend <a class="el" href="classbdm_1_1BM.html" title="Bayesian Model of a system, i.e. all uncertainty is modeled by probabilities.">BM</a> to use rvc. <table border="0" cellpadding="0" cellspacing="0"> |
| 87 | | const <a class="el" href="classbdm_1_1eprod.html">eprod</a> * </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1MixEF.html#ea8be6f0703d87b7c4c3e77fd07e28c8">_e</a> () const </td></tr> |
| 88 | | |
| 89 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">Returns a pointer to the <a class="el" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a> representing posterior density on parameters. Use with care! <br></td></tr> |
| 90 | | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5105973c0f790f08d1dfb79c2a3f6e1c"></a><!-- doxytag: member="bdm::MixEF::predictor" ref="5105973c0f790f08d1dfb79c2a3f6e1c" args="(const RV &rv) const " --> |
| 91 | | <a class="el" href="classbdm_1_1emix.html">emix</a> * </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1MixEF.html#5105973c0f790f08d1dfb79c2a3f6e1c">predictor</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &<a class="el" href="classbdm_1_1BM.html#18d6db4af8ee42077741d9e3618153ca">rv</a>) const </td></tr> |
| 92 | | |
| 93 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">Constructs a predictive density (marginal density on data). <br></td></tr> |
| | 85 | const <a class="el" href="classbdm_1_1eprod.html">eprod</a> * </td><td class="memItemRight" valign="bottom"><b>_e</b> () const </td></tr> |
| | 86 | |
| | 87 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="edc50e9640f049b846084748b18469a2"></a><!-- doxytag: member="bdm::MixEF::epredictor" ref="edc50e9640f049b846084748b18469a2" args="() const " --> |
| | 88 | <a class="el" href="classbdm_1_1emix.html">emix</a> * </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1MixEF.html#edc50e9640f049b846084748b18469a2">epredictor</a> () const </td></tr> |
| | 89 | |
| | 90 | <tr><td class="mdescLeft"> </td><td class="mdescRight">Constructs a predictive density <img class="formulaInl" alt="$ f(d_{t+1} |d_{t}, \ldots d_{0}) $" src="form_112.png">. <br></td></tr> |
| 126 | | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="40a3c891996391e3135518053a917793"></a><!-- doxytag: member="bdm::MixEF::_rv" ref="40a3c891996391e3135518053a917793" args="() const " --> |
| 127 | | const <a class="el" href="classbdm_1_1RV.html">RV</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#40a3c891996391e3135518053a917793">_rv</a> () const </td></tr> |
| 128 | | |
| 129 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">access function <br></td></tr> |
| | 127 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="598b25e3f3d96a5bc00a5faeb5b3c912"></a><!-- doxytag: member="bdm::MixEF::predictor" ref="598b25e3f3d96a5bc00a5faeb5b3c912" args="() const " --> |
| | 128 | virtual <a class="el" href="classbdm_1_1mpdf.html">mpdf</a> * </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#598b25e3f3d96a5bc00a5faeb5b3c912">predictor</a> () const </td></tr> |
| | 129 | |
| | 130 | <tr><td class="mdescLeft"> </td><td class="mdescRight">Constructs a conditional density 1-step ahead predictor. <br></td></tr> |
| | 131 | <tr><td colspan="2"><div class="groupHeader">Access to attributes</div></td></tr> |
| 197 | | <hr><a name="_details"></a><h2>Detailed Description</h2> |
| 198 | | Mixture of Exponential Family Densities. |
| 199 | | <p> |
| 200 | | An approximate estimation method for models with latent discrete variable, such as mixture models of the following kind: <p class="formulaDsp"> |
| 201 | | <img class="formulaDsp" alt="\[ f(y_t|\psi_t, \Theta) = \sum_{i=1}^{n} w_i f(y_t|\psi_t, \theta_i) \]" src="form_66.png"> |
| 202 | | <p> |
| 203 | | where <img class="formulaInl" alt="$\psi$" src="form_67.png"> is a known function of past outputs, <img class="formulaInl" alt="$w=[w_1,\ldots,w_n]$" src="form_68.png"> are component weights, and component parameters <img class="formulaInl" alt="$\theta_i$" src="form_69.png"> are assumed to be mutually independent. <img class="formulaInl" alt="$\Theta$" src="form_70.png"> is an aggregation af all component parameters and weights, i.e. <img class="formulaInl" alt="$\Theta = [\theta_1,\ldots,\theta_n,w]$" src="form_71.png">.<p> |
| 204 | | The characteristic feature of this model is that if the exact values of the latent variable were known, estimation of the parameters can be handled by a single model. For example, for the case of mixture models, posterior density for each component parameters would be a BayesianModel from Exponential Family.<p> |
| 205 | | This class uses EM-style type algorithms for estimation of its parameters. Under this simplification, the posterior density is a product of exponential family members, hence under EM-style approximate estimation this class itself belongs to the exponential family.<p> |
| 206 | | TODO: Extend <a class="el" href="classbdm_1_1BM.html" title="Bayesian Model of a system, i.e. all uncertainty is modeled by probabilities.">BM</a> to use rvc. <hr><h2>Member Function Documentation</h2> |
| | 191 | <hr><h2>Member Function Documentation</h2> |
| 247 | | <p>References <a class="el" href="libEF_8h-source.html#l00096">bdm::BMEF::_copy_()</a>, <a class="el" href="mixef_8h-source.html#l00057">build_est()</a>, <a class="el" href="mixef_8h-source.html#l00046">Coms</a>, <a class="el" href="mixef_8h-source.html#l00050">est</a>, <a class="el" href="mixef_8h-source.html#l00044">n</a>, <a class="el" href="libEF_8h-source.html#l00300">bdm::multiBM::set_parameters()</a>, <a class="el" href="libEF_8cpp-source.html#l00008">bdm::UniRNG</a>, and <a class="el" href="mixef_8h-source.html#l00048">weights</a>.</p> |
| | 232 | <p>References <a class="el" href="libEF_8h-source.html#l00096">bdm::BMEF::_copy_()</a>, <a class="el" href="mixef_8h-source.html#l00057">build_est()</a>, <a class="el" href="mixef_8h-source.html#l00046">Coms</a>, <a class="el" href="mixef_8h-source.html#l00050">est</a>, <a class="el" href="mixef_8h-source.html#l00044">n</a>, <a class="el" href="libEF_8h-source.html#l00297">bdm::multiBM::set_parameters()</a>, <a class="el" href="libEF_8cpp-source.html#l00008">bdm::UniRNG</a>, and <a class="el" href="mixef_8h-source.html#l00048">weights</a>.</p> |
| | 261 | |
| | 262 | </div> |
| | 263 | </div><p> |
| | 264 | <a class="anchor" name="c0f027ff91d8459937c6f60ff8e553ff"></a><!-- doxytag: member="bdm::MixEF::_copy_" ref="c0f027ff91d8459937c6f60ff8e553ff" args="()" --> |
| | 265 | <div class="memitem"> |
| | 266 | <div class="memproto"> |
| | 267 | <table class="memname"> |
| | 268 | <tr> |
| | 269 | <td class="memname">virtual <a class="el" href="classbdm_1_1BM.html">BM</a>* bdm::BM::_copy_ </td> |
| | 270 | <td>(</td> |
| | 271 | <td class="paramname"> </td> |
| | 272 | <td> ) </td> |
| | 273 | <td><code> [inline, virtual, inherited]</code></td> |
| | 274 | </tr> |
| | 275 | </table> |
| | 276 | </div> |
| | 277 | <div class="memdoc"> |
| | 278 | |
| | 279 | <p> |
| | 280 | Copy function required in vectors, Arrays of <a class="el" href="classbdm_1_1BM.html" title="Bayesian Model of a system, i.e. all uncertainty is modeled by probabilities.">BM</a> etc. Have to be DELETED manually! Prototype: <div class="fragment"><pre class="fragment"> BM* <a class="code" href="classbdm_1_1BM.html#c0f027ff91d8459937c6f60ff8e553ff">_copy_</a>(){<span class="keywordflow">return</span> <span class="keyword">new</span> BM(*<span class="keyword">this</span>);} |
| | 281 | </pre></div> |
| | 282 | <p>Reimplemented in <a class="el" href="classbdm_1_1ARX.html#60c40b5c6abc4c7e464b4ccae64a5a61">bdm::ARX</a>.</p> |
