1 | /*! |
---|
2 | \file |
---|
3 | \brief Probability distributions for Mixtures of pdfs |
---|
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 MX_H |
---|
14 | #define MX_H |
---|
15 | |
---|
16 | #include "libBM.h" |
---|
17 | #include "libEF.h" |
---|
18 | //#include <std> |
---|
19 | |
---|
20 | using namespace itpp; |
---|
21 | |
---|
22 | //this comes first because it is used inside emix! |
---|
23 | |
---|
24 | /*! \brief Class representing ratio of two densities |
---|
25 | which arise e.g. by applying the Bayes rule. |
---|
26 | It represents density in the form: |
---|
27 | \f[ |
---|
28 | f(rv|rvc) = \frac{f(rv,rvc)}{f(rvc)} |
---|
29 | \f] |
---|
30 | where \f$ f(rvc) = \int f(rv,rvc) d\ rv \f$. |
---|
31 | |
---|
32 | In particular this type of arise by conditioning of a mixture model. |
---|
33 | |
---|
34 | At present the only supported operation is evalcond(). |
---|
35 | */ |
---|
36 | class mratio: public mpdf { |
---|
37 | protected: |
---|
38 | //! Nominator in the form of mpdf |
---|
39 | const epdf* nom; |
---|
40 | //!Denominator in the form of epdf |
---|
41 | epdf* den; |
---|
42 | //!flag for destructor |
---|
43 | bool destroynom; |
---|
44 | public: |
---|
45 | //!Default constructor. By default, the given epdf is not copied! |
---|
46 | //! It is assumed that this function will be used only temporarily. |
---|
47 | mratio(const epdf* nom0, const RV &rv, bool copy=false):mpdf(rv,RV()){ |
---|
48 | if (copy){ |
---|
49 | // nom = nom0->_copy_(); |
---|
50 | destroynom=true; |
---|
51 | } else { |
---|
52 | nom = nom0; |
---|
53 | destroynom = false; |
---|
54 | } |
---|
55 | rvc = nom->_rv().subt(rv); |
---|
56 | it_assert_debug(rvc.length()>0,"Makes no sense to use this object!"); |
---|
57 | den = nom->marginal(rvc); |
---|
58 | }; |
---|
59 | double evalcond(const vec &val, const vec &cond) const { |
---|
60 | return exp(nom->evalpdflog(concat(val,cond)) - den->evalpdflog(cond)); |
---|
61 | } |
---|
62 | //! Object takes ownership of nom and will destroy it |
---|
63 | void ownnom(){destroynom=true;} |
---|
64 | //! Default destructor |
---|
65 | ~mratio(){delete den; if (destroynom) {delete nom;}} |
---|
66 | }; |
---|
67 | |
---|
68 | /*! |
---|
69 | * \brief Mixture of epdfs |
---|
70 | |
---|
71 | Density function: |
---|
72 | \f[ |
---|
73 | f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. |
---|
74 | \f] |
---|
75 | where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component, |
---|
76 | |
---|
77 | */ |
---|
78 | class emix : public epdf { |
---|
79 | protected: |
---|
80 | //! weights of the components |
---|
81 | vec w; |
---|
82 | //! Component (epdfs) |
---|
83 | Array<epdf*> Coms; |
---|
84 | //!Flag if owning Coms |
---|
85 | bool destroyComs; |
---|
86 | public: |
---|
87 | //!Default constructor |
---|
88 | emix ( const RV &rv ) : epdf ( rv ) {}; |
---|
89 | //! Set weights \c w and components \c Coms |
---|
90 | //!By default Coms are copied inside. \param copy can be set to false if Coms live externally. Use method ownComs() if Coms should be destroyed by the destructor. |
---|
91 | void set_parameters ( const vec &w, const Array<epdf*> &Coms, bool copy=true ); |
---|
92 | |
---|
93 | vec sample() const; |
---|
94 | vec mean() const { |
---|
95 | int i; vec mu = zeros ( rv.count() ); |
---|
96 | for ( i = 0;i < w.length();i++ ) {mu += w ( i ) * Coms ( i )->mean(); } |
---|
97 | return mu; |
---|
98 | } |
---|
99 | double evalpdflog ( const vec &val ) const { |
---|
100 | int i; |
---|
101 | double sum = 0.0; |
---|
102 | for ( i = 0;i < w.length();i++ ) {sum += w ( i ) * Coms ( i )->evalpdflog ( val );} |
---|
103 | return log ( sum ); |
---|
104 | }; |
---|
105 | vec evalpdflog_m ( const mat &Val ) const { |
---|
106 | vec x=ones(Val.cols()); |
---|
107 | vec y(Val.cols()); |
---|
108 | for (int i = 0; i < w.length(); i++ ) { |
---|
109 | y = w ( i )*exp(Coms ( i )->evalpdflog_m ( Val ) ); |
---|
110 | elem_mult_inplace(y,x); //result is in x |
---|
111 | } |
---|
112 | return log(x); |
---|
113 | }; |
---|
114 | |
---|
115 | emix* marginal ( const RV &rv ) const; |
---|
116 | mratio* condition ( const RV &rv ) const; //why not mratio!! |
---|
117 | |
---|
118 | //Access methods |
---|
119 | //! returns a pointer to the internal mean value. Use with Care! |
---|
120 | vec& _w() {return w;} |
---|
121 | virtual ~emix() {if ( destroyComs ) {for ( int i=0;i<Coms.length();i++ ) {delete Coms ( i );}}} |
---|
122 | //! Auxiliary function for taking ownership of the Coms() |
---|
123 | void ownComs() {destroyComs=true;} |
---|
124 | }; |
---|
125 | |
---|
126 | /*! \brief Chain rule decomposition of epdf |
---|
127 | |
---|
128 | Probability density in the form of Chain-rule decomposition: |
---|
129 | \[ |
---|
130 | f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) |
---|
131 | \] |
---|
132 | Note that |
---|
133 | */ |
---|
134 | class mprod: public compositepdf, public mpdf { |
---|
135 | protected: |
---|
136 | //! pointers to epdfs - shortcut to mpdfs()._epdf() |
---|
137 | Array<epdf*> epdfs; |
---|
138 | //! Indeces of rvc in common rvc |
---|
139 | Array<ivec> irvcs_rvc; |
---|
140 | //! Indeces of common rvc in rvcs |
---|
141 | Array<ivec> irvc_rvcs; |
---|
142 | public: |
---|
143 | /*!\brief Constructor from list of mFacs, |
---|
144 | */ |
---|
145 | mprod ( Array<mpdf*> mFacs ) : compositepdf ( mFacs ), mpdf ( getrv ( true ),RV() ), epdfs ( n ), irvcs_rvc ( n ), irvc_rvcs ( n ) { |
---|
146 | setrvc ( rv,rvc ); |
---|
147 | setindices ( rv ); |
---|
148 | for ( int i = 0;i < n;i++ ) { |
---|
149 | // establish link between rvc and rvcs |
---|
150 | rvc.dataind ( mpdfs ( i )->_rvc(), irvc_rvcs ( i ), irvcs_rvc ( i ) ); |
---|
151 | } |
---|
152 | |
---|
153 | for ( int i=0;i<n;i++ ) { |
---|
154 | epdfs ( i ) =& ( mpdfs ( i )->_epdf() ); |
---|
155 | } |
---|
156 | }; |
---|
157 | |
---|
158 | double evalcond ( const vec &val, const vec &cond ) { |
---|
159 | int i; |
---|
160 | double res = 0.0; |
---|
161 | vec condi; |
---|
162 | for ( i = n - 1;i >= 0;i-- ) { |
---|
163 | if ( ( irvcs_rvc ( i ).length() > 0 ) || ( irvcs_rv ( i ).length() > 0 ) ) { |
---|
164 | condi = zeros ( irvcs_rvc ( i ).length() +irvcs_rv ( i ).length() ); |
---|
165 | //copy part of the rvc into condi |
---|
166 | set_subvector ( condi, irvcs_rvc ( i ), get_vec ( cond,irvc_rvcs ( i ) ) ); |
---|
167 | //copy part of the rv into condi |
---|
168 | set_subvector ( condi, irvcs_rv ( i ), get_vec ( val,irv_rvcs ( i ) ) ); |
---|
169 | mpdfs ( i )->condition ( condi ); |
---|
170 | } |
---|
171 | // add logarithms |
---|
172 | res += epdfs ( i )->evalpdflog ( val ( rvsinrv ( i ) ) ); |
---|
173 | } |
---|
174 | return exp ( res ); |
---|
175 | } |
---|
176 | vec samplecond ( const vec &cond, double &ll ) { |
---|
177 | vec smp=zeros ( rv.count() ); |
---|
178 | vec condi; |
---|
179 | vec smpi; |
---|
180 | ll = 0; |
---|
181 | for ( int i = ( n - 1 );i >= 0;i-- ) { |
---|
182 | if ( ( irvcs_rvc ( i ).length() > 0 ) || ( irvcs_rv ( i ).length() > 0 ) ) { |
---|
183 | condi = zeros ( irvcs_rv ( i ).length() + irvcs_rvc ( i ).length() ); |
---|
184 | // copy data in condition |
---|
185 | set_subvector ( condi,irvcs_rvc ( i ), get_vec ( cond, irvc_rvcs ( i ) ) ); |
---|
186 | // copy data in already generated sample |
---|
187 | set_subvector ( condi,irvcs_rv ( i ), get_vec ( smp,irv_rvcs ( i ) ) ); |
---|
188 | |
---|
189 | mpdfs ( i )->condition ( condi ); |
---|
190 | } |
---|
191 | smpi = epdfs ( i )->sample(); |
---|
192 | // copy contribution of this pdf into smp |
---|
193 | set_subvector ( smp,rvsinrv ( i ), smpi ); |
---|
194 | // add ith likelihood contribution |
---|
195 | ll+=epdfs ( i )->evalpdflog ( smpi ); |
---|
196 | } |
---|
197 | return smp; |
---|
198 | } |
---|
199 | mat samplecond ( const vec &cond, vec &ll, int N ) { |
---|
200 | mat Smp ( rv.count(),N ); |
---|
201 | for ( int i=0;i<N;i++ ) {Smp.set_col ( i,samplecond ( cond,ll ( i ) ) );} |
---|
202 | return Smp; |
---|
203 | } |
---|
204 | |
---|
205 | ~mprod() {}; |
---|
206 | }; |
---|
207 | |
---|
208 | //! Product of independent epdfs. For dependent pdfs, use mprod. |
---|
209 | class eprod: public epdf { |
---|
210 | protected: |
---|
211 | //! Components (epdfs) |
---|
212 | Array<const epdf*> epdfs; |
---|
213 | //! Array of indeces |
---|
214 | Array<ivec> rvinds; |
---|
215 | public: |
---|
216 | eprod ( const Array<const epdf*> epdfs0 ) : epdf ( RV() ),epdfs ( epdfs0 ),rvinds ( epdfs.length() ) { |
---|
217 | bool independent=true; |
---|
218 | for ( int i=0;i<epdfs.length();i++ ) { |
---|
219 | independent=rv.add ( epdfs ( i )->_rv() ); |
---|
220 | it_assert_debug ( independent==true, "eprod:: given components are not independent ." ); |
---|
221 | rvinds ( i ) = ( epdfs ( i )->_rv() ).dataind ( rv ); |
---|
222 | } |
---|
223 | } |
---|
224 | |
---|
225 | vec mean() const { |
---|
226 | vec tmp ( rv.count() ); |
---|
227 | for ( int i=0;i<epdfs.length();i++ ) { |
---|
228 | vec pom = epdfs ( i )->mean(); |
---|
229 | set_subvector ( tmp,rvinds ( i ), pom ); |
---|
230 | } |
---|
231 | return tmp; |
---|
232 | } |
---|
233 | vec sample() const { |
---|
234 | vec tmp ( rv.count() ); |
---|
235 | for ( int i=0;i<epdfs.length();i++ ) { |
---|
236 | vec pom = epdfs ( i )->sample(); |
---|
237 | set_subvector ( tmp,rvinds ( i ), pom ); |
---|
238 | } |
---|
239 | return tmp; |
---|
240 | } |
---|
241 | double evalpdflog ( const vec &val ) const { |
---|
242 | double tmp=0; |
---|
243 | for ( int i=0;i<epdfs.length();i++ ) { |
---|
244 | tmp+=epdfs ( i )->evalpdflog ( val ( rvinds ( i ) ) ); |
---|
245 | } |
---|
246 | return tmp; |
---|
247 | } |
---|
248 | //!access function |
---|
249 | const epdf* operator () ( int i ) const {it_assert_debug ( i<epdfs.length(),"wrong index" );return epdfs ( i );} |
---|
250 | }; |
---|
251 | |
---|
252 | |
---|
253 | /*! \brief Mixture of mpdfs with constant weights, all mpdfs are of equal type |
---|
254 | |
---|
255 | */ |
---|
256 | class mmix : public mpdf { |
---|
257 | protected: |
---|
258 | //! Component (epdfs) |
---|
259 | Array<mpdf*> Coms; |
---|
260 | //!Internal epdf |
---|
261 | emix Epdf; |
---|
262 | public: |
---|
263 | //!Default constructor |
---|
264 | mmix ( RV &rv, RV &rvc ) : mpdf ( rv, rvc ), Epdf ( rv ) {ep = &Epdf;}; |
---|
265 | //! Set weights \c w and components \c R |
---|
266 | void set_parameters ( const vec &w, const Array<mpdf*> &Coms ) { |
---|
267 | Array<epdf*> Eps ( Coms.length() ); |
---|
268 | |
---|
269 | for ( int i = 0;i < Coms.length();i++ ) { |
---|
270 | Eps ( i ) = & ( Coms ( i )->_epdf() ); |
---|
271 | } |
---|
272 | Epdf.set_parameters ( w, Eps ); |
---|
273 | }; |
---|
274 | |
---|
275 | void condition ( const vec &cond ) { |
---|
276 | for ( int i = 0;i < Coms.length();i++ ) {Coms ( i )->condition ( cond );} |
---|
277 | }; |
---|
278 | }; |
---|
279 | |
---|
280 | #endif //MX_H |
---|