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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">

<HTML>
<HEAD>
   <TITLE>class  HMM</TITLE>
   <META NAME="GENERATOR" CONTENT="DOC++ 3.4.8">
</HEAD>
<BODY BGCOLOR="#ffffff">

<H2>class  <A HREF="#DOC.DOCU">HMM</A></H2></H2><BLOCKQUOTE>This class implements a Hidden Markov Model distribution.</BLOCKQUOTE>
<HR>

<H2>Inheritance:</H2>
<APPLET CODE="ClassGraph.class" WIDTH=600 HEIGHT=185>
<param name=classes value="CObject,MObject.html,CMachine,MMachine.html,CGradientMachine,MGradientMachine.html,CDistribution,MDistribution.html,CHMM,MHMM.html,CSpeechHMM,MSpeechHMM.html">
<param name=before value="M,M,M,M,M,M^_">
<param name=after value="Md_SPSPSP,Md_SPSP,Md_SP,Md_,M,M">
<param name=indent value="0,1,2,3,4,4">
<param name=arrowdir value="down">
</APPLET>
<HR>

<DL>
<P><DL>
<DT><H3>Public Fields</H3><DD><DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif><!1><A HREF="SeqDataSet.html">SeqDataSet</A>* <B><A HREF="#DOC.98.1">data</A></B>
<DD><I>keep the training data to compute the size of the longest sequence</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>int <B><A HREF="#DOC.98.2">n_states</A></B>
<DD><I>The number of states of the HMM.</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>real <B><A HREF="#DOC.98.3">prior_transitions</A></B>
<DD><I>a prior on the transition probabilities</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif><!1><A HREF="Distribution.html">Distribution</A>** <B><A HREF="#DOC.98.4">states</A></B>
<DD><I>keep the emission distributions</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif><!1><A HREF="Distribution.html">Distribution</A>** <B><A HREF="#DOC.98.5">unique_states</A></B>
<DD><I>in the case where the emission distribution share their parameters, <TT>unique_states</TT> contains the prototypes which will be used for updates (otherwise, it is a pointer to <TT>states</TT>).</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>int <B><A HREF="#DOC.98.6">n_unique_states</A></B>
<DD><I>if <TT>unique_states</TT> is given, n_unique_states is its size</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>real** <B><A HREF="#DOC.98.7">transitions</A></B>
<DD><I>the initial transitions between states are kept as a matrix</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>real** <B><A HREF="#DOC.98.8">log_transitions</A></B>
<DD><I>in fact, we keep the transitions in log</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>real** <B><A HREF="#DOC.98.9">dlog_transitions</A></B>
<DD><I>the derivative of the log transitions for gradient descent</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>real** <B><A HREF="#DOC.98.10">transitions_acc</A></B>
<DD><I>the accumulators of the transitions for EM</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>real** <B><A HREF="#DOC.98.11">log_alpha</A></B>
<DD><I>accumulator used in the forward phase to compute log likelihood </I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>real** <B><A HREF="#DOC.98.12">log_beta</A></B>
<DD><I>accumulator used in the backward phase to compute log likelihood </I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>int** <B><A HREF="#DOC.98.13">arg_viterbi</A></B>
<DD><I>for each state, for each time step, keep the best predecessor </I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>int* <B><A HREF="#DOC.98.14">viterbi_sequence</A></B>
<DD><I>for each time step, keep the best state </I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>real** <B><A HREF="#DOC.98.15">log_probabilities_s</A></B>
<DD><I>keep for each time step and each model its emission log probability</I>
</DL></P>

<P><DL>
<DT><H3>Public Methods</H3><DD><DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>virtual   void <B><A HREF="#DOC.98.16">printTransitions</A></B>(bool real_values=false, bool transitions_only=false)
<DD><I>this method can be used for debugging purpose to see the transitions</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>virtual   void <B><A HREF="#DOC.98.17">logAlpha</A></B>(<!1><A HREF="SeqExample.html">SeqExample</A>* ex)
<DD><I>computes the log_alpha during forward phase of EM</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>virtual   void <B><A HREF="#DOC.98.18">logBeta</A></B>(<!1><A HREF="SeqExample.html">SeqExample</A>* ex)
<DD><I>computes the log_beta during backward phase of EM</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>virtual   void <B><A HREF="#DOC.98.19">logViterbi</A></B>(<!1><A HREF="SeqExample.html">SeqExample</A>* ex)
<DD><I>computes the log_viterbi during forward phase of Viterbi</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>virtual   void <B><A HREF="#DOC.98.20">decode</A></B>(<!1><A HREF="List.html">List</A>* input)
<DD><I>this method returns the state sequence associated to the input</I>
<DT>
<IMG ALT="[more]" BORDER=0 SRC=icon1.gif>virtual   void <B><A HREF="#DOC.98.21">logProbabilities</A></B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>)
<DD><I>computes for each state and each time step of the sequence <TT>inputs</TT> its associated emission probability</I>
</DL></P>

</DL>
<HR><H3>Inherited from <A HREF="Distribution.html">Distribution</A>:</H3>
<DL>
<P><DL>
<DT><H3>Public Fields</H3><DD><DT>
<IMG ALT="o" SRC=icon2.gif>int <B>n_observations</B>
<DT>
<IMG ALT="o" SRC=icon2.gif>int <B>tot_n_frames</B>
<DT>
<IMG ALT="o" SRC=icon2.gif>int <B>max_n_frames</B>
<DT>
<IMG ALT="o" SRC=icon2.gif>real <B>log_probability</B>
<DT>
<IMG ALT="o" SRC=icon2.gif>real* <B>log_probabilities</B>
</DL></P>

<P><DL>
<DT><H3>Public Methods</H3><DD><DT>
<IMG ALT="o" SRC=icon2.gif>virtual   real <B>logProbability</B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   real <B>viterbiLogProbability</B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   real <B>frameLogProbability</B>(real* <!1><A HREF="SeqExample.html#DOC.107.4">observations</A>, real* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>, int t)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>frameExpectation</B>(real* <!1><A HREF="SeqExample.html#DOC.107.4">observations</A>, real* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>, int t)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>eMIterInitialize</B>()
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>iterInitialize</B>()
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>eMSequenceInitialize</B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>sequenceInitialize</B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>eMAccPosteriors</B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>, real log_posterior)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>frameEMAccPosteriors</B>(real* <!1><A HREF="SeqExample.html#DOC.107.4">observations</A>, real log_posterior, real* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>, int t)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>viterbiAccPosteriors</B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>, real log_posterior)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>frameViterbiAccPosteriors</B>(real* <!1><A HREF="SeqExample.html#DOC.107.4">observations</A>, real log_posterior, real* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>, int t)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>eMUpdate</B>()
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>eMForward</B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>viterbiForward</B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>frameBackward</B>(real* <!1><A HREF="SeqExample.html#DOC.107.4">observations</A>, real* <!1><A HREF="QCMachine.html#DOC.40.5">alpha</A>, real* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>, int t)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>viterbiBackward</B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>, real* <!1><A HREF="QCMachine.html#DOC.40.5">alpha</A>)
</DL></P>

</DL>
<HR><H3>Inherited from <A HREF="GradientMachine.html">GradientMachine</A>:</H3>
<DL>
<P><DL>
<DT><H3>Public Fields</H3><DD><DT>
<IMG ALT="o" SRC=icon2.gif>bool <B>is_free</B>
<DT>
<IMG ALT="o" SRC=icon2.gif><!1><A HREF="List.html">List</A>* <B>params</B>
<DT>
<IMG ALT="o" SRC=icon2.gif><!1><A HREF="List.html">List</A>* <B>der_params</B>
<DT>
<IMG ALT="o" SRC=icon2.gif>int <B>n_params</B>
<DT>
<IMG ALT="o" SRC=icon2.gif>real* <B>beta</B>
</DL></P>

<P><DL>
<DT><H3>Public Methods</H3><DD><DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>init</B>()
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   int <B>numberOfParams</B>()
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>backward</B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>, real* <!1><A HREF="QCMachine.html#DOC.40.5">alpha</A>)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>allocateMemory</B>()
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>freeMemory</B>()
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>loadFILE</B>(FILE* <!1><A HREF="Measurer.html#DOC.30.2">file</A>)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>saveFILE</B>(FILE* <!1><A HREF="Measurer.html#DOC.30.2">file</A>)
</DL></P>

</DL>
<HR><H3>Inherited from <A HREF="Machine.html">Machine</A>:</H3>
<DL>
<P><DL>
<DT><H3>Public Fields</H3><DD><DT>
<IMG ALT="o" SRC=icon2.gif>int <B>n_inputs</B>
<DT>
<IMG ALT="o" SRC=icon2.gif>int <B>n_outputs</B>
<DT>
<IMG ALT="o" SRC=icon2.gif><!1><A HREF="List.html">List</A>* <B>outputs</B>
</DL></P>

<P><DL>
<DT><H3>Public Methods</H3><DD><DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>forward</B>(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>)
<DT>
<IMG ALT="o" SRC=icon2.gif>virtual   void <B>reset</B>()
</DL></P>

</DL>
<HR><H3>Inherited from <A HREF="Object.html">Object</A>:</H3>
<DL>
<P><DL>
<DT><H3>Public Methods</H3><DD><DT>
<IMG ALT="o" SRC=icon2.gif>void <B>addOption</B>(const char* <!1><A HREF="SeqExample.html#DOC.107.9">name</A>, int size, void* <!1><A HREF="Vec.html#DOC.81.3">ptr</A>, const char* <!1><A HREF="CmdLine.html#DOC.7.3">help</A>="", bool is_allowed_after_init=false)
<DT>
<IMG ALT="o" SRC=icon2.gif>void <B>addIOption</B>(const char* <!1><A HREF="SeqExample.html#DOC.107.9">name</A>, int* <!1><A HREF="Vec.html#DOC.81.3">ptr</A>, int init_value, const char* <!1><A HREF="CmdLine.html#DOC.7.3">help</A>="", bool is_allowed_after_init=false)
<DT>
<IMG ALT="o" SRC=icon2.gif>void <B>addROption</B>(const char* <!1><A HREF="SeqExample.html#DOC.107.9">name</A>, real* <!1><A HREF="Vec.html#DOC.81.3">ptr</A>, real init_value, const char* <!1><A HREF="CmdLine.html#DOC.7.3">help</A>="", bool is_allowed_after_init=false)
<DT>
<IMG ALT="o" SRC=icon2.gif>void <B>addBOption</B>(const char* <!1><A HREF="SeqExample.html#DOC.107.9">name</A>, bool* <!1><A HREF="Vec.html#DOC.81.3">ptr</A>, bool init_value, const char* <!1><A HREF="CmdLine.html#DOC.7.3">help</A>="", bool is_allowed_after_init=false)
<DT>
<IMG ALT="o" SRC=icon2.gif>void <B>setOption</B>(const char* <!1><A HREF="SeqExample.html#DOC.107.9">name</A>, void* <!1><A HREF="Vec.html#DOC.81.3">ptr</A>)
<DT>
<IMG ALT="o" SRC=icon2.gif>void <B>setIOption</B>(const char* <!1><A HREF="SeqExample.html#DOC.107.9">name</A>, int option)
<DT>
<IMG ALT="o" SRC=icon2.gif>void <B>setROption</B>(const char* <!1><A HREF="SeqExample.html#DOC.107.9">name</A>, real option)
<DT>
<IMG ALT="o" SRC=icon2.gif>void <B>setBOption</B>(const char* <!1><A HREF="SeqExample.html#DOC.107.9">name</A>, bool option)
<DT>
<IMG ALT="o" SRC=icon2.gif>void <B>load</B>(const char* filename)
<DT>
<IMG ALT="o" SRC=icon2.gif>void <B>save</B>(const char* filename)
</DL></P>

</DL>

<A NAME="DOC.DOCU"></A>
<HR>
<H2>Documentation</H2>
<BLOCKQUOTE>This class implements a Hidden Markov Model distribution. In fact,
it also implements the Input Output version (IOHMM). It can be trained
either by EM, Viterbi, or Gradient Descent.

<P>Note that this kind of HMM always contain one initial state and
one final state. Both are non-emitting.

<P></BLOCKQUOTE>
<DL>

<A NAME="data"></A>
<A NAME="DOC.98.1"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B><!1><A HREF="SeqDataSet.html">SeqDataSet</A>* data</B></TT>
<DD>keep the training data to compute the size of the longest sequence
<DL><DT><DD></DL><P>
<A NAME="n_states"></A>
<A NAME="DOC.98.2"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>int n_states</B></TT>
<DD>The number of states of the HMM.
the first model is the initial state,
the last model is the final (absorbing) state,
(neither of them are emitting).
hence, n_states &gt; 2
<DL><DT><DD></DL><P>
<A NAME="prior_transitions"></A>
<A NAME="DOC.98.3"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>real prior_transitions</B></TT>
<DD>a prior on the transition probabilities
<DL><DT><DD></DL><P>
<A NAME="states"></A>
<A NAME="DOC.98.4"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B><!1><A HREF="Distribution.html">Distribution</A>** states</B></TT>
<DD>keep the emission distributions
<DL><DT><DD></DL><P>
<A NAME="unique_states"></A>
<A NAME="DOC.98.5"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B><!1><A HREF="Distribution.html">Distribution</A>** unique_states</B></TT>
<DD>in the case where the emission distribution share their
parameters, <TT>unique_states</TT> contains the prototypes which
will be used for updates (otherwise, it is a pointer to
<TT>states</TT>). Note that if given, and as for <TT>states</TT>,
<TT>unique_states</TT> contains an empty state for positions
0 (initial state) and <TT>n_states</TT> - 1 (final state)
<DL><DT><DD></DL><P>
<A NAME="n_unique_states"></A>
<A NAME="DOC.98.6"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>int n_unique_states</B></TT>
<DD>if <TT>unique_states</TT> is given, n_unique_states is its size
<DL><DT><DD></DL><P>
<A NAME="transitions"></A>
<A NAME="DOC.98.7"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>real** transitions</B></TT>
<DD>the initial transitions between states are kept as a matrix
<DL><DT><DD></DL><P>
<A NAME="log_transitions"></A>
<A NAME="DOC.98.8"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>real** log_transitions</B></TT>
<DD>in fact, we keep the transitions in log
<DL><DT><DD></DL><P>
<A NAME="dlog_transitions"></A>
<A NAME="DOC.98.9"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>real** dlog_transitions</B></TT>
<DD>the derivative of the log transitions for gradient descent
<DL><DT><DD></DL><P>
<A NAME="transitions_acc"></A>
<A NAME="DOC.98.10"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>real** transitions_acc</B></TT>
<DD>the accumulators of the transitions for EM
<DL><DT><DD></DL><P>
<A NAME="log_alpha"></A>
<A NAME="DOC.98.11"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>real** log_alpha</B></TT>
<DD>accumulator used in the forward phase to compute log likelihood 
<DL><DT><DD></DL><P>
<A NAME="log_beta"></A>
<A NAME="DOC.98.12"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>real** log_beta</B></TT>
<DD>accumulator used in the backward phase to compute log likelihood 
<DL><DT><DD></DL><P>
<A NAME="arg_viterbi"></A>
<A NAME="DOC.98.13"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>int** arg_viterbi</B></TT>
<DD>for each state, for each time step, keep the best predecessor 
<DL><DT><DD></DL><P>
<A NAME="viterbi_sequence"></A>
<A NAME="DOC.98.14"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>int* viterbi_sequence</B></TT>
<DD>for each time step, keep the best state 
<DL><DT><DD></DL><P>
<A NAME="log_probabilities_s"></A>
<A NAME="DOC.98.15"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>real** log_probabilities_s</B></TT>
<DD>keep for each time step and each model its emission log probability
<DL><DT><DD></DL><P>
<A NAME="printTransitions"></A>
<A NAME="DOC.98.16"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>virtual   void printTransitions(bool real_values=false, bool transitions_only=false)</B></TT>
<DD>this method can be used for debugging purpose to see the transitions
<DL><DT><DD></DL><P>
<A NAME="logAlpha"></A>
<A NAME="DOC.98.17"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>virtual   void logAlpha(<!1><A HREF="SeqExample.html">SeqExample</A>* ex)</B></TT>
<DD>computes the log_alpha during forward phase of EM
<DL><DT><DD></DL><P>
<A NAME="logBeta"></A>
<A NAME="DOC.98.18"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>virtual   void logBeta(<!1><A HREF="SeqExample.html">SeqExample</A>* ex)</B></TT>
<DD>computes the log_beta during backward phase of EM
<DL><DT><DD></DL><P>
<A NAME="logViterbi"></A>
<A NAME="DOC.98.19"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>virtual   void logViterbi(<!1><A HREF="SeqExample.html">SeqExample</A>* ex)</B></TT>
<DD>computes the log_viterbi during forward phase of Viterbi
<DL><DT><DD></DL><P>
<A NAME="decode"></A>
<A NAME="DOC.98.20"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>virtual   void decode(<!1><A HREF="List.html">List</A>* input)</B></TT>
<DD>this method returns the state sequence associated to the input
<DL><DT><DD></DL><P>
<A NAME="logProbabilities"></A>
<A NAME="DOC.98.21"></A>
<DT><IMG ALT="o" BORDER=0 SRC=icon2.gif><TT><B>virtual   void logProbabilities(<!1><A HREF="List.html">List</A>* <!1><A HREF="SeqExample.html#DOC.107.3">inputs</A>)</B></TT>
<DD>computes for each state and each time step of the sequence <TT>inputs</TT>
its associated emission probability
<DL><DT><DD></DL><P></DL>
<HR>
<DL><DT><B>Direct child classes:
</B><DD><A HREF="SpeechHMM.html">SpeechHMM</A><BR>
</DL>

<DL><DT><DT><B>Author:</B><DD>Samy Bengio (bengio@idiap.ch)
<DD></DL><P><P><I><A HREF="index.html">Alphabetic index</A></I> <I><A HREF="HIER.html">HTML hierarchy of classes</A> or <A HREF="HIERjava.html">Java</A></I></P><HR>
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