models.tex

隐马尔科夫模型工具箱

{\sf
\begin{tabbing}
++++ \= ++++++++ \= ++ \= +++++++++++++++++ \= +++ \=  \kill
\> optmacro = \> $\sim$o globalOpts 
\end{tabbing}
}
\noindent
or they can be included in one or more HMM definitions.  Global
options may be repeated but no definition can change a previous
definition.  All global options must be defined before any other
macro definition is processed.  In practice this means that any
HMM system which uses parameter tying must have a \hmmt{o} option macro 
at the head of the first macro file processed.

The full set of global options is given below.  Every HMM set must
define the vector size (via \hmkw{VecSize}\index{vecsize@$<$VecSize$>$}), the stream widths  
(via \hmkw{StreamInfo}\index{streaminfo@$<$StreamInfo$>$})
and the observation parameter kind.  However, if only the stream
widths are given, then the vector size will be inferred.  If
only the vector size is given, then a single stream of identical
width will be assumed.  All other options default to null.
{\sf
\begin{tabbing}
++++ \= ++++++++ \= ++ \= +++++++++++++++++ \= +++ \=  \kill
\> globalOpts = \> option \{ option \} \\
\>  option = \> $<$HmmSetId$>$ string $|$ \\ 
\>\>  $<$StreamInfo$>$ short \{ short \} $|$  \\
\>\>   $<$VecSize$>$    short $|$  \\
\>\>   $<$InputXform$>$ inputXform $|$  \\
\>\>   covkind $|$ \\
\>\>   durkind $|$ \\
\>\>   parmkind 
\end{tabbing}
}
\noindent
The {\sf $<$HmmSetId$>$} option allows the user to give the MMF an
identifier. This is used as a sanity check to make sure that a TMF can
be safely applied to this MMF.
The arguments to the
{\sf $<$StreamInfo$>$} option are the number of streams (default 1) and then
for each stream, the width of that stream.  The {\sf $<$VecSize$>$} option 
gives the total number of elements in each input vector.  
If both \hmkw{VecSize} and \hmkw{StreamInfo} are included then the
sum of all the stream widths must equal the input vector size.

The {\sf covkind } defines the kind of the covariance matrix
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>  covkind =\> $<$DiagC$>$ $|$ $<$InvDiagC$>$ $|$ $<$FullC$>$ $|$ \\
\>\>            $<$LLTC$>$ $|$ $<$XformC$>$ 
\end{tabbing}
}
\noindent
where {\sf $<$InvDiagC$>$} is used internally.  {\sf $<$LLTC$>$}
and {\sf $<$XformC$>$} are not used in \HTK\ Version 2.0.
Setting the covariance kind as a global option forces all components to
have this kind.  In particular, it prevents mixing full and diagonal covariances
within a HMM set.

The {\sf durkind} denotes the type of duration
model used according to the following rules
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>  durkind =\> $<$nullD$>$ $|$ $<$poissonD$>$ $|$ $<$gammaD$>$ $|$ $<$genD$>$ 
\end{tabbing}
}
\noindent
For anything other than {\sf $<$nullD$>$}, a duration vector\index{duration vector} must
be supplied for the model or each state as described below. Note that no
current HTK tool can estimate or use such duration vectors.  

The parameter kind is any legal parameter kind including qualified forms
(see section~\ref{s:genio})
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>  parmkind =\> $<$basekind\{\_D$|$\_A$|$\_T$|$\_E$|$\_N$|$\_Z$|$\_O$|$\_V$|$\_C$|$\_K\}$>$ \\
\>  basekind =\> $<$discrete$>$$|$$<$lpc$>$$|$$<$lpcepstra$>$$|$$<$mfcc$>$ $|$ $<$fbank$>$ $|$ \\
 \> \>          $<$melspec$>$$|$ $<$lprefc$>$$|$$<$lpdelcep$>$ $|$ $<$user$>$ 
\end{tabbing}
}
\noindent
where the syntax rule for {\sf parmkind} is non-standard in that no spaces
are allowed between the base kind and any subsequent qualifiers.
As noted in chapter~\ref{c:speechio}, {\sf $<$lpdelcep$>$} is 
provided only for compatibility
with earlier versions of \HTK\ and its further use should be avoided.

Each state of each HMM must have its own section defining the parameters
associated with that state
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\> state =\>  $<$State: Exp $>$ short stateinfo
\end{tabbing}
}
\noindent
where the  short following {\sf $<$State: Exp $>$} is the state number.  State
information can be defined in any order.  The syntax is as follows
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>   stateinfo = \> $\sim$s macro $|$ \\
  \>\>              [ mixes ] [ weights ] stream \{ stream \} [ duration ] \\
\>   macro     = \> string
\end{tabbing}
}
\noindent
A {\sf stateinfo} definition consists of an 
optional specification of the number of mixtures, an optional set of stream weights,
followed by a block of information for each stream, optionally terminated with
a duration vector.  Alternatively, {\sf $\sim$s macro} can be
written where {\sf macro} is the name of a previously defined macro.

The optional {\sf mixes} in a {\sf stateinfo} definition specify
the number of mixture components (or discrete codebook size) for 
each stream of that state
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>   mixes = \>  $<$NumMixes$>$ short \{short\}
\end{tabbing}
}
\noindent
where there should be one {\sf short} for each stream.  If this
specification is omitted, it is assumed that all streams
have just one mixture component.

The optional {\sf weights} in a {\sf stateinfo} definition define
a set of exponent weights for each independent data stream.  The
syntax is
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>   weights = \> $\sim$w macro $|$ $<$SWeights$>$ short vector \\
\>   vector  = \> float \{ float \} 
\end{tabbing}
}
\noindent
where the {\sf short} gives the number $S$ of weights (which should match the
value given in the \hmkw{StreamInfo} option) and the {\sf vector}
contains the $S$ stream weights $\gamma_s$ (see section~\ref{s:HMMparm}).

The definition of each  {\sf stream} 
depends on the kind of HMM set.  In the normal case, it
consists of a sequence of mixture
component
definitions optionally preceded by the stream number.  If the stream
number is omitted then it is assumed to be 1.  For tied-mixture
and discrete HMM sets, special forms are used.
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>   stream = \> [ $<$Stream$>$ short ] \\
\>            \> (mixture \{ mixture \} $|$ tmixpdf $|$ discpdf)
\end{tabbing}
}

The definition of each mixture component consists of a Gaussian
pdf optionally preceded by the mixture number and its weight
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>   mixture = \> [ $<$Mixture$>$ short float ] mixpdf
\end{tabbing}
}
\noindent
If the \hmkw{Mixture}\index{mixture@$<$Mixture$>$} part is missing then mixture 1 is assumed and the
weight defaults to 1.0. 

The {\sf tmixpdf} option is used only for fully 
tied mixture sets.  Since the {\sf mixpdf} parts are all macros in
a tied mixture system and since they are identical for every stream
and state, it is only necessary to know the mixture weights.  The
{\sf tmixpdf} syntax allows these to be specified in the following
compact form
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>   tmixpdf = \> $<$TMix$>$ macro weightList \\
\>   weightList = \> repShort \{ repShort \} \\
\>   repShort = \> short [ $\ast$ char ]
\end{tabbing}
}
\noindent
where each {\sf short} is a mixture component weight scaled so that
a weight of 1.0 is represented by the integer 32767.  
The optional asterix 
followed by a {\sf char} is used to indicate
a repeat count.  For example, {\tt 0*5} is equivalent to 5 zeroes.
The Gaussians which make-up the pool of tied-mixtures are defined 
using  \hmmt{m} macros called
{\sf macro1}, {\sf macro2}, {\sf macro3}, etc. 

Discrete probability HMMs are defined in a similar way
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>   discpdf = \> $<$DProb$>$ weightList
\end{tabbing}
}
\noindent
The only difference is that the weights in the \textsf{weightList}
are scaled log probabilities as defined in section~\ref{s:dischmm}.

The definition of a Gaussian pdf requires the mean vector to 
be given and one of the possible forms of covariance 
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>   mixpdf = \> $\sim$m macro $|$ [ rclass ] mean cov [ $<$GConst$>$ float ] \\
\>   rclass = \> $<$RClass$>$ short \\
\>   mean = \> $\sim$u macro $|$ $<$Mean$>$ short vector \\
\>   cov =  \> var $|$ inv $|$ xform \\
\>   var = \> $\sim$v macro $|$ $<$Variance$>$ short vector \\
\>   inv = \> $\sim$i macro $|$ \\
\>        \> ($<$InvCovar$>$ $|$ $<$LLTCovar$>$) short tmatrix \\
\>   xform = \> $\sim$x macro $|$ $<$Xform$>$ short short matrix \\
\>   matrix = \> float \{float\} \\
\>   tmatrix = \> matrix \\
\end{tabbing}
}
\noindent
In {\sf mean} and {\sf var}, the {\sf short} preceding the {\sf vector}
defines the length of the vector, in {\sf inv} the {\sf short} preceding the {\sf
tmatrix} gives the size of this square upper triangular matrix, and in {\sf xform} the
two {\sf short}'s preceding the {\sf matrix} give the number of rows and
columns. 
The optional {\sf $<$GConst$>$}\footnote{specifically, in equation 
~\ref{e:gnorm} 
the GCONST value seen in HMM sets is calculated by multiplying the determinant 
of the covariance matrix by $\bm{(2 \pi)^n}$} \index{GCONST value} gives 
that part of the log
probability of a Gaussian that can be precomputed.  If it is omitted, then
it will be computed during load-in, including it simply saves some time.
\HTK\ tools which output HMM definitions always include this field.
The optional {\sf $<$RClass$>$} stores the regression base class index that
this mixture component belongs to, as specified by the regression
class tree (which is also stored in the model set). \HTK\ tools which
output HMM definitions always include this field, and if there is no
regression class tree then the regression identifier is set to zero.


In addition to defining the output distributions, a state can have a
duration probability distribution defined for it. However, no current HTK
tool can estimate or use these.
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>   duration = \> $\sim$d macro $|$ $<$Duration$>$ short vector
\end{tabbing}
}
\noindent
Alternatively, as shown by the top level syntax for a {\sf hmmdef},
duration parameters can be specified for a whole model.

A binary regression class tree (for the purposes of HMM adaptation as in
chapter~\ref{c:Adapt}) may also exist for an HMM set. This is defined
by 
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>   regTree = \> $\sim$r macro tree \\
\>   tree    = \> $<$RegTree$>$ short nodes \\
\>   nodes   = \> ($<$Node$>$ short short short $|$ $<$TNode$>$ short
int) [ nodes ]
\end{tabbing}
}
\noindent
In {\sf tree} the {\sf short} preceding the {\sf nodes} refers to
the number of terminal nodes or leaves that the regression tree
contains. Each node in {\sf nodes} can either be a non-terminal {\sf
$<$Node$>$} or a terminal (leaf) {\sf $<$TNode$>$}. For a {\sf
$<$Node$>$} the three following {\sf short}s refer to the node's index
number and the index numbers of its children. For a {\sf
$<$TNode$>$}, the {\sf short} refers to the leaf's index (which
correspond to a regression base class index as stored at the
component level in {\sf RClass}, see above), while the {\sf int}
refers to the number of mixture components in this leaf cluster.

The transition matrix is defined by
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>   transP = \> $\sim$t macro $|$ $<$TransP$>$ short matrix
\end{tabbing}
}
\noindent
where the {\sf short} in this case should be equal to the number of
states in the model. 

Finally the input transform is defined by
{\sf
\begin{tabbing}
++++ \= ++++++++ \=  \kill
\>  inputXform  = \> $\sim$j macro $|$ inhead inmatrix\\
\>  inhead      = \> $<$MMFIdMask$>$ string parmkind [$<$PreQual$>$]\\
\>  inmatrix    = \> $<$LinXform$>$ $<$VecSize$>$ short $<$BlockInfo$>$ 
short short \{short\} block \{block\}\\
\>  block       = \> $<$Block$>$ short xform
\end{tabbing}
}
\noindent
where the {\sf short} following \hmkw{VecSize} is the number of dimensions
after applyingthe linear transform and must match the vector size
of the HMM definition. The first {\sf short} after \hmkw{BlockInfo}
is the number of block, this is followed by the number of output
dimensions from each of the blocks.


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