models.tex

隐马尔科夫模型工具箱

\>\>\>    \hmkw{Mean} 4 \\
\>\>\>\>       0.1 0.0 0.0 0.8  \\
\>\>\>    \hmkw{Variance} 4 \\
\>\>\>\>       1.0 1.0 1.0 1.0  \\
\>\hmkw{State} 3 \hmkw{NumMixes} 2  \\
\>\>    \hmkw{Mixture} 1 0.7 \\
\>\>\>    \hmkw{Mean} 4 \\
\>\>\>\>       0.1 0.2 0.6 1.4 \\ 
\>\>\>    \hmkw{Variance} 4 \\
\>\>\>\>       1.0 1.0 1.0 1.0 \\ 
\>\>    \hmkw{Mixture} 2 0.3 \\
\>\>\>    \hmkw{Mean} 4 \\
\>\>\>\>       2.1 0.0 1.0 1.8  \\
\>\>\>    \hmkw{Variance} 4 \\
\>\>\>\>       1.0 1.0 1.0 1.0 \\ 
\> \hmkw{TransP} 4 \\
\>\>   0.0 1.0 0.0 0.0 \\
\>\>   0.0 0.5 0.5 0.0 \\
\>\>   0.0 0.0 0.6 0.4 \\
\>\>   0.0 0.0 0.0 0.0 \\
\hmkw{EndHMM} 
}{}

Notice that only the second
state has a full covariance Gaussian component.  The first state
has a mixture of two diagonal variance Gaussian components.  Again, this
illustrates the flexibility of HMM definition in \HTK.  If required
the structure of every
Gaussian can be individually configured.

Another possible way to store covariance information is in the form
of the Choleski decomposition\index{Choleski decomposition} $L$ of the 
inverse covariance matrix
i.e. $\bm{\Sigma}^{-1} = LL'$.
Again this is stored externally in upper triangular form so $L'$ is
actually stored.  It is distinguished from the normal inverse covariance
matrix by using the keyword \hmkw{LLTCovar}\index{lltcovar@$<$LLTCovar$>$} 
in place of \hmkw{InvCovar}\footnote{
The Choleski storage format is not used by default in \HTK\ Version 2}.  


The definition for \textsf{hmm3} also illustrates another
macro type, that is, \hmmt{o}.  This macro is used as an alternative
way of specifying global options and, in fact, it is the format used
by \HTK\ tools when they write out a HMM definition.  It is provided so that global
options can be specifed ahead of any other HMM parameters.  As will
be seen later, this is useful when using many types of macro.
\index{HMM definition!global options macro}

As noted earlier, the observation vectors used to represent
the speech signal can be divided into two or more statistically
independent data streams.  This corresponds to the splitting-up
of the input speech vectors as described in section~\ref{s:streams}.
In HMM definitions, the use of multiple data
streams must be indicated by specifying the number of streams and
the width (i.e\ dimension) of each stream as a global
option.  This is done using the keyword \hmkw{StreamInfo}
\index{streaminfo@$<$StreamInfo$>$} followed
by the number of streams, and then a sequence of numbers indicating
the width of each stream.  The sum of these
stream widths must equal the original vector size as indicated
by the  \hmkw{VecSize} keyword. 

An example of a HMM definition for multiple data 
streams\index{HMM definition!multiple data streams}
is \textsf{hmm4} shown in 
Fig~\href{f:hmm4def}.  This HMM is intended to model 2 distinct
streams, the first has 3 components and the second has 1.
This is indicated by the global option \hmkw{StreamInfo} 2 3 1.
The definition of each state output distribution now
includes means and variances for each individual stream.

Thus, in Fig~\href{f:hmm4def}, each state is subdivided into
2 streams using the \hmkw{Stream}\index{stream@$<$Stream$>$} keyword followed by the stream
number.  Note also, that each individual stream can be weighted.
In state 2 of \textsf{hmm4}, the vector following the
\hmkw{SWeights}\index{sweights@$<$SWeights$>$} keyword indicates that
stream 1 has a weight of 0.9 whereas
stream 2 has a weight of 1.1.  There is no stream weight
\index{HMM definition! stream weight} vector
in state 3 and hence the default weight of 1.0 will be
assigned to each stream.

\vspace{1.0cm}


\putprog{hmm3def}{100}{HMM with Full Covariance}{
\hmmt{o}  \hmkw{VecSize} 4 \hmkw{MFCC} \\
\hmmc{h}{hmm3} \\
\hmkw{BeginHMM}  \\
\> \hmkw{NumStates} 4  \\
\> \hmkw{State} 2 \hmkw{NumMixes} 2 \\
\>\>   \hmkw{Mixture} 1 0.4 \\
\>\>\>    \hmkw{Mean} 4 \\
\>\>\> \>      0.3 0.2 0.2 1.0 \\ 
\>\>\>    \hmkw{Variance} 4 \\
\>\>\> \>      1.0 1.0 1.0 1.0 \\ 
\>\>\>   \hmkw{Mixture} 2 0.6 \\
\>\>\>    \hmkw{Mean} 4 \\
\>\>\>\>       0.1 0.0 0.0 0.8  \\
\>\>\>    \hmkw{Variance} 4 \\
\>\> \>\>      1.0 1.0 1.0 1.0 \\ 
\> \hmkw{State} 3 \hmkw{NumMixes} 1 \\
\>\>   \hmkw{Mean} 4 \\
\>\>\>       0.1 \> 0.2 \> 0.6 \> 1.4 \\ 
\>\>    \hmkw{InvCovar} 4 \\
\>\>\>       1.0 \> 0.1 \> 0.0 \> 0.0\\
\>\>\>       \>  1.0 \>  0.2 \> 0.0\\
\>\>\>       \>\>  1.0 \>  0.1\\
\>\>\>       \>\>\> 1.0 \\
\> \hmkw{TransP} 4 \\
\>\>   0.0 1.0 0.0 0.0 \\
\>\>   0.0 0.5 0.5 0.0 \\
\>\>   0.0 0.0 0.6 0.4 \\
\>\>   0.0 0.0 0.0 0.0 \\
\hmkw{EndHMM}
}

No \HTK\ tools are supplied for estimating optimal stream 
weight\index{HMM definition!stream weight} 
values.  Hence, they must either be set manually or derived
from some outside source.  However, once set, they are used in
the calculation of output probabilities as specified in 
equations~\ref{e:cdpdf} and \ref{e:ddpdf}, and hence they will
affect the operation of both the training and recognition tools.

\putprog{hmm4def}{100}{HMM with 2 Data Streams}{
\hmmt{o} \>  \hmkw{VecSize} 4 \hmkw{MFCC} \\
\> \hmkw{StreamInfo} 2 3 1 \\
\hmmc{h}{hmm4} \\
\hmkw{BeginHMM}  \\
\> \hmkw{NumStates} 4 \\
\> \hmkw{State} 2 \\
\>\>   \hmkw{SWeights} 2 0.9 1.1 \\
\>\>   \hmkw{Stream} 1 \\
\>\>\>     \hmkw{Mean} 3 \\
\>\>\>\>      0.2 0.1 0.1 \\
\>\>\>     \hmkw{Variance} 3 \\
\>\>\>\>       1.0 1.0 1.0 \\
\>\>   \hmkw{Stream} 2 \\
\>\>\>     \hmkw{Mean} 1 0.0 \\
\>\>\>     \hmkw{Variance} 1 4.0 \\
\> \hmkw{State} 3 \\
\>\>   \hmkw{Stream} 1 \\
\>\>\>     \hmkw{Mean} 3 \\
\>\>\>\>       0.3 0.2 0.0 \\
\>\>\>     \hmkw{Variance} 3 \\
\>\>\>\>       1.0 1.0 1.0 \\
\>\>   \hmkw{Stream} 2 \\
\>\>\>     \hmkw{Mean} 1 0.5 \\
\>\>\>     \hmkw{Variance} 1 3.0 \\
\> \hmkw{TransP} 4 \\
\>\>   0.0 1.0 0.0 0.0 \\
\>\>   0.0 0.6 0.4 0.0 \\
\>\>   0.0 0.0 0.4 0.6 \\
\>\>   0.0 0.0 0.0 0.0 \\
\hmkw{EndHMM}
}

\mysect{Macro Definitions}{HMMmac}

So far, basic model definitions have been described in which
all of the information required to define a HMM has been
given directly between the  \hmkw{BeginHMM} and \hmkw{EndHMM}
keywords.  As an alternative, \HTK\ allows the internal
parts of a definition to be written as separate units, possibly
in several different files, and then referenced by name wherever they
are needed.  Such definitions are called \textit{macros}.  


\sideprog{mac5def}{50}{Simple Macro Definitions}{
\hmmt{o} \hmkw{VecSize} 4 \hmkw{MFCC} \\
\\
\hmmc{v}{var} \\
\> \hmkw{Variance} 4 \\
\>\>    1.0 1.0 1.0 1.0  \\
}{}

HMM (\hmmt{h}) and global option macros
\index{macros}\index{HMM definition!macros} (\hmmt{o})
have already been described.  In fact, these are both rather
special cases since neither is ever referenced explicitly by
another definition.  Indeed, the option macro is unusual in that
since it is global and must be unique, it has no name.
As an illustration of the use of macros, it may be observed
that the variance vectors in the HMM definition \textsf{hmm2} given
in Fig~\href{f:hmm2def} are all identical.  If this was
intentional, then the variance vector could be defined as a macro
as illustrated in Fig~\href{f:mac5def}.  

A macro definition\index{macro definition} consists of a macro type indicator
followed by a user-defined macro name.  In this case, the indicator is \hmmt{v}
and the name is \textsf{var}. Notice that a global options macro is included
before the definition for \textsf{var}. \HTK\ must know these before it can
process any other definitions thus the first macro file specified on the
command line of any \HTK\ tool must have the global options macro.  Global
options macro need not be repeated at the head of every definition file, but it
does no harm to do so.

\sideprog{hmm5def}{60}{A Definition Using Macros}{

\hmmc{h}{hmm5} \\
\hmkw{BeginHMM} \\
\> \hmkw{NumStates} 4  \\
\> \hmkw{State} 2 \hmkw{NumMixes} 2 \\
\>\>   \hmkw{Mixture} 1 0.4 \\
\>\>\>    \hmkw{Mean} 4 \\
\>\>\>\>       0.3 0.2 0.2 1.0  \\
\>\>\>    \hmmc{v}{var} \\
\>\>   \hmkw{Mixture} 2 0.6 \\
\>\>\>    \hmkw{Mean} 4 \\
\>\>\>\>      0.1 0.0 0.0 0.8  \\
\>\>\>    \hmmc{v}{var} \\
\> \hmkw{State} 3 \hmkw{NumMixes} 2 \\
\>\>   \hmkw{Mixture} 1 0.7 \\
\>\>\>    \hmkw{Mean} 4 \\
\>\>\>\>       0.1 0.2 0.6 1.4  \\
\>\>\>    \hmmc{v}{var} \\
\>\>   \hmkw{Mixture} 2 0.3 \\
\>\>\>    \hmkw{Mean} 4 \\
\>\>\>\>       2.1 0.0 1.0 1.8  \\
\>\>\>    \hmmc{v}{var} \\
\> \hmkw{TransP} 4 \\
\>\>   0.0 1.0 0.0 0.0 \\
\>\>   0.0 0.5 0.5 0.0 \\
\>\>  0.0 0.0 0.6 0.4 \\
\>\>   0.0 0.0 0.0 0.0 \\
\hmkw{EndHMM} 

}{}

Once defined,  a macro is used simply by writing the type
indicator and name exactly as written in the definition.
Thus, for example, Fig~\href{f:hmm5def} defines a HMM called
\textsf{hmm5} which uses the variance macro  \textsf{var} but
is otherwise identical to the earlier HMM definition \textsf{hmm2}.

\index{macro substitution}
The definition for \textsf{hmm5} can be understood by substituting
the textual body of the \textsf{var} macro everywhere that it is
referenced.  Textually this would make the definition for \textsf{hmm5}
identical to that for \textsf{hmm2}, and indeed, if input to a recogniser,
their effects would be similar.  
However, as will become clear in later chapters,
the HMM definitions \textsf{hmm2} and  \textsf{hmm5} differ
in two ways.  Firstly,  if
any attempt was made to re-estimate the parameters of \textsf{hmm2},
the values of the variance vectors would almost certainly
diverge.  However,
the variance vectors of \textsf{hmm5} are tied together and are
guaranteed to remain identical, even after re-estimation.  Thus,
in general, the use of a macro enforces a \textit{tying} which
results in the corresponding parameters being shared amongst
all the HMM structures which reference that macro.
Secondly, when used in a recognition tool, the computation required
to decode using HMMs with tied parameters will often be reduced.
This is particularly true when higher level parts of a HMM definition
are tied such as whole states.

There are many different macro types\index{HMM definition!macro types}\index{macros!types}.  Some have special
meanings but the following correspond to
the various distinct points in the hierarchy of HMM parameters which
can be tied.  
\begin{tabbing}
+ \= ++++ \=  \kill
\> \hmmt{s} \>  shared state distribution\\
\> \hmmt{m} \>  shared Gaussian mixture component \\
\> \hmmt{u} \>  shared mean vector \\
\> \hmmt{v} \>  shared diagonal variance vector \\
\> \hmmt{i} \>  shared inverse full covariance matrix \\
\> \hmmt{c} \>  shared choleski $L'$ matrix \\
\> \hmmt{x} \>  shared arbitrary transform matrix\footnote{
Transform matrices are not used by any of the supported HTK tools.
}
 \\
\> \hmmt{t} \>  shared transition matrix \\
\> \hmmt{d} \>  shared duration parameters \\
\> \hmmt{w} \>  shared stream weight vector 
\end{tabbing}

Fig~\href{f:hierarch} illustrates these potential
tie points\index{parameter tie points} graphically for the case of continuous density HMMs.
In this figure, each solid black circle represents a potential
tie point, and the associated macro type is indicated alongside it.

\centrefig{hierarch}{120}{HMM Hierarchy and Potential Tie Points}

\noindent
The tie points for discrete HMMs are identical except that the
macro types \hmmt{m}, \hmmt{v}, \hmmt{c}, \hmmt{i} and \hmmt{u} are not
relevant and are therefore excluded.

The macros with special meanings\index{macros!special meanings} are as follows
\begin{tabbing}
+ \= ++++ \= ++++++++++++++ \= ++++ \=\kill
\> \hmmt{l} \>  logical HMM \> \hmmt{h} \>  physical HMM \\
\> \hmmt{o} \>  global option values \> \hmmt{p} \>  tied mixture \\
\> \hmmt{r} \>  regression class tree \> \hmmt{j} \> linear transform
\end{tabbing}
The distinction between logical and physical HMMs will be explained
in the next section and option macros have already been described.
The \hmmt{p} macro is used by the HMM editor \htool{HHEd}
for building tied mixture systems (see section~\ref{s:tmix}).
The \hmmt{l} or \hmmt{p} macros are special in the sense
that they are created implicitly in order to represent specific kinds 
of parameter sharing and they never occur explicitly in HMM definitions.

\mysect{HMM Sets}{hmmsets}

The previous sections have described how a single HMM definition
can be specified.  However, many \HTK\ tools require complete model
sets to be specified rather than just a single model.\index{HMM sets}
When this is the case, the individual HMMs which belong to the set
are listed in a file rather than being enumerated explicitly on
the command line.  Thus, for example, a typical invocation of
the tool \htool{HERest} might be as follows
\begin{verbatim}