hhed.tex

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Duplicates a set of HMMs.  This command is used to replicate a
set of HMMs whilst allowing control over which structures will
be shared between them.
The first parameter controls duplication of tied structures.  Any
macros whose type appears in string \texttt{s} are duplicated
with new names and only used in the duplicate model set.  The remaining
shared structures are common through all the model sets (original and
duplicates).
The second parameter defines the number of times the current
HMM set should be duplicated with the remaining \texttt{n} parameters
providing suffices to make the original macro identifiers unique
in each duplicated HMM set.

For instance the following script could be used to duplicate
a set of tied state models to produce gender dependent ones
with tied variances.
\begin{verbatim}
    MM "v_" { (*).state[2-4].mix[1-2].cov }
    DP "v" 2 ":m" ":f" 
\end{verbatim}
The \texttt{MM} command converts all variances into macros
(with each macro referring to only one variance).
The \texttt{DP} command then duplicates the current HMM set twice.
Each of the duplicate sets will share the tied variances with
the original set but will have new mixture means, weights and
state macros.  The new macro names will be constructed by
appending the id \texttt{":m"} or \texttt{":f"} to the original 
macro name whilst the model names have the id appended after
the base phone name (so \texttt{ax-b+d} becomes \texttt{ax-b:m+d} or
\texttt{ax-b:f+d}.

\subsubsection*{\tt FA varscale}

Computes an average within state variance vector for a given HMM set,
using statistics generated by \htool{HERest} (see {\tt LS} for loading
stats).  The average variance vector is scaled and stored in the HMM
set, any variance floor vectors present are replaced. Subsequently,
the variance floor is applied to all variances in the model set. This
can be inhibited by setting \texttt{APPLYVFLOOR} to \texttt{FALSE}.

\subsubsection*{\tt FC}

Converts all covariances in the modelset to full. This command
takes an HMM set with diagonal covariances and creates full
covariances which are initialised with the variances of the diagonal
system. The tying structure of the original system is kept intact.

\subsubsection*{\tt FV file} 

Loads one variance floor macro per stream from file. The file
containing the variance floor macros can, for example, be generated by
\htool{HCompV}. Any variance floor vectors present in the model set
are replaced. Secondly the variance floor is applied to all variances.
This can be inhibited but setting \texttt{APPLYVFLOOR} to
\texttt{FALSE}.

\subsubsection*{\tt HK hsetkind}

Converts model set from one kind to another.  Although hsetkind can
take the value PLAINHS, SHAREDHS, TIEDHS or DISCRETEHS, the HK command is
most likely to be used when building tied-mixture systems (hsetkind=TIEDHS).

\subsubsection*{\tt JO size minw}

Set the size and minimum mixture weight for subsequent
Tie (\texttt{TI}) commands applied to pdf's.  
The value of \texttt{size} sets the total number of
mixtures in the tied mixture set ({\it codebook}) and \texttt{minw}
sets a floor on the mixture weights as a multiple of \texttt{MINMIX}.
This command only applies to tying item lists of type ``p''
(see the Tie \texttt{ TI} command below).

\subsubsection*{\tt LS statsfile}

This command is used to read in the \htool{HERest} statistics file 
(see the \htool{HERest} \texttt{-s} option) stored in \texttt{statsfile}.  These
statistics are needed for certain clustering operations.
The statistics file contains the occupation count for every HMM state. 

\subsubsection*{\tt LT treesfile}

This command reads in the decision trees stored in \texttt{treesfile}.
The trees file will consist of a set of questions defining contexts
that may appear in the subsequent trees.  The trees are used to
identify either the state or the model that should be used in
a particular context.  The file would normally be produced by
\texttt{ST} after tree based clustering has been performed.

\subsubsection*{\tt MD nmix itemlist}

Decrease the number of mixture components in each pdf in the
\texttt{itemList} to \texttt{m}. This employs a stepwise greedy
merging strategy. For a given set of mixture components the pair with
minimal merging cost is found and merged. This is repeated until only
\texttt{m} mixture components are left. Any defunct mixture components
(i.e. components with a weight below \texttt{MINMIX}) are deleted
prior to this process.

Note that after application of this command a pdf in {\tt itemlist}
may consist of fewer, but not more than \texttt{m} mixture components.

As an example, the command
\begin{verbatim}
         MD 6 {*-aa+*.state[3].mix}
\end{verbatim}
would decrease the number of mixture components in state 3 of all
triphones of \texttt{aa} to 6.

\subsubsection*{\tt MM macro itemList}

This command makes each item (I=1..N) in \texttt{itemList} into a 
macro with name \texttt{nameI} and a usage of one.  This command
can prevent unnecessary duplication of structures when HMMs
are cloned or duplicated.

\subsubsection*{\tt MT triList newTriList}

Make  a set of triphones by merging the currently loaded set of
biphones.  This is a very specialised command.  All currently
loaded HMMs must have 3 emitting states and be either left
or right context-dependent biphones.  The list of HMMs stored
in \texttt{triList} should contain one or more triphones.  For
each triphone in \texttt{triList} of the form \texttt{X-Y+Z}, there
must be currently loaded biphones \texttt{X-Y} and \texttt{Y+Z}.
A new triphone \texttt{X-Y+Z} is then synthesised by first cloning
\texttt{Y+Z} and then replacing the state information for the
initial emitting state by the state information for the initial
emitting state of \texttt{X-Y}.  Note that the underlying physical
names of the biphones used to create the triphones are recorded
so that where possible, triphones generated from tied biphones
are also tied.  On completion, the new list of triphones including
aliases is written to the file \texttt{newTriList}.

\subsubsection*{\tt MU m itemList(p)}

Increase the number of non-defunct mixture components
in each pdf in the \texttt{itemList} to \texttt{m} (when \texttt{m} 
is just a number) or by \texttt{m} (when \texttt{m} is a number 
preceeded by a \texttt{+} sign.  A defunct mixture
is one for which the weight has fallen below \texttt{MINMIX}. This command
works in two steps.  Firstly, the weight of each mixture
in each pdf is checked.  If any defunct mixtures are discovered, 
then each is successively replaced by a non-defunct
mixture component until either the required total number of non-defunct
mixtures is reached or there are no defunct mixtures left.
This replacement works by first deleting the defunct mixture
and then finding the mixture with the largest weight and splitting
it.
The split operation is as follows.  The weight of the mixture
component is first halved and then the mixture is cloned.  The
two identical mean vectors are then perturbed by adding $0.2$
standard deviations to one and subtracting the same amount
from the other.

In the second step, the mixture component with the largest
weight is split as above.  This is repeated until the required
number of mixture components are obtained.
Whenever, a mixture is split, a count is incremented  for that mixture
so that splitting occurs evenly across the mixtures.  Furthermore,
a mixture whose {\it gconst} value falls more than four standard
deviations below the mean is not split.

As an example, the command
\begin{verbatim}
         MU 6 {*-aa+*.state[3].mix}
\end{verbatim}
would increase the number of mixture components in state 3
of all triphones of \texttt{aa} to 6.

\subsubsection*{\tt NC N macro itemList(s)}

N-cluster the states listed in the 
\texttt{itemList} and tie each cluster \texttt{i} as macro \texttt{macroi}
where \texttt{i} is 1,2,3,\ldots,\texttt{N}.
The set of states in the \texttt{itemList} are divided into \texttt{N}
clusters using the following furthest neighbour hierarchical
cluster algorithm:
\begin{verbatim}
         create 1 cluster for each state;
         n = number of clusters;
         while (n>N) {
            find i and j for which g(i,j) is minimum;
            merge clusters i and j;
         }
\end{verbatim}
Here \texttt{g(i,j)} is the inter-group distance between
clusters \texttt{i} and \texttt{j} defined as the maximum
distance between any state in cluster \texttt{i} and any state
in cluster \texttt{j}.  The calculation of the inter-state
distance depends on the type of HMMs involved.  Single
mixture Gaussians use
\begin{equation}
  d(i,j) = \frac{1}{S} \sum_{s=1}^S
        \left[  
           \frac{1}{V_s} \sum_{k=1}^{V_s}
                 \frac{(\bm{\mu}_{isk} - \bm{\mu}_{jsk})^2}{
                         \bm{\sigma}_{isk}\bm{\sigma}_{jsk}}
        \right]^{\frac{1}{2}}
\end{equation}
where $V_s$ is the dimensionality of stream $s$.  Fully tied
mixture systems (ie \texttt{TIEDHS}) use
\begin{equation}
  d(i,j) = \frac{1}{S} \sum_{s=1}^S
        \left[  
           \frac{1}{M_s} \sum_{m=1}^{M_s}
                (c_{ism} - c_{jsm})^2
        \right]^{\frac{1}{2}}
\end{equation}
and all others use
\begin{equation}
  d(i,j) = - \frac{1}{S} \sum_{s=1}^S
         \frac{1}{M_s} \sum_{m=1}^{M_s}
          \log[b_{js}(\bm{\mu}_{ism})] + \log[b_{is}(\bm{\mu}_{jsm})]
\end{equation}
where $b_{js}(\bm{x})$ is as defined in equation~\ref{e:cdpdf} for
the continuous case and equation~\ref{e:ddpdf} for the discrete case.  The actual
tying of the states in each cluster is performed exactly as for
the Tie (\texttt{TI}) command below.  The macro for the \texttt{i}'th
tied cluster is called \texttt{macroi}.

\subsubsection*{\tt PS nstates power [numiters]   }

This command sets the number of Gaussians in each HMM state
proportional to a power of the number of frames available for training it.  The
number of frames is obtained from a ``stats'' file output by \htool{HERest},
which is loaded by the \texttt{LS} command.  Typical usage might be:
\begin{verbatim}
 LS <statsfile> 
 PS 16 0.2 
\end{verbatim}
in order to acheive an average of 16 Gaussians per state with a power
of 0.2.  

It is always advisable when increasing the number of Gaussians in states to
increase the number by small increments and re-estimate HMMs using
\htool{HERest} once or more in between.  It may be difficult to avoid a
large increase in number of Gaussians in particular states when moving from
a HMM set with a constant number of Gaussians per state to one controlled
by a power law.  Therefore the PS command has a facility for increasing
the number of Gaussians gradually where the target is larger than the
initial number of Gaussians, so that HERest can be run in between.  In this
example, one could use the \htool{HHEd} command \texttt{PS}~16~0.2~3, run
\htool{HERest}, use the command \texttt{PS}~16~0.2~2, run \htool{HERest},
and then run \texttt{PS}~16~0.2~1 before the final re-estimation with
\htool{HERest}.  The last argument is the number of iterations remaining.
A fairly similar effect could be obtained by increasing the power linearly
from zero.


\subsubsection*{\tt QS name itemList(h)}

Define a question \texttt{name} which is true for all the models in
\texttt{itemList}.  These questions can subsequently be used as part 
of the decision tree based clustering procedure (see \texttt{TB}
command below).

\subsubsection*{\tt RC N identifier [itemlist]}

This command is used to grow a regression class tree for adaptation
purposes. A regression class tree is grown with
\texttt{N} terminal or leaf nodes, using the centroid splitting algorithm
with a Euclidean distance measure to cluster the model set's mixture
components. Hence each leaf node specifies a particular mixture
component cluster. The regression class tree is saved with the macro
identifier \texttt{identifier\_N}. Each Gaussian component is also