train.tex

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    HInit -S trainlist -H globals -M dir1 -l ih -L labs proto
    mv dir1/proto dir1/ih
\end{verbatim}
where the option \texttt{-l} defines the name of the sub-word model, and 
the file \texttt{trainlist} is assumed to hold
\begin{verbatim}
    data/tr1.mfc
    data/tr2.mfc
    data/tr3.mfc
    data/tr4.mfc
    data/tr5.mfc
    data/tr6.mfc
\end{verbatim}
In this case,  \htool{HInit} will first try to find label
\index{model training!sub-word initialisation}
files corresponding to each data file.  In the example here, the 
standard \texttt{-L}\index{standard options!aaal@\texttt{-L}} option 
indicates that they are
stored in a directory called \texttt{labs}.  As an alternative, they
could be stored in a Master Label File\index{master label files} (MLF) and 
loaded via the standard option \texttt{-I}.
Once the label files have been loaded, each data file is scanned and all segments
corresponding the label \texttt{ih} are loaded.  Figure~\href{f:hinitdp}
illustrates this process.

All \HTK\ tools support the \texttt{-T}
\index{standard options!aaat@\texttt{-T}} trace option and although the details of 
tracing varies from tool to tool, setting the least signicant bit (e.g.\ by \texttt{-T 1}), 
causes all tools to output top level progress information.  In the case
of \htool{HInit}, this information includes the log likelihood at each iteration and hence
it is very useful for monitoring convergence\index{monitoring convergence}.  For example, enabling top level tracing
in the previous example might result in the following being output
\begin{verbatim}
    Initialising  HMM proto . . . 
     States   :   2  3  4 (width)
     Mixes  s1:   1  1  1 ( 26  )
     Num Using:   0  0  0
     Parm Kind:  MFCC_E_D
     Number of owners = 1
     SegLab   :  ih
     maxIter  :  20
     epsilon  :  0.000100
     minSeg   :  3
     Updating :  Means Variances MixWeights/DProbs TransProbs
    16 Observation Sequences Loaded
    Starting Estimation Process
    Iteration 1: Average LogP =  -898.24976
    Iteration 2: Average LogP =  -884.05402  Change =    14.19574
    Iteration 3: Average LogP =  -883.22119  Change =     0.83282
    Iteration 4: Average LogP =  -882.84381  Change =     0.37738
    Iteration 5: Average LogP =  -882.76526  Change =     0.07855
    Iteration 6: Average LogP =  -882.76526  Change =     0.00000
    Estimation converged at iteration 7
    Output written to directory :dir1:
\end{verbatim}
The first part summarises the structure of the HMM, in this case, the data is
single stream MFCC coefficients with energy and deltas appended.  The HMM has
3 emitting states, each single Gaussian and the stream width is 26.  The current
option settings are then given followed by the convergence information.  In this
example, convergence was reached after 6 iterations, however if the \texttt{maxIter}
limit was reached, then the process would terminate regardless.

\htool{HInit} provides a variety of command line options for controlling 
its detailed behaviour.
\index{model training!update control}
The types of parameter 
estimated by \htool{HInit} can be controlled
using the \texttt{-u} option, for example, \texttt{-u mtw} would update the means, 
transition matrices and
mixture component weights but would leave the variances untouched.  
A variance floor\index{variance floors}
can be applied using the \texttt{-v} to prevent any variance getting too small.   This
option applies the same variance floor to all speech vector elements.  More precise
control can be obtained by specifying a variance macro (i.e.\ a \texttt{~v} macro)
called \texttt{varFloor1}\index{varfloorn@\texttt{varFloorN}} for 
stream 1, \texttt{varFloor2} for stream 2, etc.  Each
element of these variance vectors then defines a floor for the corresponding HMM variance
components.

The full list of options supported by \htool{HInit} is described in the \refpart.

\mysect{Flat Starting with \htool{HCompV}}{flatstart}

One limitation of using \htool{HInit} for the initialisation
of sub-word models is that it requires labelled training data.
For cases where this is not readily available, an alternative
initialisation strategy is to make all models equal initially and
move straight to embedded training using \htool{HERest}.  The
idea behind this so-called \textit{flat start} training is similar to the
uniform segmentation strategy adopted by \htool{HInit} since by making
all states of all models equal, the first iteration of embedded training
will effectively rely on a uniform segmentation of the data.

\centrefig{flatst}{90}{Flat Start Initialisation}

Flat start\index{flat start} initialisation is provided by the \HTK\ tool \htool{HCompV} whose operation
is illustrated by Fig~\href{f:flatst}.  The input/output of HMM definition files
and training files in \htool{HCompV}\index{hcompv@\htool{HCompV}} works in exactly the same way as described above for
\htool{HInit}.  It reads in a prototype HMM definition and some training data
and outputs a new definition in which every mean and covariance is equal to 
the global speech mean and covariance.  Thus, for example, the following
command would read a prototype definition called \texttt{proto}, read in all speech
vectors from \texttt{data1}, \texttt{data2}, \texttt{data3}, etc, 
compute the global mean and covariance
and write out a new version of \texttt{proto} in \texttt{dir1} with this mean and
covariance.
\begin{verbatim}
    HCompV -m -H globals -M dir1 proto data1 data2 data3 ...
\end{verbatim}

The default operation of \htool{HCompV} is only to update the covariances of the HMM
and leave the means unchanged.  The use of the \texttt{-m} option above causes the
means to be updated too.  This apparently curious default behaviour arises because
\htool{HCompV} is also used to initialise the variances in so-called
\textit{Fixed-Variance} HMMs. These are HMMs initialised in the normal way except
that all covariances are set equal to the global speech covariance and never
subsequently changed.\index{fixed-variance}

Finally, it should be noted that \htool{HCompV} can also be used to generate 
variance floor macros by using the \texttt{-f} option.
\index{variance floor macros!generating}

\mysect{Isolated Unit Re-Estimation using \htool{HRest}}{resthmm}

\sidefig{restloop}{60}{\htool{HRest} Operation}{2}{ \htool{HRest} is the final tool in the set
designed to manipulate isolated unit HMMs.  Its operation is very similar to
\htool{HInit} except that, as shown in Fig~\href{f:restloop},  it expects the input
HMM definition to have been initialised and it uses Baum-Welch 
re-estimation\index{Baum-Welch re-estimation!isolated unit} in place
of Viterbi training.  This involves finding the probability of being in each
state at each time frame using the \textit{Forward-Backward} algorithm.
This probability is then used to form weighted averages
for the HMM parameters.  Thus, whereas Viterbi training makes a hard decision
as to which state each training vector was ``generated'' by,  Baum-Welch 
takes a soft decision.  This can be helpful when estimating phone-based HMMs
since there are no hard boundaries between phones in real speech and using
a soft decision may give better results.\index{forward-backward!isolated unit}
The mathematical details of the Baum-Welch re-estimation
process are given below in section~\ref{s:bwformulae}.

\htool{HRest} is usually applied directly to the models generated by \htool{HInit}. Hence for
example, the generation of a sub-word model for the phone \texttt{ih} begun
in section~\ref{s:inithmm}
would be continued by executing the following command
}

\begin{verbatim}
    HRest -S trainlist -H dir1/globals -M dir2 -l ih -L labs dir1/ih
\end{verbatim}
This will load the HMM definition for \texttt{ih} from \texttt{dir1},
re-estimate the parameters using the speech segments labelled with \texttt{ih}
and write the new definition to directory \texttt{dir2}.

If \htool{HRest} is used to build models with a large number of mixture components per state,
a strategy must be chosen for dealing with \textit{defunct mixture components}.
These are mixture components which have very little associated training data and
as a consequence either the variances or the corresponding mixture weight becomes
very small. If either of these events happen, the mixture component is effectively
deleted and provided that at least one component in that state is left, a warning
is issued.  If this behaviour is not desired then the variance can be floored as
described previously using the \texttt{-v} option (or a variance floor macro)
and/or the mixture weight can be floored using the \texttt{-w} option.  
\index{defunct mixture components}

Finally, a problem which can arise when
using  \htool{HRest} to initialise sub-word models 
is that of over-short training 
segments\index{over-short training segments}.  By default, 
\htool{HRest} ignores all training examples which have fewer frames than
the model has emitting states.    For example, suppose that a 
particular phone with 3 emitting states had only a few training
examples with more than 2 frames of data.  In this case, there would be two
solutions.  Firstly, the number of emitting states could be reduced.  Since
\HTK\ does not require all models to have the same number of states,
this is perfectly feasible.
Alternatively, some skip transitions could be added and the default
reject mechanism disabled by setting the \texttt{-t} option.
Note here that \htool{HInit} has the same reject mechanism and suffers
from the same problems.  \htool{HInit}, however, does not allow
the reject mechanism to be suppressed since the uniform segmentation
process would otherwise fail.

\mysect{Embedded Training using \htool{HERest}}{eresthmm}

\index{model training!embedded}
Whereas isolated unit training is sufficient for  building whole  word
models and initialisation of models using hand-labelled \textit{bootstrap}
data,  the main HMM training procedures for building sub-word systems
revolve around the  concept of \textit{embedded training}. Unlike the
processes described so far,  embedded training\index{embedded training} simultaneously updates all
of the HMMs in a system using all of the training data.  It is performed by
\htool{HERest}\index{herest@\htool{HERest}} which, unlike \htool{HRest}, performs just a single iteration.  
\index{Baum-Welch re-estimation!embedded unit}

In outline, \htool{HERest} works as follows.  On startup, \htool{HERest} 
loads in a complete
set of HMM definitions.  Every training file must have an associated
label file which gives a transcription for that file.  Only the
sequence of labels is used by \htool{HERest}, however, and any boundary location
information is ignored.  Thus, these transcriptions can be generated
automatically from the known orthography of what was said and 
a pronunciation dictionary.

\htool{HERest} processes each training file in turn.  After loading it into memory,
it uses the associated transcription to 
construct a  composite HMM which spans the whole utterance.
This composite HMM is made by concatenating instances of the phone HMMs 
corresponding to each label in the transcription.  The Forward-Backward
algorithm is then applied and the sums needed to form the weighted
averages accumulated in the normal way.  When all of the training
files have been processed, the new parameter estimates are formed
from the weighted sums and the updated HMM set is output.
\index{forward-backward!embedded}

The mathematical details of embedded Baum-Welch re-estimation
are given below in section~\ref{s:bwformulae}.

In order to use \htool{HERest}, it is first necessary to construct a 
file containing a list
of all HMMs in the model set with each model name being written on a separate line.
The names of the models in this\index{HMM lists}
list must correspond to the labels used in the transcriptions and there
must be a corresponding model for every distinct transcription label.
\htool{HERest} is typically invoked by a command line of the form
\begin{verbatim}
    HERest -S trainlist -I labs -H dir1/hmacs -M dir2 hmmlist
\end{verbatim}
where \texttt{hmmlist} contains the list of HMMs.  On startup, \htool{HERest} will 
load the HMM master macro file (MMF) \texttt{hmacs} (there may be
several of these).  It then searches for a definition for each
HMM listed in the \texttt{hmmlist}, if any HMM name is not found, 
it attempts to open a file of the same name in the current directory
(or a directory designated by the \texttt{-d} option).
Usually in large subword systems, however, all of the HMM definitions
will be stored in MMFs.  Similarly, all of the required transcriptions
will be stored in one or more Master Label Files
\index{master label files} (MLFs), and in the
example, they are stored in the single MLF called \texttt{labs}.

\centrefig{herestdp}{90}{File Processing in \htool{HERest}}

Once all MMFs and MLFs have been loaded, \htool{HERest} processes each file in the
\texttt{trainlist}, and accumulates the required statistics as described
above.  On completion, an updated  MMF is output to the directory
\texttt{dir2}.  If a second iteration is required, then \htool{HERest} is reinvoked
reading in the MMF from \texttt{dir2} and outputing 
a new one to \texttt{dir3}, and so on.
This process is illustrated by Fig~\href{f:herestdp}.

When performing embedded training,  it is good practice to
monitor the performance of the models on unseen test data
and stop training when no further improvement is obtained.  Enabling
top level tracing by setting \texttt{-T 1} will cause \htool{HERest} to
output the overall log likelihood per frame of the training data.
This measure could be used as a termination condition for
repeated application of \htool{HERest}.  However, 
repeated re-estimation to convergence\index{monitoring convergence} 
may take an impossibly long time.
Worse still, it can lead to over-training since the models can become too
closely matched to the training data and fail to generalise well on unseen
test data.  Hence in practice around 2 to 5 cycles of 
embedded re-estimation are normally sufficient when training phone
models.

In order to get accurate acoustic models, a large amount of training
data is needed.  Several hundred
utterances are needed for speaker dependent recognition and
several thousand are needed for
speaker independent recognition.  In the latter case, a single
iteration of embedded training
might take several hours to compute.  There are two mechanisms for 
speeding up this computation.  Firstly, \htool{HERest} has a pruning
\index{model training!pruning} mechanism
incorporated into its forward-backward computation.  \htool{HERest} calculates
the backward probabilities $\beta_j(t)$ first and then the forward probabilities
$\alpha_j(t)$.
The full computation of these probabilities for all values of state $j$
and time $t$ is unnecessary since many of these combinations will be highly
improbable.   On the forward pass, \htool{HERest} restricts the computation of
the $\alpha$ values to just those for which the total log likelihood 
as determined by the product $\alpha_j(t)\beta_j(t)$ is
within a fixed distance from the total likelihood $P(\bm{O}|M)$.  This
pruning is always enabled since it is completely safe and causes no loss
of modelling accuracy.  

Pruning on the backward pass is also possible.
However, in this case, the likelihood product $\alpha_j(t)\beta_j(t)$
is unavailable since $\alpha_j(t)$ has yet to be computed, and hence a 
much broader {\it beam} must be set to
avoid pruning errors.  Pruning on the backward path is therefore under
user control. It is set using the \texttt{-t} option which has two 
forms.  In the simplest case, a fixed pruning beam is set.  For example,
using \texttt{-t 250.0} would set a fixed beam of 250.0.  This method
is adequate when there is sufficient compute time available to 
use a generously wide beam.  When a narrower beam is used, \htool{HERest} will 
reject any utterance for which the beam proves to be too narrow.