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##

Learning with known state sequence

Sometimes we want to use the switching NSSM to model data we already
know something about. With speech data, for instance, we may know the
``correct'' sequence of phonemes in the utterance. This does not mean
that learning the HMM part would be unnecessary. The correct
segmentation requires determining the times of transitions between the
states. Now only the states the model has to pass and their order are
given.

Such problems can be solved by estimating the HMM states for a
modified model, namely the one that only allows transitions in the
correct sequence. These probabilities can then be transformed back to
the true state probabilities for the adaptation of the other model
parameters. The forward-backward procedure must also be modified
slightly as the first and the last state of a sequence are now known
for sure.

When the correct state sequences are known, the different orderings of
HMM states are no longer equivalent. Therefore the HMM output
distribution parameters can, and actually should, all be initialised
to zeros. Random initialisation could make the output model for
certain state very different from the true output thus making the
learning much more difficult.

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Antti Honkela
2001-05-30