ForwardBackward Algorithm
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Forwardbackward algorithm
The `useful' problems assosciated with HMMs are those of
evaluation and decoding  they permit either a measurement of a
model's relative applicability, or an estimate of what the
underlying model is doing (what `really happened'). It can be
seen that they both depend upon foreknowledge of the HMM
parameters  the state transition matrix, the observation
matrix, and the
vector.
There are, however, many circumstances
in practical problems where these are not directly measurable,
and have to be estimated  this is the learning problem. The
forwardbackward algorithm permits this estimate to be made on
the basis of a sequence of observations known to come from a
given set, that represents a known hidden set following a Markov
model.
An example may be a large speech processing database,
where the underlying speech may be modelled by a Markov process
based on known phonemes, and the obervations may be modelled as
recognisable states (perhaps via some vector quantisation), but
there will be no (straightforward) way of deriving empirically
the HMM parameters.
