Forward-Backward Algorithm

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Forward-backward 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 P 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 forward-backward 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.