Viterbi Criterion.

[Jiahn K]

If a state does not have memory, how can it compare all the paths to the state and compare which one wins and discard the rest?

[Simon]

We need to clearly separate the model from the algorithm,

The HMM is the model. It has no memory other than the state, which has to encapsulate all information required to do computation (e.g., to generate an observation).

There are various algorithms available to perform computations with this model. These all take advantage of the memoryless nature of the model in order to simplify that computation.

The Viterbi algorithm computes the single most likely state sequence (= path through the model) to have generated a given observation sequence. The key step in the Viterbi algorithm is to compare all the paths arriving at a particular state at a particular time and keep only the most probable. This is possible because we do not need to know anything more about those paths other than the fact they are all in the same state.

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