Viterbi Algorithm

Finding probable states
Definition
Example
Summary

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We can find the most probable sequence of hidden states by listing all possible sequences of hidden states and finding the probability of the observed sequence for each of the combinations. The most probable sequence of hidden states is that combination that maximises

Pr(observed sequence | hidden state combination).

For example, for the observation sequence in the trellis shown, the most probable sequence of hidden states is the sequence that maximises :

Pr(dry,damp,soggy | sunny,sunny,sunny), Pr(dry,damp,soggy | sunny,sunny,cloudy), Pr(dry,damp,soggy | sunny,sunny,rainy), . . . . Pr(dry,damp,soggy | rainy,rainy,rainy)

This approach is viable, but to find the most probable sequence by exhaustively calculating each combination is computationally expensive. As with the forward algorithm, we can use the time invariance of the probabilities to reduce the complexity of the calculation.