The forward-backward procedure is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations.
An HMM innovation consists of a state and an observation in the state.
In a (discrete) hidden Markov model, the state is not directly visible, but output, dependent on the state, is visible.
The Viterbi algorithm is a dynamic programming algorithm for finding the most likely sequence of hidden states - called the Viterbi path - that results in a sequence of observed events, especially in the context of Markov information sources and hidden Markov models.
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